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How Are Bayesian Networks Constructed?
 Subjective construction: Identification of (direct) causal structure
 People are quite good at identifying direct causes from a given set of variables & whether the set contains all relevant direct causes
 Markovian assumption: Each variable becomes independent of its noneffects once its direct causes are known
 E.g., S ‹— F —› A ‹— T, path S—›A is blocked once we know F—›A
 HMM (Hidden Markov Model): often used to model dynamic systems whose states are not observable, yet their outputs are
 Synthesis from other specifications
 E.g., from a formal system design: block diagrams & info flow
 Learning from data
 E.g., from medical records or student admission record
 Learn parameters give its structure or learn both structure and parms
 Maximum likelihood principle: favors Bayesian networks that maximize the probability of observing the given data set
Training Bayesian Networks: Several Scenarios
 Scenario 1: Given both the network structure and all variables observable: compute only the CPT entries
 Scenario 2: Network structure known, some variables hidden: gradient descent (greedy hillclimbing) method, i.e., search for a solution along the steepest descent of a criterion function
 Weights are initialized to random probability values
 At each iteration, it moves towards what appears to be the best solution at the moment, w.o. backtracking
 Weights are updated at each iteration & converge to local optimum
 Scenario 3: Network structure unknown, all variables observable: search through the model space to reconstruct network topology
 Scenario 4: Unknown structure, all hidden variables: No good algorithms known for this purpose
 D. Heckerman. A Tutorial on Learning with Bayesian Networks. In Learning in Graphical Models, M. Jordan, ed. MIT Press, 1999.
Classification by Backpropagation
 Backpropagation: A neural network learning algorithm
 Started by psychologists and neurobiologists to develop and test computational analogues of neurons
 A neural network: A set of connected input/output units where each connection has a weight associated with it
 During the learning phase, the network learns by adjusting the weights so as to be able to predict the correct class label of the input tuples
 Also referred to as connectionist learning due to the connections between units
Neuron: A Hidden/Output Layer Unit
 An ndimensional input vector x is mapped into variable y by means of the scalar product and a nonlinear function mapping
 The inputs to unit are outputs from the previous layer. They are multiplied by their corresponding weights to form a weighted sum, which is added to the bias associated with unit. Then a nonlinear activation function is applied to it.
How A MultiLayer Neural Network Works
 The inputs to the network correspond to the attributes measured for each training tuple
 Inputs are fed simultaneously into the units making up the input layer
 They are then weighted and fed simultaneously to a hidden layer
 The number of hidden layers is arbitrary, although usually only one
 The weighted outputs of the last hidden layer are input to units making up the output layer, which emits the network's prediction
 The network is feedforward: None of the weights cycles back to an input unit or to an output unit of a previous layer
 From a statistical point of view, networks perform nonlinear regression: Given enough hidden units and enough training samples, they can closely approximate any function
Defining a Network Topology
 Decide the network topology: Specify # of units in the input layer, # of hidden layers (if > 1), # of units in each hidden layer, and # of units in the output layer
 Normalize the input values for each attribute measured in the training tuples to [0.0—1.0]
 One input unit per domain value, each initialized to 0
 Output, if for classification and more than two classes, one output unit per class is used
 Once a network has been trained and its accuracy is unacceptable, repeat the training process with a different network topology or a different set of initial weights
A MultiLayer FeedForward Neural Network
Backpropagation
 Iteratively process a set of training tuples & compare the network's prediction with the actual known target value
 For each training tuple, the weights are modified to minimize the mean squared error between the network's prediction and the actual target value
 Modifications are made in the “backwards” direction: from the output layer, through each hidden layer down to the first hidden layer, hence “backpropagation”
 Steps
 Initialize weights to small random numbers, associated with biases
 Propagate the inputs forward (by applying activation function)
 Backpropagate the error (by updating weights and biases)
 Terminating condition (when error is very small, etc.)
Efficiency and Interpretability
 Efficiency of backpropagation: Each epoch (one iteration through the training set) takes O(D * w), with D tuples and w weights, but # of epochs can be exponential to n, the number of inputs, in worst case
 For easier comprehension: Rule extraction by network pruning
 Simplify the network structure by removing weighted links that have the least effect on the trained network
 Then perform link, unit, or activation value clustering
 The set of input and activation values are studied to derive rules describing the relationship between the input and hidden unit layers
 Sensitivity analysis: assess the impact that a given input variable has on a network output. The knowledge gained from this analysis can be represented in rules
Neural Network as a Classifier
 Weakness
 Long training time
 Require a number of parameters typically best determined empirically, e.g., the network topology or “structure.”
 Poor interpretability: Difficult to interpret the symbolic meaning behind the learned weights and of “hidden units” in the network
 Strength
 High tolerance to noisy data
 Ability to classify untrained patterns
 Wellsuited for continuousvalued inputs and outputs
 Successful on an array of realworld data, e.g., handwritten letters
 Algorithms are inherently parallel
 Techniques have recently been developed for the extraction of rules from trained neural networks
Classification: A Mathematical Mapping
 Classification: predicts categorical class labels
 E.g., Personal homepage classification
 xi = (x1, x2, x3, …), yi = +1 or –1
 x1 : # of word “homepage”
 x2 : # of word “welcome”
 Mathematically, x ∈ X = R^n, y ∈ Y = {+1, –1},
 We want to derive a function f: X → Y
 Linear Classification
 Binary Classification problem
 Data above the red line belongs to class ‘x’
 Data below red line belongs to class ‘o’
 Examples: SVM, Perceptron, Probabilistic Classifiers
Discriminative Classifiers
 Prediction accuracy is generally high
 As compared to Bayesian methods – in general
 Robust, works when training examples contain errors
 Fast evaluation of the learned target function
 Bayesian networks are normally slow
 Criticism
 Long training time
 Difficult to understand the learned function (weights)
 Bayesian networks can be used easily for pattern discovery
 Not easy to incorporate domain knowledge
 Easy in the form of priors on the data or distributions
Perceptron & Winnow
SVM—Support Vector Machines
 A relatively new classification method for both linear and nonlinear data
 It uses a nonlinear mapping to transform the original training data into a higher dimension
 With the new dimension, it searches for the linear optimal separating hyperplane (i.e., “decision boundary”)
 With an appropriate nonlinear mapping to a sufficiently high dimension, data from two classes can always be separated by a hyperplane
 SVM finds this hyperplane using support vectors (“essential” training tuples) and margins (defined by the support vectors)
SVM—History and Applications
 Vapnik and colleagues (1992)—groundwork from Vapnik & Chervonenkis’ statistical learning theory in 1960s
 Features: training can be slow but accuracy is high owing to their ability to model complex nonlinear decision boundaries (margin maximization)
 Used for: classification and numeric prediction
 Applications:
 handwritten digit recognition, object recognition, speaker identification, benchmarking timeseries prediction tests
SVM—General Philosophy
SVM—Margins and Support Vectors
SVM—When Data Is Linearly Separable
SVM—Linearly Separable
 A separating hyperplane can be written as
 where W={w1, w2, …, wn} is a weight vector and b a scalar (bias)
 For 2D it can be written as
 The hyperplane defining the sides of the margin:
 H1: w + w1 x1 + w2 x2 ≥ 1 for yi = +1, and
 H2: w + w1 x1 + w2 x2 ≤ – 1 for yi = –1
 Any training tuples that fall on hyperplanes H1 or H2 (i.e., the sides defining the margin) are support vectors
 This becomes a constrained (convex) quadratic optimization problem: Quadratic objective function and linear constraints → Quadratic Programming (QP) → Lagrangian multipliers
Why Is SVM Effective on High Dimensional Data?
 The complexity of trained classifier is characterized by the # of support vectors rather than the dimensionality of the data
 The support vectors are the essential or critical training examples —they lie closest to the decision boundary (MMH)
 If all other training examples are removed and the training is repeated, the same separating hyperplane would be found
 The number of support vectors found can be used to compute an (upper) bound on the expected error rate of the SVM classifier, which is independent of the data dimensionality
 Thus, an SVM with a small number of support vectors can have good generalization, even when the dimensionality of the data is high
SVM—Linearly Inseparable
 Transform the original input data into a higher dimensional space
 Search for a linear separating hyperplane in the new space
SVM: Different Kernel functions
 Instead of computing the dot product on the transformed data, it is math. equivalent to applying a kernel function K(Xi, Xj) to the original data, i.e., K(Xi, Xj) = Φ(Xi) Φ(Xj)
 Typical Kernel Functions
 SVM can also be used for classifying multiple (> 2) classes and for regression analysis (with additional parameters)
Scaling SVM by Hierarchical MicroClustering
 SVM is not scalable to the number of data objects in terms of training time and memory usage
 H. Yu, J. Yang, and J. Han, “Classifying Large Data Sets Using SVM with Hierarchical Clusters”, KDD'03)
 CBSVM (ClusteringBased SVM)
 Given limited amount of system resources (e.g., memory), maximize the SVM performance in terms of accuracy and the training speed
 Use microclustering to effectively reduce the number of points to be considered
 At deriving support vectors, decluster microclusters near “candidate vector” to ensure high classification accuracy
CFTree: Hierarchical Microcluster
 Read the data set once, construct a statistical summary of the data (i.e., hierarchical clusters) given a limited amount of memory
 Microclustering: Hierarchical indexing structure
 provide finer samples closer to the boundary and coarser samples farther from the boundary
Selective Declustering: Ensure High Accuracy
 CF tree is a suitable base structure for selective declustering
 Decluster only the cluster Ei such that
 Di – Ri < Ds, where Di is the distance from the boundary to the center point of Ei and Ri is the radius of Ei
 Decluster only the cluster whose subclusters have possibilities to be the support cluster of the boundary
 “Support cluster”: The cluster whose centroid is a support vector
CBSVM Algorithm: Outline
 Construct two CFtrees from positive and negative data sets independently
 Need one scan of the data set
 Train an SVM from the centroids of the root entries
 Decluster the entries near the boundary into the next level
 The children entries declustered from the parent entries are accumulated into the training set with the nondeclustered parent entries
 Train an SVM again from the centroids of the entries in the training set
 Repeat until nothing is accumulated
Accuracy and Scalability on Synthetic Dataset
 Experiments on large synthetic data sets shows better accuracy than random sampling approaches and far more scalable than the original SVM algorithm
SVM vs. Neural Network
 SVM
 Deterministic algorithm
 Nice generalization properties
 Hard to learn – learned in batch mode using quadratic programming techniques
 Using kernels can learn very complex functions
 Neural Network
 Nondeterministic algorithm
 Generalizes well but doesn’t have strong mathematical foundation
 Can easily be learned in incremental fashion
 To learn complex functions—use multilayer perceptron (nontrivial)
SVM Related Links
 SVM Website: http://www.kernelmachines.org/
 Representative implementations
 LIBSVM: an efficient implementation of SVM, multiclass classifications, nuSVM, oneclass SVM, including also various interfaces with java, python, etc.
 SVMlight: simpler but performance is not better than LIBSVM, support only binary classification and only in C
 SVMtorch: another recent implementation also written in C
Associative Classification
 Associative classification: Major steps
 Mine data to find strong associations between frequent patterns (conjunctions of attributevalue pairs) and class labels
 Association rules are generated in the form of
 P1 ^ p2 … ^ pl →“Aclass = C” (conf, sup)
 Organize the rules to form a rulebased classifier
 Why effective?
 It explores highly confident associations among multiple attributes and may overcome some constraints introduced by decisiontree induction, which considers only one attribute at a time
 Associative classification has been found to be often more accurate than some traditional classification methods, such as C4.5
Typical Associative Classification Methods
 CBA (Classification Based on Associations: Liu, Hsu & Ma, KDD’98)
 Mine possible association rules in the form of
 Condset (a set of attributevalue pairs) → class label
 Build classifier: Organize rules according to decreasing precedence based on confidence and then support
 CMAR (Classification based on Multiple Association Rules: Li, Han, Pei, ICDM’01)
 Classification: Statistical analysis on multiple rules
 CPAR (Classification based on Predictive Association Rules: Yin & Han, SDM’03)
 Generation of predictive rules (FOILlike analysis) but allow covered rules to retain with reduced weight
 Prediction using best k rules
 High efficiency, accuracy similar to CMAR
Frequent PatternBased Classification
 H. Cheng, X. Yan, J. Han, and C.W. Hsu, “Discriminative Frequent Pattern Analysis for Effective Classification”, ICDE'07
 Accuracy issue
 Increase the discriminative power
 Increase the expressive power of the feature space
 Scalability issue
 It is computationally infeasible to generate all feature combinations and filter them with an information gain threshold
 Efficient method (DDPMine: FPtree pruning): H. Cheng, X. Yan, J. Han, and P. S. Yu, "Direct Discriminative Pattern Mining for Effective Classification", ICDE'08
Frequent Pattern vs. Single Feature

The discriminative power of some frequent patterns is higher than that of single features.
Feature Selection
 Given a set of frequent patterns, both nondiscriminative and redundant patterns exist, which can cause overfitting
 We want to single out the discriminative patterns and remove redundant ones
 The notion of Maximal Marginal Relevance (MMR) is borrowed
 A document has high marginal relevance if it is both relevant to the query and contains minimal marginal similarity to previously selected documents
DDPMine: BranchandBound Search
DDPMine Efficiency: Runtime
Lazy vs. Eager Learning
 Lazy vs. eager learning
 Lazy learning (e.g., instancebased learning): Simply stores training data (or only minor processing) and waits until it is given a test tuple
 Eager learning (the above discussed methods): Given a set of training tuples, constructs a classification model before receiving new (e.g., test) data to classify
 Lazy: less time in training but more time in predicting
 Accuracy
 Lazy method effectively uses a richer hypothesis space since it uses many local linear functions to form an implicit global approximation to the target function
 Eager: must commit to a single hypothesis that covers the entire instance space
Lazy Learner: InstanceBased Methods
 Instancebased learning:
 Store training examples and delay the processing (“lazy evaluation”) until a new instance must be classified
 Typical approaches
 knearest neighbor approach
 Instances represented as points in a Euclidean space.
 Locally weighted regression
 Constructs local approximation
 Casebased reasoning
 Uses symbolic representations and knowledgebased inference
The kNearest Neighbor Algorithm
 All instances correspond to points in the nD space
 The nearest neighbor are defined in terms of Euclidean distance, dist(X1, X2)
 Target function could be discrete or real valued
 For discretevalued, kNN returns the most common value among the k training examples nearest to xq
 Vonoroi diagram: the decision surface induced by 1NN for a typical set of training examples
Discussion on the kNN Algorithm
 kNN for realvalued prediction for a given unknown tuple
 Returns the mean values of the k nearest neighbors
 Distanceweighted nearest neighbor algorithm
 Weight the contribution of each of the k neighbors according to their distance to the query xq
\[ w=\frac{1}{d(x_{q}, x_{i})^2} \]
 Give greater weight to closer neighbors
 Robust to noisy data by averaging knearest neighbors
 Curse of dimensionality: distance between neighbors could be dominated by irrelevant attributes
 To overcome it, axes stretch or elimination of the least relevant attributes
CaseBased Reasoning (CBR)
 CBR: Uses a database of problem solutions to solve new problems
 Store symbolic description (tuples or cases)—not points in a Euclidean space
 Applications: Customerservice (productrelated diagnosis), legal ruling
 Methodology
 Instances represented by rich symbolic descriptions (e.g., function graphs)
 Search for similar cases, multiple retrieved cases may be combined
 Tight coupling between case retrieval, knowledgebased reasoning, and problem solving
 Challenges
 Find a good similarity metric
 Indexing based on syntactic similarity measure, and when failure, backtracking, and adapting to additional cases
Genetic Algorithms (GA)
 Genetic Algorithm: based on an analogy to biological evolution
 An initial population is created consisting of randomly generated rules
 Each rule is represented by a string of bits
 E.g., if A1 and ¬A2 then C2 can be encoded as 100
 If an attribute has k > 2 values, k bits can be used
 Based on the notion of survival of the fittest, a new population is formed to consist of the fittest rules and their offspring
 The fitness of a rule is represented by its classification accuracy on a set of training examples
 Offspring are generated by crossover and mutation
 The process continues until a population P evolves when each rule in P satisfies a prespecified threshold
 Slow but easily parallelizable
Rough Set Approach
 Rough sets are used to approximately or “roughly” define equivalent classes
 A rough set for a given class C is approximated by two sets: a lower approximation (certain to be in C) and an upper approximation (cannot be described as not belonging to C)
 Finding the minimal subsets (reducts) of attributes for feature reduction is NPhard but a discernibility matrix (which stores the differences between attribute values for each pair of data tuples) is used to reduce the computation intensity
Fuzzy Set Approaches
 Fuzzy logic uses truth values between 0.0 and 1.0 to represent the degree of membership (such as in a fuzzy membership graph)
 Attribute values are converted to fuzzy values. Ex.:
 Income, x, is assigned a fuzzy membership value to each of the discrete categories {low, medium, high}, e.g. $49K belongs to “medium income” with fuzzy value 0.15 but belongs to “high income” with fuzzy value 0.96
 Fuzzy membership values do not have to sum to 1.
 Each applicable rule contributes a vote for membership in the categories
 Typically, the truth values for each predicted category are summed, and these sums are combined
Multiclass Classification
 Classification involving more than two classes (i.e., > 2 Classes)
 Method 1. Onevs.all (OVA): Learn a classifier one at a time
 Given m classes, train m classifiers: one for each class
 Classifier j: treat tuples in class j as positive & all others as negative
 To classify a tuple X, the set of classifiers vote as an ensemble
 Method 2. Allvs.all (AVA): Learn a classifier for each pair of classes
 Given m classes, construct m(m1)/2 binary classifiers
 A classifier is trained using tuples of the two classes
 To classify a tuple X, each classifier votes. X is assigned to the class with maximal vote
 Comparison
 Allvs.all tends to be superior to onevs.all
 Problem: Binary classifier is sensitive to errors, and errors affect vote count
ErrorCorrecting Codes for Multiclass Classification

Originally designed to correct errors during data transmission for communication tasks by exploring data redundancy

Example
 A 7bit codeword associated with classes 14
 Given a unknown tuple X, the 7trained classifiers output: 0001010
 Hamming distance: # of different bits between two codewords

H(
X
, C1) = 5, by checking # of bits between [1111111] & [0001010]

H(
X
, C2) = 3, H(
X
, C3) = 3, H(
X
, C4) = 1, thus C4 as the label for
X
 Errorcorrecting codes can correct up to (h1)/h 1bit error, where h is the minimum Hamming distance between any two codewords
 If we use 1bit per class, it is equiv. to onevs.all approach, the code are insufficient to selfcorrect

When selecting errorcorrecting codes, there should be good rowwise and col.wise separation between the codewords
SemiSupervised Classification
 Semisupervised: Uses labeled and unlabeled data to build a classifier
 Selftraining:
 Build a classifier using the labeled data
 Use it to label the unlabeled data, and those with the most confident label prediction are added to the set of labeled data
 Repeat the above process
 Adv: easy to understand; disadv: may reinforce errors
 Cotraining: Use two or more classifiers to teach each other
 Each learner uses a mutually independent set of features of each tuple to train a good classifier, say f1
 Then f1 and f2 are used to predict the class label for unlabeled data X
 Teach each other: The tuple having the most confident prediction from f1 is added to the set of labeled data for f2, & vice versa
 Other methods, e.g., joint probability distribution of features and labels
Active Learning
 Class labels are expensive to obtain
 Active learner: query human (oracle) for labels
 Poolbased approach: Uses a pool of unlabeled data
 L: a small subset of D is labeled, U: a pool of unlabeled data in D
 Use a query function to carefully select one or more tuples from U and request labels from an oracle (a human annotator)
 The newly labeled samples are added to L, and learn a model
 Goal: Achieve high accuracy using as few labeled data as possible
 Evaluated using learning curves: Accuracy as a function of the number of instances queried (# of tuples to be queried should be small)
 Research issue: How to choose the data tuples to be queried?
 Uncertainty sampling: choose the least certain ones
 Reduce version space, the subset of hypotheses consistent w. the training data
 Reduce expected entropy over U: Find the greatest reduction in the total number of incorrect predictions
Transfer Learning: Conceptual Framework
 Transfer learning: Extract knowledge from one or more source tasks and apply the knowledge to a target task
 Traditional learning: Build a new classifier for each new task
 Transfer learning: Build new classifier by applying existing knowledge learned from source tasks
Transfer Learning: Methods and Applications
 Applications: Especially useful when data is outdated or distribution changes, e.g., Web document classification, email spam filtering
 Instancebased transfer learning: Reweight some of the data from source tasks and use it to learn the target task
 TrAdaBoost (Transfer AdaBoost)
 Assume source and target data each described by the same set of attributes (features) & class labels, but rather diff. distributions
 Require only labeling a small amount of target data
 Use source data in training: When a source tuple is misclassified, reduce the weight of such tupels so that they will have less effect on the subsequent classifier
 Research issues
 Negative transfer: When it performs worse than no transfer at all
 Heterogeneous transfer learning: Transfer knowledge from different feature space or multiple source domains
 Largescale transfer learning
What Is Prediction?
 (Numerical) prediction is similar to classification
 construct a model
 use model to predict continuous or ordered value for a given input
 Prediction is different from classification
 Classification refers to predict categorical class label
 Prediction models continuousvalued functions
 Major method for prediction: regression
 model the relationship between one or more independent or predictor variables and a dependent or response variable
 Regression analysis
 Linear and multiple regression
 Nonlinear regression
 Other regression methods: generalized linear model, Poisson regression, loglinear models, regression trees
Linear Regression
 Linear regression: involves a response variable y and a single predictor variable x
\[ y=w_{0}+w_{1}x \]
where w0 (yintercept) and w1 (slope) are regression coefficients
 Method of least squares: estimates the bestfitting straight line
\[ w_{1}=\frac{\sum_{i=1}^{D}(x_{i}\bar{x})(y_{i}\bar{y})}{\sum_{i=1}^{D}(x_{i}\bar{x})^2} \]
\[ w_{0}=\bar{y}w_{1}\bar{x} \]
 Multiple linear regression: involves more than one predictor variable
 Training data is of the form (X1, y1), (X2, y2),…, (XD, yD)
 Ex. For 2D data, we may have:
\[ y=w+w_{1}x_{1}+w_{2}x_{2} \]  Solvable by extension of least square method or using SAS, SPlus
 Many nonlinear functions can be transformed into the above
Nonlinear Regression
 Some nonlinear models can be modeled by a polynomial function
 A polynomial regression model can be transformed into linear regression model. For example,
\[ y=w+w_{1}x+w_{2}x^{2}+w_{3}x^{3} \]
 convertible to linear with new variables: \[ x_{2} = x^{2}, x_{3}= x^{3} \]
\[ y=w+w_{1}x+w_{2}x_{2}+w_{3}x_{3} \]
 Other functions, such as power function, can also be transformed to linear model
 Some models are intractable nonlinear (e.g., sum of exponential terms)
 possible to obtain least square estimates through extensive calculation on more complex formulae
Other RegressionBased Models
 Generalized linear model:
 Foundation on which linear regression can be applied to modeling categorical response variables
 Variance of y is a function of the mean value of y, not a constant
 Logistic regression: models the prob. of some event occurring as a linear function of a set of predictor variables
 Poisson regression: models the data that exhibit a Poisson distribution
 Loglinear models: (for categorical data)
 Approximate discrete multidimensional prob. distributions
 Also useful for data compression and smoothing
 Regression trees and model trees
 Trees to predict continuous values rather than class labels
Regression Trees and Model Trees
 Regression tree: proposed in CART system (Breiman et al. 1984)
 CART: Classification And Regression Trees
 Each leaf stores a continuousvalued prediction
 It is the average value of the predicted attribute for the training tuples that reach the leaf
 Model tree: proposed by Quinlan (1992)
 Each leaf holds a regression model—a multivariate linear equation for the predicted attribute
 A more general case than regression tree
 Regression and model trees tend to be more accurate than linear regression when the data are not represented well by a simple linear model
Predictive Modeling in Multidimensional Databases
 Predictive modeling: Predict data values or construct generalized linear models based on the database data
 One can only predict value ranges or category distributions
 Method outline:
 Minimal generalization
 Attribute relevance analysis
 Generalized linear model construction
 Prediction
 Determine the major factors which influence the prediction
 Data relevance analysis: uncertainty measurement, entropy analysis, expert judgement, etc.
 Multilevel prediction: drilldown and rollup analysis
Prediction: Numerical Data
Prediction: Categorical Data
SVM—Introductory Literature
 “Statistical Learning Theory” by Vapnik: extremely hard to understand, containing many errors too.
 C. J. C. Burges. A Tutorial on Support Vector Machines for Pattern Recognition. Knowledge Discovery and Data Mining, 2(2), 1998.
 Better than the Vapnik’s book, but still written too hard for introduction, and the examples are so notintuitive
 The book “An Introduction to Support Vector Machines” by N. Cristianini and J. ShaweTaylor
 Also written hard for introduction, but the explanation about the mercer’s theorem is better than above literatures
 The neural network book by Haykins
 Contains one nice chapter of SVM introduction
Notes about SVM—Introductory Literature
 “Statistical Learning Theory” by Vapnik: difficult to understand, containing many errors.
 C. J. C. Burges. A Tutorial on Support Vector Machines for Pattern Recognition. Knowledge Discovery and Data Mining, 2(2), 1998.
 Easier than Vapnik’s book, but still not introductory level; the examples are not so intuitive
 The book An Introduction to Support Vector Machines by Cristianini and ShaweTaylor
 Not introductory level, but the explanation about Mercer’s Theorem is better than above literatures
 Neural Networks and Learning Machines by Haykin
 Contains a nice chapter on SVM introduction
Associative Classification Can Achieve High Accuracy and Efficiency (Cong et al. SIGMOD05)
A Closer Look at CMAR
 CMAR (Classification based on Multiple Association Rules: Li, Han, Pei, ICDM’01)
 Efficiency: Uses an enhanced FPtree that maintains the distribution of class labels among tuples satisfying each frequent itemset
 Rule pruning whenever a rule is inserted into the tree
 Given two rules, R1 and R2, if the antecedent of R1 is more general than that of R2 and conf(R1) ≥ conf(R2), then prune R2
 Prunes rules for which the rule antecedent and class are not positively correlated, based on a χ2 test of statistical significance
 Classification based on generated/pruned rules
 If only one rule satisfies tuple X, assign the class label of the rule
 If a rule set S satisfies X, CMAR
 divides S into groups according to class labels
 uses a weighted χ2 measure to find the strongest group of rules, based on the statistical correlation of rules within a group
 assigns X the class label of the strongest group
Summary
 Effective and advanced classification methods
 Bayesian belief network (probabilistic networks)
 Backpropagation (Neural networks)
 Support Vector Machine (SVM)
 Patternbased classification
 Other classification methods: lazy learners (KNN, casebased reasoning), genetic algorithms, rough set and fuzzy set approaches
 Additional Topics on Classification
 Multiclass classification
 Semisupervised classification
 Active learning
 Transfer learning
References
 C. M. Bishop, Neural Networks for Pattern Recognition. Oxford University Press, 1995
 C. J. C. Burges. A Tutorial on Support Vector Machines for Pattern Recognition. Data Mining and Knowledge Discovery, 2(2): 121168, 1998
 H. Cheng, X. Yan, J. Han, and C.W. Hsu, Discriminative Frequent pattern Analysis for Effective Classification, ICDE'07
 H. Cheng, X. Yan, J. Han, and P. S. Yu, Direct Discriminative Pattern Mining for Effective Classification, ICDE'08
 N. Cristianini and J. ShaweTaylor, Introduction to Support Vector Machines and Other KernelBased Learning Methods, Cambridge University Press, 2000
 A. J. Dobson. An Introduction to Generalized Linear Models. Chapman & Hall, 1990
 G. Dong and J. Li. Efficient mining of emerging patterns: Discovering trends and differences. KDD'99
 R. O. Duda, P. E. Hart, and D. G. Stork. Pattern Classification, 2ed. John Wiley, 2001
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Hastie, R. Tibshirani, and J. Friedman. The Elements of Statistical
Learning: Data Mining, Inference, and Prediction. SpringerVerlag, 2001
 S. Haykin, Neural Networks and Learning Machines, Prentice Hall, 2008
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