Agenda

  • Why Data Mining?
  • What Is Data Mining?
  • A Multi-Dimensional View of Data Mining
  • What Kinds of Data Can Be Mined?
  • What Kinds of Patterns Can Be Mined?
  • What Kinds of Technologies Are Used?
  • What Kinds of Applications Are Targeted?
  • Major Issues in Data Mining
  • A Brief History of Data Mining and Data Mining Society
  • Summary

Why Data Mining?

  • The Explosive Growth of Data: from terabytes to petabytes
    • Data collection and data availability
      • Automated data collection tools, database systems, Web, computerized society
    • Major sources of abundant data
      • Business: Web, e-commerce, transactions, stocks, …
      • Science: Remote sensing, bioinformatics, scientific simulation, …
      • Society and everyone: news, digital cameras, YouTube
  • We are drowning in data, but starving for knowledge!
  • “Necessity is the mother of invention”—Data mining—Automated analysis of massive data sets

Evolution of Sciences: New Data Science Era

  • Before 1600: Empirical science
  • 1600-1950s: Theoretical science
    • Each discipline has grown a theoretical component. Theoretical models often motivate experiments and generalize our understanding.
  • 1950s-1990s: Computational science
    • Over the last 50 years, most disciplines have grown a third, computational branch (e.g. empirical, theoretical, and computational ecology, or physics, or linguistics.)
    • Computational Science traditionally meant simulation. It grew out of our inability to find closed-form solutions for complex mathematical models.
  • 1990-now: Data science
    • The flood of data from new scientific instruments and simulations
    • The ability to economically store and manage petabytes of data online
    • The Internet and computing Grid that makes all these archives universally accessible
    • Scientific info. management, acquisition, organization, query, and visualization tasks scale almost linearly with data volumes
    • Data mining is a major new challenge!
  • Jim Gray and Alex Szalay, The World Wide Telescope: An Archetype for Online Science, Comm. ACM, 45(11): 50-54, Nov. 2002

What Is Data Mining?

  • Data mining (knowledge discovery from data)
    • Extraction of interesting (non-trivial, implicit, previously unknown and potentially useful) patterns or knowledge from huge amount of data
    • Data mining: a misnomer?
  • Alternative names
    • Knowledge discovery (mining) in databases (KDD), knowledge extraction, data/pattern analysis, data archeology, data dredging, information harvesting, business intelligence, etc.
  • Watch out: Is everything “data mining”?
    • Simple search and query processing
    • (Deductive) expert systems

Knowledge Discovery (KDD) Process

  • This is a view from typical database systems and data warehousing communities
  • Data mining plays an essential role in the knowledge discovery process

Example: A Web Mining Framework

  • Web mining usually involves
    • Data cleaning
    • Data integration from multiple sources
    • Warehousing the data
    • Data cube construction
    • Data selection for data mining
    • Data mining
    • Presentation of the mining results
    • Patterns and knowledge to be used or stored into knowledge-base

Data Mining in Business Intelligence


KDD Process: A Typical View from ML and Statistics

  • This is a view from typical machine learning and statistics communities

Which View Do You Prefer?

  • Which view do you prefer?
    • KDD vs. ML/Stat. vs. Business Intelligence
    • Depending on the data, applications, and your focus
  • Data Mining vs. Data Exploration
    • Business intelligence view
      • Warehouse, data cube, reporting but not much mining
    • Business objects vs. data mining tools
    • Supply chain example: mining vs. OLAP vs. presentation tools
    • Data presentation vs. data exploration

Multi-Dimensional View of Data Mining

  • Data to be mined
    • Database data (extended-relational, object-oriented, heterogeneous, legacy), data warehouse, transactional data, stream, spatiotemporal, time-series, sequence, text and web, multi-media, graphs & social and information networks
  • Knowledge to be mined (or: Data mining functions)
    • Characterization, discrimination, association, classification, clustering, trend/deviation, outlier analysis, etc.
    • Descriptive vs. predictive data mining
    • Multiple/integrated functions and mining at multiple levels
  • Techniques utilized
    • Data-intensive, data warehouse (OLAP), machine learning, statistics, pattern recognition, visualization, high-performance, etc.
  • Applications adapted
    • Retail, telecommunication, banking, fraud analysis, bio-data mining, stock market analysis, text mining, Web mining, etc.

Data Mining: On What Kinds of Data?

  • Database-oriented data sets and applications
    • Relational database, data warehouse, transactional database
  • Advanced data sets and advanced applications
    • Data streams and sensor data
    • Time-series data, temporal data, sequence data (incl. bio-sequences)
    • Structure data, graphs, social networks and multi-linked data
    • Object-relational databases
    • Heterogeneous databases and legacy databases
    • Spatial data and spatiotemporal data
    • Multimedia database
    • Text databases
    • The World-Wide Web

Data Mining Function:  Generalization

  • Information integration and data warehouse construction
    • Data cleaning, transformation, integration, and multidimensional data model
  • Data cube technology
    • Scalable methods for computing (i.e., materializing) multidimensional aggregates
    • OLAP (online analytical processing)
  • Multidimensional concept description: Characterization and discrimination
    • Generalize, summarize, and contrast data characteristics, e.g., dry vs. wet region

Data Mining Function: Association and Correlation Analysis

  • Frequent patterns (or frequent itemsets)
    • What items are frequently purchased together in your Walmart?
  • Association, correlation vs. causality
    • A typical association rule
      • Diaper → Beer [0.5%, 75%] (support, confidence)
    • Are strongly associated items also strongly correlated?
  • How to mine such patterns and rules efficiently in large datasets?
  • How to use such patterns for classification, clustering, and other applications?

Data Mining Function: Classification

  • Classification and label prediction
    • Construct models (functions) based on some training examples
    • Describe and distinguish classes or concepts for future prediction
      • E.g., classify countries based on (climate), or classify cars based on (gas mileage)
    • Predict some unknown class labels
  • Typical methods
    • Decision trees, naïve Bayesian classification, support vector machines, neural networks, rule-based classification, pattern-based classification, logistic regression, …
  • Typical applications:
    • Credit card fraud detection, direct marketing, classifying stars, diseases, web-pages, …

Data Mining Function: Cluster Analysis

  • Unsupervised learning (i.e., Class label is unknown)
  • Group data to form new categories (i.e., clusters), e.g., cluster houses to find distribution patterns
  • Principle: Maximizing intra-class similarity & minimizing interclass similarity
  • Many methods and applications

Data Mining Function: Outlier Analysis

  • Outlier analysis
    • Outlier: A data object that does not comply with the general behavior of the data
    • Noise or exception? ― One person’s garbage could be another person’s treasure
    • Methods: by product of clustering or regression analysis, …
    • Useful in fraud detection, rare events analysis

Time and Ordering: Sequential Pattern, Trend and Evolution Analysis

  • Sequence, trend and evolution analysis
    • Trend, time-series, and deviation analysis: e.g., regression and value prediction
    • Sequential pattern mining
      • e.g., first buy digital camera, then buy large SD memory cards
    • Periodicity analysis
    • Motifs and biological sequence analysis
      • Approximate and consecutive motifs
    • Similarity-based analysis
  • Mining data streams
    • Ordered, time-varying, potentially infinite, data streams

Structure and Network Analysis

  • Graph mining
    • Finding frequent subgraphs (e.g., chemical compounds), trees (XML), substructures (web fragments)
  • Information network analysis
    • Social networks: actors (objects, nodes) and relationships (edges)
      • e.g., author networks in CS, terrorist networks
    • Multiple heterogeneous networks
      • A person could be multiple information networks: friends, family, classmates, …
    • Links carry a lot of semantic information: Link mining
  • Web mining
    • Web is a big information network: from PageRank to Google
    • Analysis of Web information networks
      • Web community discovery, opinion mining, usage mining, …

Evaluation of Knowledge

  • Are all mined knowledge interesting?
    • One can mine tremendous amount of “patterns” and knowledge
    • Some may fit only certain dimension space (time, location, …)
    • Some may not be representative, may be transient, …
  • Evaluation of mined knowledge → directly mine only interesting knowledge?
    • Descriptive vs. predictive
    • Coverage
    • Typicality vs. novelty
    • Accuracy
    • Timeliness

Data Mining: Confluence of Multiple Disciplines


Why Confluence of Multiple Disciplines?

  • Tremendous amount of data
    • Algorithms must be highly scalable to handle such as tera-bytes of data
  • High-dimensionality of data
    • Micro-array may have tens of thousands of dimensions
  • High complexity of data
    • Data streams and sensor data
    • Time-series data, temporal data, sequence data
    • Structure data, graphs, social networks and multi-linked data
    • Heterogeneous databases and legacy databases
    • Spatial, spatiotemporal, multimedia, text and Web data
    • Software programs, scientific simulations
  • New and sophisticated applications

Applications of Data Mining

  • Web page analysis: from web page classification, clustering to PageRank & HITS algorithms
  • Collaborative analysis & recommender systems
  • Basket data analysis to targeted marketing
  • Biological and medical data analysis: classification, cluster analysis (microarray data analysis), biological sequence analysis, biological network analysis
  • Data mining and software engineering (e.g., IEEE Computer, Aug. 2009 issue)
  • From major dedicated data mining systems/tools (e.g., SAS, MS SQL-Server Analysis Manager, Oracle Data Mining Tools) to invisible data mining

Major Issues in Data Mining

  • Mining Methodology
    • Mining various and new kinds of knowledge
    • Mining knowledge in multi-dimensional space
    • Data mining: An interdisciplinary effort
    • Boosting the power of discovery in a networked environment
    • Handling noise, uncertainty, and incompleteness of data
    • Pattern evaluation and pattern- or constraint-guided mining
  • User Interaction
    • Interactive mining
    • Incorporation of background knowledge
    • Presentation and visualization of data mining results

Major Issues in Data Mining (cont')

  • Efficiency and Scalability
    • Efficiency and scalability of data mining algorithms
    • Parallel, distributed, stream, and incremental mining methods
  • Diversity of data types
    • Handling complex types of data
    • Mining dynamic, networked, and global data repositories
  • Data mining and society
    • Social impacts of data mining
    • Privacy-preserving data mining
    • Invisible data mining

A Brief History of Data Mining Society

  • 1989 IJCAI Workshop on Knowledge Discovery in Databases
    • Knowledge Discovery in Databases (G. Piatetsky-Shapiro and W. Frawley, 1991)
  • 1991-1994 Workshops on Knowledge Discovery in Databases
    • Advances in Knowledge Discovery and Data Mining (U. Fayyad, G. Piatetsky-Shapiro, P. Smyth, and R. Uthurusamy, 1996)
  • 1995-1998 International Conferences on Knowledge Discovery in Databases and Data Mining (KDD’95-98)
    • Journal of Data Mining and Knowledge Discovery (1997)
  • ACM SIGKDD conferences since 1998 and SIGKDD Explorations
  • More conferences on data mining
    • PAKDD (1997), PKDD (1997), SIAM-Data Mining (2001), (IEEE) ICDM (2001), WSDM (2008), etc.
  • ACM Transactions on KDD (2007)

Conferences and Journals on Data Mining

  • KDD Conferences
    • ACM SIGKDD Int. Conf. on Knowledge Discovery in Databases and Data Mining (KDD)
    • SIAM Data Mining Conf. (SDM)
    • (IEEE) Int. Conf. on Data Mining (ICDM)
    • European Conf. on Machine Learning and Principles and practices of Knowledge Discovery and Data Mining (ECML-PKDD)
    • Pacific-Asia Conf. on Knowledge Discovery and Data Mining (PAKDD)
    • Int. Conf. on Web Search and Data Mining (WSDM)
  • Other related conferences
    • DB conferences: ACM SIGMOD, VLDB, ICDE, EDBT, ICDT, …
    • Web and IR conferences: WWW, SIGIR, WSDM
    • ML conferences: ICML, NIPS
    • PR conferences: CVPR,
  • Journals
    • Data Mining and Knowledge Discovery (DAMI or DMKD)
    • IEEE Trans. On Knowledge and Data Eng. (TKDE)
    • KDD Explorations
    • ACM Trans. on KDD

Where to Find References? DBLP, CiteSeer, Google

  • Data mining and KDD (SIGKDD: CDROM)
    • Conferences: ACM-SIGKDD, IEEE-ICDM, SIAM-DM, PKDD, PAKDD, etc.
    • Journal: Data Mining and Knowledge Discovery, KDD Explorations, ACM TKDD
  • Database systems (SIGMOD: ACM SIGMOD Anthology—CD ROM)
    • Conferences: ACM-SIGMOD, ACM-PODS, VLDB, IEEE-ICDE, EDBT, ICDT, DASFAA
    • Journals: IEEE-TKDE, ACM-TODS/TOIS, JIIS, J. ACM, VLDB J., Info. Sys., etc.
  • AI & Machine Learning
    • Conferences: Machine learning (ML), AAAI, IJCAI, COLT (Learning Theory), CVPR, NIPS, etc.
    • Journals: Machine Learning, Artificial Intelligence, Knowledge and Information Systems, IEEE-PAMI, etc.
  • Web and IR
    • Conferences: SIGIR, WWW, CIKM, etc.
    • Journals: WWW: Internet and Web Information Systems,
  • Statistics
    • Conferences: Joint Stat. Meeting, etc.
    • Journals: Annals of statistics, etc.
  • Visualization
    • Conference proceedings: CHI, ACM-SIGGraph, etc.
    • Journals: IEEE Trans. visualization and computer graphics, etc.

Recommended Reference Books

  • E. Alpaydin. Introduction to Machine Learning, 2nd ed., MIT Press, 2011
  • S. Chakrabarti. Mining the Web: Statistical Analysis of Hypertex and Semi-Structured Data. Morgan Kaufmann, 2002
  • R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification, 2ed., Wiley-Interscience, 2000
  • T. Dasu and T. Johnson. Exploratory Data Mining and Data Cleaning. John Wiley & Sons, 2003
  • U. M. Fayyad, G. Piatetsky-Shapiro, P. Smyth, and R. Uthurusamy. Advances in Knowledge Discovery and Data Mining. AAAI/MIT Press, 1996
  • U. Fayyad, G. Grinstein, and A. Wierse, Information Visualization in Data Mining and Knowledge Discovery, Morgan Kaufmann, 2001
  • J. Han, M. Kamber, and J. Pei, Data Mining: Concepts and Techniques. Morgan Kaufmann, 3rd ed. , 2011
  • T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd ed., Springer, 2009
  • B. Liu, Web Data Mining, Springer 2006
  • T. M. Mitchell, Machine Learning, McGraw Hill, 1997
  • Y. Sun and J. Han, Mining Heterogeneous Information Networks, Morgan & Claypool, 2012
  • P.-N. Tan, M. Steinbach and V. Kumar, Introduction to Data Mining, Wiley, 2005
  • S. M. Weiss and N. Indurkhya, Predictive Data Mining, Morgan Kaufmann, 1998
  • I. H. Witten and E. Frank, Data Mining: Practical Machine Learning Tools and Techniques with Java Implementations, Morgan Kaufmann, 2nd ed. 2005

Summary

  • Data mining: Discovering interesting patterns and knowledge from massive amount of data
  • A natural evolution of science and information technology, in great demand, with wide applications
  • A KDD process includes data cleaning, data integration, data selection, transformation, data mining, pattern evaluation, and knowledge presentation
  • Mining can be performed in a variety of data
  • Data mining functionalities: characterization, discrimination, association, classification, clustering, trend and outlier analysis, etc.
  • Data mining technologies and applications
  • Major issues in data mining

Agenda

  • Data Objects and Attribute Types
  • Basic Statistical Descriptions of Data
  • Data Visualization
  • Measuring Data Similarity and Dissimilarity
  • Summary 

Types of Data Sets

  • Record
    • Relational records
    • Data matrix, e.g., numerical matrix, crosstabs
    • Document data: text documents: term-frequency vector
    • Transaction data
  • Graph and network
    • World Wide Web
    • Social or information networks
    • Molecular Structures
  • Ordered
    • Video data: sequence of images
    • Temporal data: time-series
    • Sequential Data: transaction sequences
    • Genetic sequence data
  • Spatial, image and multimedia:
    • Spatial data: maps
    • Image data:
    • Video data:

Important Characteristics of Structured Data

  • Dimensionality
    • Curse of dimensionality
  • Sparsity
    • Only presence counts
  • Resolution
    • Patterns depend on the scale
  • Distribution
    • Centrality and dispersion

Data Objects

  • Data sets are made up of data objects.
  • A data object represents an entity.
  • Examples:
    • sales database: customers, store items, sales
    • medical database: patients, treatments
    • university database: students, professors, courses
  • Also called samples , examples, instances, data points, objects, tuples.
  • Data objects are described by attributes.
  • Database rows -> data objects; columns ->attributes.

Attributes

  • Attribute (or dimensions, features, variables): a data field, representing a characteristic or feature of a data object.
    • E.g., customer _ID, name, address
  • Types:
    • Nominal
    • Binary
    • Numeric: quantitative
      • Interval-scaled
      • Ratio-scaled

Attribute Types

  • Nominal: categories, states, or “names of things”
    • Hair_color = {auburn, black, blond, brown, grey, red, white}
    • marital status, occupation, ID numbers, zip codes
  • Binary
    • Nominal attribute with only 2 states (0 and 1)
    • Symmetric binary: both outcomes equally important
      • e.g., gender
    • Asymmetric binary: outcomes not equally important.
      • e.g., medical test (positive vs. negative)
      • Convention: assign 1 to most important outcome (e.g., HIV positive)
  • Ordinal
    • Values have a meaningful order (ranking) but magnitude between successive values is not known.
    • Size = {small, medium, large}, grades, army rankings

Numeric Attribute Types

  • Quantity (integer or real-valued)
  • Interval
      • Measured on a scale of equal-sized units
      • Values have order
        • E.g., temperature in C˚or F˚, calendar dates
      • No true zero-point
  • Ratio
      • Inherent zero-point
      • We can speak of values as being an order of magnitude larger than the unit of measurement (10 K˚ is twice as high as 5 K˚).
        • e.g., temperature in Kelvin, length, counts, monetary quantities

Discrete vs. Continuous Attributes

  • Discrete Attribute
    • Has only a finite or countably infinite set of values
      • E.g., zip codes, profession, or the set of words in a collection of documents
    • Sometimes, represented as integer variables
    • Note: Binary attributes are a special case of discrete attributes
  • Continuous Attribute
    • Has real numbers as attribute values
      • E.g., temperature, height, or weight
    • Practically, real values can only be measured and represented using a finite number of digits
    • Continuous attributes are typically represented as floating-point variables

Basic Statistical Descriptions of Data

  • Motivation
    • To better understand the data: central tendency, variation and spread
  • Data dispersion characteristics
    • median, max, min, quantiles, outliers, variance, etc.
  • Numerical dimensions correspond to sorted intervals
    • Data dispersion: analyzed with multiple granularities of precision
    • Boxplot or quantile analysis on sorted intervals
  • Dispersion analysis on computed measures
    • Folding measures into numerical dimensions
    • Boxplot or quantile analysis on the transformed cube

Measuring the Central Tendency

  •  Mean (algebraic measure) (sample vs. population):  

\[ {\bar{x}}=\frac{1}{n} \sum_{i=1}^{n}x_{i} \]
\[ \mu = \frac{\sum x}{N} \]

    • Note: n is sample size and N is population size.
    • Weighted arithmetic mean:
    • Trimmed mean: chopping extreme values

\[ {\bar{x}}=\frac{\sum_{i=1}^{n}w_{i}x_{i} }{\sum_{i=1}^{n}w_{i}}  \]

  • Median:
    • Middle value if odd number of values, or average of the middle two values otherwise
    • Estimated by interpolation (for grouped data ):  

\[ median = {L_{1}} + (\frac{\frac{n}{2}-(\sum freq)l)}{freq_{median}}) width \] 

Measuring the Central Tendency (cont')

  • Mode
    • Value that occurs most frequently in the data
    • Unimodal, bimodal, trimodal
    • Empirical formula:  
       \[ (mean-mode) = 3 \times (mean-median) \]

Symmetric vs. Skewed Data

  • Median, mean and mode of symmetric, positively and negatively skewed data 

Measuring the Dispersion of Data

  • Quartiles, outliers and boxplots
    • Quartiles: Q1 (25th percentile), Q3 (75th percentile)
    • Inter-quartile range: IQR = Q3 – Q1
    • Five number summary: min, Q1, median, Q3, max
    • Boxplot: ends of the box are the quartiles; median is marked; add whiskers, and plot outliers individually
    • Outlier: usually, a value higher/lower than 1.5 x IQR
  • Variance and standard deviation (sample: s, population: σ)
    • Variance: (algebraic, scalable computation)
\[ {s^{2}}=\frac{1}{n-1}\sum_{i=1}^{n}(x_{i}-\bar{x})^2=\frac{1}{n-1}[\sum_{i=1}^{n}x_{i}^2-\frac{1}{n}(\sum_{i=1}^{n}x_{i})^2] \]

\[ {\sigma ^{2}}=\frac{1}{N}\sum_{i=1}^{n}(x_{i}-\mu)^2=\frac{1}{N}\sum_{i=1}^{n}x_{i}^2-\mu ^2 \]
    • Standard deviation s (or σ) is the square root of variance s2 (or σ2)  

Boxplot Analysis

  • Five-number summary of a distribution
    • Minimum, Q1, Median, Q3, Maximum
  • Boxplot
    • Data is represented with a box
    • The ends of the box are at the first and third quartiles, i.e., the height of the box is IQR
    • The median is marked by a line within the box
    • Whiskers: two lines outside the box extended to Minimum and Maximum
    • Outliers: points beyond a specified outlier threshold, plotted individually

Visualization of Data Dispersion: 3-D Boxplots

Properties of Normal Distribution Curve

  • The normal (distribution) curve
    • From μ–σ to μ+σ: contains about 68% of the measurements (μ: mean, σ: standard deviation)
    • From μ–2σ to μ+2σ: contains about 95% of it
    • From μ–3σ to μ+3σ: contains about 99.7% of it

Graphic Displays of Basic Statistical Descriptions

 
  • Boxplot: graphic display of five-number summary
  • Histogram: x-axis are values, y-axis repres. frequencies
  • Quantile plot: each value xi is paired with fi indicating that approximately 100 fi % of data are ≤ xi
  • Quantile-quantile (q-q) plot: graphs the quantiles of one univariant distribution against the corresponding quantiles of another
  • Scatter plot: each pair of values is a pair of coordinates and plotted as points in the plane

Histogram Analysis

  • Histogram: Graph display of tabulated frequencies, shown as bars
  • It shows what proportion of cases fall into each of several categories
  • Differs from a bar chart in that it is the area of the bar that denotes the value, not the height as in bar charts, a crucial distinction when the categories are not of uniform width
  • The categories are usually specified as non-overlapping intervals of some variable. The categories (bars) must be adjacent

Histograms Often Tell More than Boxplots

  • The two histograms shown in the left may have the same boxplot representation
    • The same values for: min, Q1, median, Q3, max
  • But they have rather different data distributions

Quantile Plot

  • Displays all of the data (allowing the user to assess both the overall behavior and unusual occurrences)
  • Plots quantile information
    • For a data xi data sorted in increasing order, fi indicates that approximately 100 fi% of the data are below or equal to the value xi

Quantile-Quantile (Q-Q) Plot

  • Graphs the quantiles of one univariate distribution against the corresponding quantiles of another
  • View: Is there is a shift in going from one distribution to another?
  • Example shows unit price of items sold at Branch 1 vs. Branch 2 for each quantile. Unit prices of items sold at Branch 1 tend to be lower than those at Branch 2.

Scatter plot

  • Provides a first look at bivariate data to see clusters of points, outliers, etc
  • Each pair of values is treated as a pair of coordinates and plotted as points in the plane

Positively and Negatively Correlated Data


Uncorrelated Data


Data Visualization

  • Why data visualization?
    • Gain insight into an information space by mapping data onto graphical primitives
    • Provide qualitative overview of large data sets
    • Search for patterns, trends, structure, irregularities, relationships among data
    • Help find interesting regions and suitable parameters for further quantitative analysis
    • Provide a visual proof of computer representations derived
  • Categorization of visualization methods:
    • Pixel-oriented visualization techniques
    • Geometric projection visualization techniques
    • Icon-based visualization techniques
    • Hierarchical visualization techniques
    • Visualizing complex data and relations

Pixel-Oriented Visualization Techniques

  • For a data set of m dimensions, create m windows on the screen, one for each dimension
  • The m dimension values of a record are mapped to m pixels at the corresponding positions in the windows
  • The colors of the pixels reflect the corresponding values

Laying Out Pixels in Circle Segments

  • To save space and show the connections among multiple dimensions, space filling is often done in a circle segment  

Geometric Projection Visualization Techniques

  • Visualization of geometric transformations and projections of the data
  • Methods
    • Direct visualization
    • Scatterplot and scatterplot matrices
    • Landscapes
    • Projection pursuit technique: Help users find meaningful projections of multidimensional data
    • Prosection views
    • Hyperslice
    • Parallel coordinates

Direct Data Visualization

  • Ribbons with Twists Based on Vorticity

Scatterplot Matrices

  • Matrix of scatterplots (x-y-diagrams) of the k-dim. data [total of (k2/2-k) scatterplots]

Landscapes

  • Visualization of the data as perspective landscape
  • The data needs to be transformed into a (possibly artificial) 2D spatial representation which preserves the characteristics of the data 

Parallel Coordinates

  • n equidistant axes which are parallel to one of the screen axes and correspond to the attributes
  • The axes are scaled to the [minimum, maximum]: range of the corresponding attribute
  • Every data item corresponds to a polygonal line which intersects each of the axes at the point which corresponds to the value for the attribute

Parallel Coordinates of a Data Set

Icon-Based Visualization Techniques

  • Visualization of the data values as features of icons
  • Typical visualization methods
    • Chernoff Faces
    • Stick Figures
  • General techniques
    • Shape coding: Use shape to represent certain information encoding
    • Color icons: Use color icons to encode more information
    • Tile bars: Use small icons to represent the relevant feature vectors in document retrieval

Chernoff Faces

  • A way to display variables on a two-dimensional surface, e.g., let x be eyebrow slant, y be eye size, z be nose length, etc.
  • The figure shows faces produced using 10 characteristics--head eccentricity, eye size, eye spacing, eye eccentricity, pupil size, eyebrow slant, nose size, mouth shape, mouth size, and mouth opening): Each assigned one of 10 possible values, generated using Mathematica (S. Dickson)
  • REFERENCE: Gonick, L. and Smith, W. The Cartoon Guide to Statistics. New York: Harper Perennial, p. 212, 1993
  • Weisstein, Eric W. "Chernoff Face." From MathWorld--A Wolfram Web Resource. mathworld.wolfram.com/ChernoffFace.html 

Stick Figure

Hierarchical Visualization Techniques

  • Visualization of the data using a hierarchical partitioning into subspaces
  • Methods
    • Dimensional Stacking
    • Worlds-within-Worlds
    • Tree-Map
    • Cone Trees
    • InfoCube

Dimensional Stacking


  • Partitioning of the n-dimensional attribute space in 2-D subspaces, which are ‘stacked’ into each other
  • Partitioning of the attribute value ranges into classes. The important attributes should be used on the outer levels.
  • Adequate for data with ordinal attributes of low cardinality
  • But, difficult to display more than nine dimensions
  • Important to map dimensions appropriately

Dimensional Stacking

Used by permission of M. Ward, Worcester Polytechnic Institute

  • Visualization of oil mining data with longitude and latitude mapped to the outer x-, y-axes and ore grade and depth mapped to the inner x-, y-axes

Worlds-within-Worlds

  • Assign the function and two most important parameters to innermost world
  • Fix all other parameters at constant values - draw other (1 or 2 or 3 dimensional worlds choosing these as the axes)
  • Software that uses this paradigm
    • N–vision: Dynamic interaction through data glove and stereo displays, including rotation, scaling (inner) and translation (inner/outer) 
    • Auto Visual: Static interaction by means of queries

Tree-Map

  • Screen-filling method which uses a hierarchical partitioning of the screen into regions depending on the attribute values
  • The x- and y-dimension of the screen are partitioned alternately according to the attribute values (classes)

InfoCube

  • A 3-D visualization technique where hierarchical information is displayed as nested semi-transparent cubes
  • The outermost cubes correspond to the top level data, while the subnodes or the lower level data are represented as smaller cubes inside the outermost cubes, and so on

Three-D Cone Trees

   
 
  • 3D cone tree visualization technique works well for up to a thousand nodes or so
  • First build a 2D circle tree that arranges its nodes in concentric circles centered on the root node
  • Cannot avoid overlaps when projected to 2D
  • G. Robertson, J. Mackinlay, S. Card. “Cone Trees: Animated 3D Visualizations of Hierarchical Information”, ACM SIGCHI'91
  • Graph from Nadeau Software Consulting website: Visualize a social network data set that models the way an infection spreads from one person to the next

Visualizing Complex Data and Relations

  • Visualizing non-numerical data: text and social networks
  • Tag cloud: visualizing user-generated tags
    • The importance of tag is represented by font size/color
  • Besides text data, there are also methods to visualize relationships, such as visualizing social networks

Newsmap: Google News Stories in 2005

Similarity and Dissimilarity

  • Similarity
    • Numerical measure of how alike two data objects are
    • Value is higher when objects are more alike
    • Often falls in the range [0,1]
  • Dissimilarity (e.g., distance)
    • Numerical measure of how different two data objects are
    • Lower when objects are more alike
    • Minimum dissimilarity is often 0
    • Upper limit varies
  • Proximity refers to a similarity or dissimilarity

Data Matrix and Dissimilarity Matrix

   
 
  • Data matrix
    • n data points with p dimensions
    • Two modes
  • Dissimilarity matrix
    • n data points, but registers only the distance
    • A triangular matrix
    • Single mode

Proximity Measure for Nominal Attributes

  • Can take 2 or more states, e.g., red, yellow, blue, green (generalization of a binary attribute)
  • Method 1: Simple matching
    • m : # of matches, p : total # of variables

\[ d(i,j)=\frac{p-m}{p} \]

  • Method 2: Use a large number of binary attributes
    • creating a new binary attribute for each of the M nominal states

Proximity Measure for Binary Attributes

  • A contingency table for binary data

  • Distance measure for symmetric binary variables: 
\[ d(i,j)=\frac{r+s}{q+r+s+t} \]
  • Distance measure for asymmetric binary variables: 

\[ d(i,j)=\frac{r+s}{q+r+s} \]

  • Jaccard coefficient (similarity measure for asymmetric binary variables):

\[ sim_{Jaccard}(i,j)=\frac{q}{q+r+s} \]

  • Note: Jaccard coefficient is the same as “coherence”:

\[ coherence(i,j)=\frac{sup(i,j)}{sup(i)+sup(j)-sup(i,j)}=\frac{q}{(q+r)(q+s)-q} \]
 

Dissimilarity between Binary Variables

  • Example

    • Gender is a symmetric attribute
    • The remaining attributes are asymmetric binary
    • Let the values Y and P be 1, and the value N 0

Standardizing Numeric Data

  • Z-score: 

\[ z=\frac{x-\mu}{\sigma } \]

    • X: raw score to be standardized, μ: mean of the population, σ: standard deviation
    • the distance between the raw score and the population mean in units of the standard deviation
    • negative when the raw score is below the mean, “+” when above
  • An alternative way: Calculate the mean absolute deviation, where

\[ m_{f}= \frac{1}{n}(x_{1f}+x_{2f}+...+x_{nf}) \]

    • standardized measure (z-score):

\[ z_{if}=\frac{(x_{if}-m_{f})}{S_{f}} \]

  • Using mean absolute deviation is more robust than using standard deviation 
\[ s_{f}=\frac{1}{n} (|x_{1f}-m_{f}|+|x_{2f}-m_{f}|+...+|x_{nf}-m_{f}|) \]

Example: Data Matrix and Dissimilarity Matrix


Distance on Numeric Data: Minkowski Distance

  • Minkowski distance: A popular distance measure

where i = (xi1, xi2, …, xip) and j = (xj1, xj2, …, xjp) are two p-dimensional data objects, and h is the order (the distance so defined is also called L-h norm)

  • Properties
    • d(i, j) > 0 if i ≠ j, and d(i, i) = 0 (Positive definiteness)
    • d(i, j) = d(j, i) (Symmetry)
    • d(i, j) ≤ d(i, k) + d(k, j) (Triangle Inequality)
  • A distance that satisfies these properties is a metric

Special Cases of Minkowski Distance

  • h = 1: Manhattan (city block, L1 norm) distance
    • E.g., the Hamming distance: the number of bits that are different between two binary vectors
\[ d(i,j)=|x_{i1}-x_{j1}|+|x_{i2}-x_{j2}|+...+|x_{ip}-x_{jp}| \]

  • h = 2: (L2 norm) Euclidean distance

\[ d(i,j)=\sqrt{(|x_{i1}-x_{j1}|^2+|x_{i2}-x_{j2}|^2+...+|x_{ip}-x_{jp}|^2)} \]

  • h →≈ . “supremum” (Lmax norm, L norm) distance.
    • This is the maximum difference between any component (attribute) of the vectors
\[ d(i,j)=\lim_{h\rightarrow \infty }(\sum_{f=1}^{p}|x_{if}-x_{jf}|^{h})^\frac{1}{h} =max_{f}^{p}|x_{if}-x_{jf}| \]

Example: Minkowski Distance


Ordinal Variables

  • An ordinal variable can be discrete or continuous
  • Order is important, e.g., rank
  • Can be treated like interval-scaled
    • replace xif by their rank 

\[ r_{if} \epsilon \left \{ 1,...,M_{f} \right \} \]

    • map the range of each variable onto [0, 1] by replacing i-th object in the f-th variable by
    • compute the dissimilarity using methods for interval-scaled variables
 \[ z_{if} = \frac{r_{if}-1}{M_{f}-1} \]

Attributes of Mixed Type

  • A database may contain all attribute types
    • Nominal, symmetric binary, asymmetric binary, numeric, ordinal
  • One may use a weighted formula to combine their effects

\[ d(i,j) = \frac{\sum_{f=1}^{p} \delta _{ij}^{(f)} d_{ij}^{(f)}}{\sum_{f=1}^{p} \delta _{ij}^{(f)}} \]

    • f is binary or nominal:
      • dij(f) = 0 if xif = xjf , or dij(f) = 1 otherwise
    • f is numeric: use the normalized distance
    • f is ordinal
      • Compute ranks rif and
      • Treat zif as interval-scaled
\[ z_{if} = \frac{r_{if}-1}{M_{f}-1} \]

Cosine Similarity

  • A document can be represented by thousands of attributes, each recording the frequency of a particular word (such as keywords) or phrase in the document.

  • Other vector objects: gene features in micro-arrays, …
  • Applications: information retrieval, biologic taxonomy, gene feature mapping, ...
  • Cosine measure: If d1 and d2 are two vectors (e.g., term-frequency vectors), then
                 cos(d1, d2) =  (d1 ⋅ d2) /||d1|| ||d2|| ,
       where ⋅ indicates vector dot product, ||d||: the length of vector d

Example: Cosine Similarity

  • cos(d1, d2) = (d1d2) / ||d1|| ||d2|| ,
    where ⋅ indicates vector dot product, ||d|: the length of vector d
  • Ex: Find the similarity between documents 1 and 2.
    d1 = (5, 0, 3, 0, 2, 0, 0, 2, 0, 0)
    d2 = (3, 0, 2, 0, 1, 1, 0, 1, 0, 1)
    d1 d2 = 5*3+0*0+3*2+0*0+2*1+0*1+0*1+2*1+0*0+0*1 = 25
    ||d1|| = (5*5+0*0+3*3+0*0+2*2+0*0+0*0+2*2+0*0+0*0)0.5 = (42) 0.5 = 6.481
    ||d2|| = (3*3+0*0+2*2+0*0+1*1+1*1+0*0+1*1+0*0+1*1)0.5 = (17) 0.5 = 4.12
    cos(d1, d2 ) = 0.94

Summary

  • Data attribute types: nominal, binary, ordinal, interval-scaled, ratio-scaled
  • Many types of data sets, e.g., numerical, text, graph, Web, image.
  • Gain insight into the data by:
    • Basic statistical data description: central tendency, dispersion, graphical displays
    • Data visualization: map data onto graphical primitives
    • Measure data similarity
  • Above steps are the beginning of data preprocessing.
  • Many methods have been developed but still an active area of research.

References

  • W. Cleveland, Visualizing Data, Hobart Press, 1993
  • T. Dasu and T. Johnson. Exploratory Data Mining and Data Cleaning. John Wiley, 2003
  • U. Fayyad, G. Grinstein, and A. Wierse. Information Visualization in Data Mining and Knowledge Discovery, Morgan Kaufmann, 2001
  • L. Kaufman and P. J. Rousseeuw. Finding Groups in Data: an Introduction to Cluster Analysis. John Wiley & Sons, 1990.
  • H. V. Jagadish et al., Special Issue on Data Reduction Techniques. Bulletin of the Tech. Committee on Data Eng., 20(4), Dec. 1997
  • D. A. Keim. Information visualization and visual data mining, IEEE trans. on Visualization and Computer Graphics, 8(1), 2002
  • D. Pyle. Data Preparation for Data Mining. Morgan Kaufmann, 1999
  • S.  Santini and R. Jain,” Similarity measures”, IEEE Trans. on Pattern Analysis and Machine Intelligence, 21(9), 1999
  • E. R. Tufte. The Visual Display of Quantitative Information, 2nd ed., Graphics Press, 2001
  • C. Yu et al., Visual data mining of multimedia data for social and behavioral studies, Information Visualization, 8(1), 2009

Agenda

  • Data Preprocessing: An Overview
    • Data Quality
    • Major Tasks in Data Preprocessing
  • Data Cleaning
  • Data Integration
  • Data Reduction
  • Data Transformation and Data Discretization
  • Summary

Data Quality: Why Preprocess the Data?

  • Measures for data quality: A multidimensional view
    • Accuracy: correct or wrong, accurate or not
    • Completeness: not recorded, unavailable, …
    • Consistency: some modified but some not, dangling, …
    • Timeliness: timely update?
    • Believability: how trustable the data are correct?
    • Interpretability: how easily the data can be understood?

Major Tasks in Data Preprocessing

  • Data cleaning
    • Fill in missing values, smooth noisy data, identify or remove outliers, and resolve inconsistencies
  • Data integration
    • Integration of multiple databases, data cubes, or files
  • Data reduction
    • Dimensionality reduction
    • Numerosity reduction
    • Data compression
  • Data transformation and data discretization
    • Normalization
    • Concept hierarchy generation

Data Cleaning

  • Data in the Real World Is Dirty: Lots of potentially incorrect data, e.g., instrument faulty, human or computer error, transmission error
    • incomplete: lacking attribute values, lacking certain attributes of interest, or containing only aggregate data
      • e.g., Occupation=“ ” (missing data)
    • noisy: containing noise, errors, or outliers
      • e.g., Salary=“−10” (an error)
    • inconsistent: containing discrepancies in codes or names, e.g.,
      • Age=“42”, Birthday=“03/07/2010”
      • Was rating “1, 2, 3”, now rating “A, B, C”
      • discrepancy between duplicate records
    • Intentional (e.g., disguised missing data)
      • Jan. 1 as everyone’s birthday?

Incomplete (Missing) Data

  • Data is not always available
    • E.g., many tuples have no recorded value for several attributes, such as customer income in sales data
  • Missing data may be due to
    • equipment malfunction
    • inconsistent with other recorded data and thus deleted
    • data not entered due to misunderstanding
    • certain data may not be considered important at the time of entry
    • not register history or changes of the data
  • Missing data may need to be inferred

How to Handle Missing Data?

  • Ignore the tuple: usually done when class label is missing (when doing classification)—not effective when the % of missing values per attribute varies considerably
  • Fill in the missing value manually: tedious + infeasible?
  • Fill in it automatically with
    • a global constant : e.g., “unknown”, a new class?!
    • the attribute mean
    • the attribute mean for all samples belonging to the same class: smarter
    • the most probable value: inference-based such as Bayesian formula or decision tree

Noisy Data

  • Noise: random error or variance in a measured variable
  • Incorrect attribute values may be due to
    • faulty data collection instruments
    • data entry problems
    • data transmission problems
    • technology limitation
    • inconsistency in naming convention
  • Other data problems which require data cleaning
    • duplicate records
    • incomplete data
    • inconsistent data

How to Handle Noisy Data?

  • Binning
    • first sort data and partition into (equal-frequency) bins
    • then one can smooth by bin means, smooth by bin median, smooth by bin boundaries, etc.
  • Regression
    • smooth by fitting the data into regression functions
  • Clustering
    • detect and remove outliers
  • Combined computer and human inspection
    • detect suspicious values and check by human (e.g., deal with possible outliers)

Data Cleaning as a Process

  • Data discrepancy detection
    • Use metadata (e.g., domain, range, dependency, distribution)
    • Check field overloading
    • Check uniqueness rule, consecutive rule and null rule
    • Use commercial tools
      • Data scrubbing: use simple domain knowledge (e.g., postal code, spell-check) to detect errors and make corrections
      • Data auditing: by analyzing data to discover rules and relationship to detect violators (e.g., correlation and clustering to find outliers)
  • Data migration and integration
    • Data migration tools: allow transformations to be specified
    • ETL (Extraction/Transformation/Loading) tools: allow users to specify transformations through a graphical user interface
  • Integration of the two processes
    • Iterative and interactive (e.g., Potter’s Wheels)

Data Integration

  • Data integration:
    • Combines data from multiple sources into a coherent store
  • Schema integration: e.g., A.cust-id ≡ B.cust-#
    • Integrate metadata from different sources
  • Entity identification problem:
    • Identify real world entities from multiple data sources, e.g., Bill Clinton = William Clinton
  • Detecting and resolving data value conflicts
    • For the same real world entity, attribute values from different sources are different
    • Possible reasons: different representations, different scales, e.g., metric vs. British units

Handling Redundancy in Data Integration

  • Redundant data occur often when integration of multiple databases
    • Object identification: The same attribute or object may have different names in different databases
    • Derivable data: One attribute may be a “derived” attribute in another table, e.g., annual revenue
  • Redundant attributes may be able to be detected by correlation analysis and covariance analysis
  • Careful integration of the data from multiple sources may help reduce/avoid redundancies and inconsistencies and improve mining speed and quality

Correlation Analysis (Nominal Data)

  • Χ^2 (chi-square) test

\[ X^{2}=\sum \frac{(Observed-Expected)^2}{Expected} \]

  • The larger the Χ^2 value, the more likely the variables are related
  • The cells that contribute the most to the Χ2 value are those whose actual count is very different from the expected count
  • Correlation does not imply causality
    • # of hospitals and # of car-theft in a city are correlated
    • Both are causally linked to the third variable: population
 

Chi-Square Calculation: An Example

       
 

Play chess

Not play chess

Sum (row)

 

Like science fiction

250(90)

200(360)

450

 

Not like science fiction

50(210)

1000(840)

1050

 

Sum(col.)

300

1200

1500

  • X^2 (chi-square) calculation (numbers in parenthesis are expected counts calculated based on the data distribution in the two categories)  

\[ X^{2}=\frac{(250-90)^2}{90} + \frac{(50-210)^2}{210} + \frac{(200-360)^2}{360} + \frac{(1000-840)^2} {840} = 507.93 \]

  • It shows that like_science_fiction and play_chess are correlated in the group 

Correlation Analysis (Numeric Data)

  • Correlation coefficient (also called Pearson’s product moment coefficient)

    \[ {r_{A,B}}=\frac{\sum_{i=1}^{n} (a_{i}-\bar{A}) (b_{i}-\bar{B})}{(n-1)\sigma_{A} \sigma_{B}}=\frac{\sum_{i=1}^{n} (a_{i}b_{i})-n \bar{A}\bar{B}}{(n-1)\sigma_{A} \sigma_{B}} \]

    where n is the number of tuples, and are the respective means of A and B, σA and σB are the respective standard deviation of A and B, and Σ(aibi) is the sum of the AB cross-product.
  • If rA,B > 0, A and B are positively correlated (A’s values increase as B’s). The higher, the stronger correlation.
  • rA,B = 0: independent; rAB < 0: negatively correlated 

Visually Evaluating Correlation

Correlation (viewed as linear relationship)

  • Correlation measures the linear relationship between objects
  • To compute correlation, we standardize data objects, A and B, and then take their dot product

\[ a^{'}_{k} = (a_{k}-mean(A))/std(A) \]

\[ b^{'}_{k} = (b_{k}-mean(B))/std(B) \]

\[ correlation (A,B)=A^{'}.B^{'} \]

Covariance (Numeric Data)

  • Covariance is similar to correlation

Correlation coefficient:

where n is the number of tuples, and are the respective mean or expected values of A and B, σA and σB are the respective standard deviation of A and B.

  • Positive covariance: If CovA,B > 0, then A and B both tend to be larger than their expected values.
  • Negative covariance: If CovA,B < 0 then if A is larger than its expected value, B is likely to be smaller than its expected value.
  • Independence: CovA,B = 0 but the converse is not true:
    • Some pairs of random variables may have a covariance of 0 but are not independent. Only under some additional assumptions (e.g., the data follow multivariate normal distributions) does a covariance of 0 imply independence


Co-Variance: An Example

  • It can be simplified in computation as
  • Suppose two stocks A and B have the following values in one week: (2, 5), (3, 8), (5, 10), (4, 11), (6, 14).
  • Question: If the stocks are affected by the same industry trends, will their prices rise or fall together?
    • E(A) = (2 + 3 + 5 + 4 + 6)/ 5 = 20/5 = 4
    • E(B) = (5 + 8 + 10 + 11 + 14) /5 = 48/5 = 9.6
    • Cov(A,B) = (2×5+3×8+5×10+4×11+6×14)/5 − 4 × 9.6 = 4
  • Thus, A and B rise together since Cov(A, B) > 0.

Data Reduction Strategies

  • Data reduction: Obtain a reduced representation of the data set that is much smaller in volume but yet produces the same (or almost the same) analytical results
  • Why data reduction? — A database/data warehouse may store terabytes of data. Complex data analysis may take a very long time to run on the complete data set.
  • Data reduction strategies
    • Dimensionality reduction, e.g., remove unimportant attributes
      • Wavelet transforms
      • Principal Components Analysis (PCA)
      • Feature subset selection, feature creation
    • Numerosity reduction (some simply call it: Data Reduction)
      • Regression and Log-Linear Models
      • Histograms, clustering, sampling
      • Data cube aggregation
    • Data compression

Data Reduction 1: Dimensionality Reduction

  • Curse of dimensionality
    • When dimensionality increases, data becomes increasingly sparse
    • Density and distance between points, which is critical to clustering, outlier analysis, becomes less meaningful
    • The possible combinations of subspaces will grow exponentially
  • Dimensionality reduction
    • Avoid the curse of dimensionality
    • Help eliminate irrelevant features and reduce noise
    • Reduce time and space required in data mining
    • Allow easier visualization
  • Dimensionality reduction techniques
    • Wavelet transforms
    • Principal Component Analysis
    • Supervised and nonlinear techniques (e.g., feature selection)

Mapping Data to a New Space

  • Fourier transform
  • Wavelet transform 

What Is Wavelet Transform?

  • Decomposes a signal into different frequency subbands
    • Applicable to n-dimensional signals
  • Data are transformed to preserve relative distance between objects at different levels of resolution
  • Allow natural clusters to become more distinguishable
  • Used for image compression

Wavelet Transformation

  • Discrete wavelet transform (DWT) for linear signal processing, multi-resolution analysis
  • Compressed approximation: store only a small fraction of the strongest of the wavelet coefficients
  • Similar to discrete Fourier transform (DFT), but better lossy compression, localized in space
  • Method:
    • Length, L, must be an integer power of 2 (padding with 0’s, when necessary)
    • Each transform has 2 functions: smoothing, difference
    • Applies to pairs of data, resulting in two set of data of length L/2
    • Applies two functions recursively, until reaches the desired length

Wavelet Decomposition

  • Wavelets: A math tool for space-efficient hierarchical decomposition of functions
  • S = [2, 2, 0, 2, 3, 5, 4, 4] can be transformed to

    \[ S^ = [2\frac{3}{4}, -1\frac{1}{4}, \frac{1}{2}, 0, 0, -1, -1, 0] \]
  • Compression: many small detail coefficients can be replaced by 0’s, and only the significant coefficients are retained
 

Why Wavelet Transform?

  • Use hat-shape filters
    • Emphasize region where points cluster
    • Suppress weaker information in their boundaries
  • Effective removal of outliers
    • Insensitive to noise, insensitive to input order
  • Multi-resolution
    • Detect arbitrary shaped clusters at different scales
  • Efficient
    • Complexity O(N)
  • Only applicable to low dimensional data

Principal Component Analysis (PCA)

  • Find a projection that captures the largest amount of variation in data
  • The original data are projected onto a much smaller space, resulting in dimensionality reduction. We find the eigenvectors of the covariance matrix, and these eigenvectors define the new space

  • Given N data vectors from n-dimensions, find kn orthogonal vectors (principal components) that can be best used to represent data
    • Normalize input data: Each attribute falls within the same range
    • Compute k orthonormal (unit) vectors, i.e., principal components
    • Each input data (vector) is a linear combination of the k principal component vectors
    • The principal components are sorted in order of decreasing “significance” or strength
    • Since the components are sorted, the size of the data can be reduced by eliminating the weak components, i.e., those with low variance (i.e., using the strongest principal components, it is possible to reconstruct a good approximation of the original data)
  • Works for numeric data only

Principal Component Analysis (Steps)

Attribute Subset Selection

  • Another way to reduce dimensionality of data
  • Redundant attributes
    • Duplicate much or all of the information contained in one or more other attributes
    • E.g., purchase price of a product and the amount of sales tax paid
  • Irrelevant attributes
    • Contain no information that is useful for the data mining task at hand
    • E.g., students' ID is often irrelevant to the task of predicting students' GPA

Heuristic Search in Attribute Selection

  • There are 2d possible attribute combinations of d attributes
  • Typical heuristic attribute selection methods:
    • Best single attribute under the attribute independence assumption: choose by significance tests
    • Best step-wise feature selection:
      • The best single-attribute is picked first
      • Then next best attribute condition to the first, ...
    • Step-wise attribute elimination:
      • Repeatedly eliminate the worst attribute
    • Best combined attribute selection and elimination
    • Optimal branch and bound:
      • Use attribute elimination and backtracking

Attribute Creation (Feature Generation)

  • Create new attributes (features) that can capture the important information in a data set more effectively than the original ones
  • Three general methodologies
    • Attribute extraction
      • Domain-specific
    • Mapping data to new space (see: data reduction)
      • E.g., Fourier transformation, wavelet transformation, manifold approaches (not covered)
    • Attribute construction
      • Combining features (see: discriminative frequent patterns in Chapter 7)
      • Data discretization

Data Reduction 2: Numerosity Reduction

  • Reduce data volume by choosing alternative, smaller forms of data representation
  • Parametric methods (e.g., regression)
    • Assume the data fits some model, estimate model parameters, store only the parameters, and discard the data (except possible outliers)
    • Ex.: Log-linear models—obtain value at a point in m-D space as the product on appropriate marginal subspaces
  • Non-parametric methods
    • Do not assume models
    • Major families: histograms, clustering, sampling, …

Parametric Data Reduction: Regression and Log-Linear Models

  • Linear regression
    • Data modeled to fit a straight line
    • Often uses the least-square method to fit the line
  • Multiple regression
    • Allows a response variable Y to be modeled as a linear function of multidimensional feature vector
  • Log-linear model
    • Approximates discrete multidimensional probability distributions

Regression Analysis

  • Regression analysis: A collective name for techniques for the modeling and analysis of numerical data consisting of values of a dependent variable (also called response variable or measurement) and of one or more independent variables (aka. explanatory variables or predictors)
  • The parameters are estimated so as to give a "best fit" of the data
  • Most commonly the best fit is evaluated by using the least squares method, but other criteria have also been used
  • Used for prediction (including forecasting of time-series data), inference, hypothesis testing, and modeling of causal relationships

  • Linear regression: Y = w X + b
    • Two regression coefficients, w and b, specify the line and are to be estimated by using the data at hand
    • Using the least squares criterion to the known values of Y1, Y2, …, X1, X2, ….
  • Multiple regression: Y = b + b1 X1 + b2 X2
    • Many nonlinear functions can be transformed into the above
  • Log-linear models:
    • Approximate discrete multidimensional probability distributions
    • Estimate the probability of each point (tuple) in a multi-dimensional space for a set of discretized attributes, based on a smaller subset of dimensional combinations
    • Useful for dimensionality reduction and data smoothing

Regress Analysis and Log-Linear Models

Histogram Analysis

  • Divide data into buckets and store average (sum) for each bucket
  • Partitioning rules:
    • Equal-width: equal bucket range
    • Equal-frequency (or equal-depth)

Clustering

  • Partition data set into clusters based on similarity, and store cluster representation (e.g., centroid and diameter) only
  • Can be very effective if data is clustered but not if data is “smeared”
  • Can have hierarchical clustering and be stored in multi-dimensional index tree structures
  • There are many choices of clustering definitions and clustering algorithms
  • Cluster analysis will be studied in depth in Chapter 10

Sampling

  • Sampling: obtaining a small sample s to represent the whole data set N
  • Allow a mining algorithm to run in complexity that is potentially sub-linear to the size of the data
  • Key principle: Choose a representative subset of the data
    • Simple random sampling may have very poor performance in the presence of skew
    • Develop adaptive sampling methods, e.g., stratified sampling:
  • Note: Sampling may not reduce database I/Os (page at a time)

Types of Sampling

  • Simple random sampling
    • There is an equal probability of selecting any particular item
  • Sampling without replacement
    • Once an object is selected, it is removed from the population
  • Sampling with replacement
    • A selected object is not removed from the population
  • Stratified sampling:
    • Partition the data set, and draw samples from each partition (proportionally, i.e., approximately the same percentage of the data)
    • Used in conjunction with skewed data

Sampling: With or without Replacement

Sampling: Cluster or Stratified Sampling

Data Cube Aggregation

  • The lowest level of a data cube (base cuboid)
    • The aggregated data for an individual entity of interest
    • E.g., a customer in a phone calling data warehouse
  • Multiple levels of aggregation in data cubes
    • Further reduce the size of data to deal with
  • Reference appropriate levels
    • Use the smallest representation which is enough to solve the task
  • Queries regarding aggregated information should be answered using data cube, when possible

Data Reduction 3: Data Compression

  • String compression
    • There are extensive theories and well-tuned algorithms
    • Typically lossless, but only limited manipulation is possible without expansion
  • Audio/video compression
    • Typically lossy compression, with progressive refinement
    • Sometimes small fragments of signal can be reconstructed without reconstructing the whole
  • Time sequence is not audio
    • Typically short and vary slowly with time
  • Dimensionality and numerosity reduction may also be considered as forms of data compression

Data Compression

Data Transformation

  • A function that maps the entire set of values of a given attribute to a new set of replacement values s.t. each old value can be identified with one of the new values
  • Methods
    • Smoothing: Remove noise from data
    • Attribute/feature construction
      • New attributes constructed from the given ones
    • Aggregation: Summarization, data cube construction
    • Normalization: Scaled to fall within a smaller, specified range
      • min-max normalization
      • z-score normalization
      • normalization by decimal scaling
    • Discretization: Concept hierarchy climbing

Normalization

  • Min-max normalization: to [new_minA, new_maxA]

\[ v^{'}=\frac{v-min_{A}}{max_{A}-min_{A}}(newmax_{A} - newmin_{A})+ newmin_{A} \]

    • Ex. Let income range $12,000 to $98,000 normalized to [0.0, 1.0]. Then $73,000 is mapped to

\[ \frac{73,600-12,000}{98,000-12,000}(1.0 - 0)+ 0 = 0.716 \]

  • Z-score normalization (μ: mean, σ: standard deviation):

\[ v^{'} = \frac{v-\mu_{A}}{\sigma _{A}} \]

    • Ex. Let μ = 54,000, σ = 16,000. Then

\[ \frac{73,600-54,000}{16,000} = 1.225 \]

  • Normalization by decimal scaling
\[ v^{'} = \frac{v}{10^{j}} \]

Where j is the smallest integer such that Max(|ν’|) < 1



Discretization

  • Three types of attributes
    • Nominal—values from an unordered set, e.g., color, profession
    • Ordinal—values from an ordered set, e.g., military or academic rank
    • Numeric—real numbers, e.g., integer or real numbers
  • Discretization: Divide the range of a continuous attribute into intervals
    • Interval labels can then be used to replace actual data values
    • Reduce data size by discretization
    • Supervised vs. unsupervised
    • Split (top-down) vs. merge (bottom-up)
    • Discretization can be performed recursively on an attribute
    • Prepare for further analysis, e.g., classification

Data Discretization Methods

  • Typical methods: All the methods can be applied recursively
    • Binning
      • Top-down split, unsupervised
    • Histogram analysis
      • Top-down split, unsupervised
    • Clustering analysis (unsupervised, top-down split or bottom-up merge)
    • Decision-tree analysis (supervised, top-down split)
    • Correlation (e.g., X^2) analysis (unsupervised, bottom-up merge)

Simple Discretization: Binning

  • Equal-width (distance) partitioning
    • Divides the range into N intervals of equal size: uniform grid
    • if A and B are the lowest and highest values of the attribute, the width of intervals will be: W = (B A)/N.
    • The most straightforward, but outliers may dominate presentation
    • Skewed data is not handled well
  • Equal-depth (frequency) partitioning
    • Divides the range into N intervals, each containing approximately same number of samples
    • Good data scaling
    • Managing categorical attributes can be tricky

Binning Methods for Data Smoothing

  • Sorted data for price (in dollars): 4, 8, 9, 15, 21, 21, 24, 25, 26, 28, 29, 34
  • * Partition into equal-frequency (equi-depth) bins:
  • - Bin 1: 4, 8, 9, 15
  • - Bin 2: 21, 21, 24, 25
  • - Bin 3: 26, 28, 29, 34
  • * Smoothing by bin means:
  • - Bin 1: 9, 9, 9, 9
  • - Bin 2: 23, 23, 23, 23
  • - Bin 3: 29, 29, 29, 29
  • * Smoothing by bin boundaries:
  • - Bin 1: 4, 4, 4, 15
  • - Bin 2: 21, 21, 25, 25
  • - Bin 3: 26, 26, 26, 34

Discretization Without Using Class Labels(Binning vs. Clustering)

Discretization by Classification & Correlation Analysis

  • Classification (e.g., decision tree analysis)
    • Supervised: Given class labels, e.g., cancerous vs. benign
    • Using entropy to determine split point (discretization point)
    • Top-down, recursive split
    • Details to be covered in Chapter 7
  • Correlation analysis (e.g., Chi-merge: χ2-based discretization)
    • Supervised: use class information
    • Bottom-up merge: find the best neighboring intervals (those having similar distributions of classes, i.e., low χ2 values) to merge
    • Merge performed recursively, until a predefined stopping condition

Concept Hierarchy Generation

  • Concept hierarchy organizes concepts (i.e., attribute values) hierarchically and is usually associated with each dimension in a data warehouse
  • Concept hierarchies facilitate drilling and rolling in data warehouses to view data in multiple granularity
  • Concept hierarchy formation: Recursively reduce the data by collecting and replacing low level concepts (such as numeric values for age) by higher level concepts (such as youth, adult, or senior)
  • Concept hierarchies can be explicitly specified by domain experts and/or data warehouse designers
  • Concept hierarchy can be automatically formed for both numeric and nominal data. For numeric data, use discretization methods shown.

Concept Hierarchy Generation for Nominal Data

  • Specification of a partial/total ordering of attributes explicitly at the schema level by users or experts
    • street < city < state < country
  • Specification of a hierarchy for a set of values by explicit data grouping
    • {Urbana, Champaign, Chicago} < Illinois
  • Specification of only a partial set of attributes
    • E.g., only street < city, not others
  • Automatic generation of hierarchies (or attribute levels) by the analysis of the number of distinct values
    • E.g., for a set of attributes: {street, city, state, country}

Automatic Concept Hierarchy Generation

  • Some hierarchies can be automatically generated based on the analysis of the number of distinct values per attribute in the data set
    • The attribute with the most distinct values is placed at the lowest level of the hierarchy
    • Exceptions, e.g., weekday, month, quarter, year

Summary

  • Data quality: accuracy, completeness, consistency, timeliness, believability, interpretability
  • Data cleaning: e.g. missing/noisy values, outliers
  • Data integration from multiple sources:
    • Entity identification problem
    • Remove redundancies
    • Detect inconsistencies
  • Data reduction
    • Dimensionality reduction
    • Numerosity reduction
    • Data compression
  • Data transformation and data discretization
    • Normalization
    • Concept hierarchy generation

References

  • D. P. Ballou and G. K. Tayi. Enhancing data quality in data warehouse environments. Comm. of ACM, 42:73-78, 1999
  • T. Dasu and T. Johnson. Exploratory Data Mining and Data Cleaning. John Wiley, 2003
  • T. Dasu, T. Johnson, S. Muthukrishnan, V. Shkapenyuk. Mining Database Structure; Or, How to Build a Data Quality Browser. SIGMOD’02
  • H. V. Jagadish et al., Special Issue on Data Reduction Techniques. Bulletin of the Technical Committee on Data Engineering, 20(4), Dec. 1997
  • D. Pyle. Data Preparation for Data Mining. Morgan Kaufmann, 1999
  • E. Rahm and H. H. Do. Data Cleaning: Problems and Current Approaches. IEEE Bulletin of the Technical Committee on Data Engineering. Vol.23, No.4
  • V. Raman and J. Hellerstein. Potters Wheel: An Interactive Framework for Data Cleaning and Transformation, VLDB’2001
  • T. Redman. Data Quality: Management and Technology. Bantam Books, 1992
  • R. Wang, V. Storey, and C. Firth. A framework for analysis of data quality research. IEEE Trans. Knowledge and Data Engineering, 7:623-640, 1995
  • 3/13/2013

Agenda

  • Data Warehouse: Basic Concepts
  • Data Warehouse Modeling: Data Cube and OLAP
  • Data Warehouse Design and Usage
  • Data Warehouse Implementation
  • Data Generalization by Attribute-Oriented Induction
  • Summary

What is a Data Warehouse?

  • Defined in many different ways, but not rigorously.
    • A decision support database that is maintained separately from the organization’s operational database
    • Support information processing by providing a solid platform of consolidated, historical data for analysis.
  • “A data warehouse is a subject-oriented, integrated, time-variant, and nonvolatile collection of data in support of management’s decision-making process.”—W. H. Inmon
  • Data warehousing:
    • The process of constructing and using data warehouses

Data Warehouse—Subject-Oriented

  • Organized around major subjects, such as customer, product, sales
  • Focusing on the modeling and analysis of data for decision makers, not on daily operations or transaction processing
  • Provide a simple and concise view around particular subject issues by excluding data that are not useful in the decision support process

Data Warehouse—Integrated

  • Constructed by integrating multiple, heterogeneous data sources
    • relational databases, flat files, on-line transaction records
  • Data cleaning and data integration techniques are applied.
    • Ensure consistency in naming conventions, encoding structures, attribute measures, etc. among different data sources
      • E.g., Hotel price: currency, tax, breakfast covered, etc.
    • When data is moved to the warehouse, it is converted.

Data Warehouse—Time Variant

  • The time horizon for the data warehouse is significantly longer than that of operational systems
    • Operational database: current value data
    • Data warehouse data: provide information from a historical perspective (e.g., past 5-10 years)
  • Every key structure in the data warehouse
    • Contains an element of time, explicitly or implicitly
    • But the key of operational data may or may not contain “time element”

Data Warehouse—Nonvolatile

  • A physically separate store of data transformed from the operational environment
  • Operational update of data does not occur in the data warehouse environment
    • Does not require transaction processing, recovery, and concurrency control mechanisms
    • Requires only two operations in data accessing:
      • initial loading of data and access of data

OLTP vs. OLAP

 OLTPOLAP
usersclerk, IT professional
knowledge worker

function

DB design

day to day operations

application-oriented

decision support

subject-oriented

datasurrent, up-to-date detailed, flat relational isolated
historical, summarized, multidimensional integrated, sonsolidated

usage

access

repetetive

read/write index/hash on prim key

ad-hoc

lots of scans

unit of work

#records accessed

short, simple transaction

tens

complex query

millions

#users

DB size

metric

thousands

100MB-GB

transaction throughput

hundreds

100GB-TB

query throughput, response


Why a Separate Data Warehouse?

  • High performance for both systems
    • DBMS— tuned for OLTP: access methods, indexing, concurrency control, recovery
    • Warehouse—tuned for OLAP: complex OLAP queries, multidimensional view, consolidation
  • Different functions and different data:
    • missing data: Decision support requires historical data which operational DBs do not typically maintain
    • data consolidation: DS requires consolidation (aggregation, summarization) of data from heterogeneous sources
    • data quality: different sources typically use inconsistent data representations, codes and formats which have to be reconciled
  • Note: There are more and more systems which perform OLAP analysis directly on relational databases

Data Warehouse: A Multi-Tiered ArchitectureUntitled

 

Three Data Warehouse Models

  • Enterprise warehouse
    • collects all of the information about subjects spanning the entire organization
  • Data Mart
    • a subset of corporate-wide data that is of value to a specific groups of users. Its scope is confined to specific, selected groups, such as marketing data mart
      • Independent vs. dependent (directly from warehouse) data mart
  • Virtual warehouse
    • A set of views over operational databases
    • Only some of the possible summary views may be materialized

Extraction, Transformation, and Loading (ETL)

  • Data extraction
    • get data from multiple, heterogeneous, and external sources
  • Data cleaning
    • detect errors in the data and rectify them when possible
  • Data transformation
    • convert data from legacy or host format to warehouse format
  • Load
    • sort, summarize, consolidate, compute views, check integrity, and build indicies and partitions
  • Refresh
    • propagate the updates from the data sources to the warehouse

Metadata Repository

  • Meta data is the data defining warehouse objects. It stores:
  • Description of the structure of the data warehouse
    • schema, view, dimensions, hierarchies, derived data defn, data mart locations and contents
  • Operational meta-data
    • data lineage (history of migrated data and transformation path), currency of data (active, archived, or purged), monitoring information (warehouse usage statistics, error reports, audit trails)
  • The algorithms used for summarization
  • The mapping from operational environment to the data warehouse
  • Data related to system performance
    • warehouse schema, view and derived data definitions
  • Business data
    • business terms and definitions, ownership of data, charging policies

From Tables and Spreadsheets to Data Cubes

  • A data warehouse is based on a multidimensional data model which views data in the form of a data cube
  • A data cube, such as sales, allows data to be modeled and viewed in multiple dimensions
    • Dimension tables, such as item (item_name, brand, type), or time(day, week, month, quarter, year)
    • Fact table contains measures (such as dollars_sold) and keys to each of the related dimension tables
  • In data warehousing literature, an n-D base cube is called a base cuboid. The top most 0-D cuboid, which holds the highest-level of summarization, is called the apex cuboid. The lattice of cuboids forms a data cube.

Cube: A Lattice of Cuboids

Conceptual Modeling of Data Warehouses

  • Modeling data warehouses: dimensions & measures
    • Star schema: A fact table in the middle connected to a set of dimension tables
    • Snowflake schema: A refinement of star schema where some dimensional hierarchy is normalized into a set of smaller dimension tables, forming a shape similar to snowflake
    • Fact constellations: Multiple fact tables share dimension tables, viewed as a collection of stars, therefore called galaxy schema or fact constellation

Example of Star Schema


Example of Snowflake Schema


Example of Fact Constellation