### CS276: Information Retrieval and Web Search

Pandu Nayak and Prabhakar Raghavan

Lecture 11: Text Classification;

Vector space classification

[Borrows slides from Ray Mooney]

### Recap: Naïve Bayes classifiers

• Classify based on prior weight of class and conditional parameter for what each word says: • Training is done by counting and dividing: • Don’t forget to smooth

### The rest of text classification

• Today:

• Vector space methods for Text Classification

• Vector space classification using centroids (Rocchio)

• K Nearest Neighbors

• Decision boundaries, linear and nonlinear classifiers

• Dealing with more than 2 classes

• Later in the course

• More text classification

• Support Vector Machines

• Text-specific issues in classification

### Recall: Vector Space Representation

• Each document is a vector, one component for each term (= word).

• Normally normalize vectors to unit length.

• High-dimensional vector space:

• Terms are axes

• 10,000+ dimensions, or even 100,000+

• Docs are vectors in this space

• How can we do classification in this space?

### Classification Using Vector Spaces

• As before, the training set is a set of documents, each labeled with its class (e.g., topic)

• In vector space classification, this set corresponds to a labeled set of points (or, equivalently, vectors) in the vector space

• Premise 1: Documents in the same class form a contiguous region of space

• Premise 2: Documents from different classes don’t overlap (much)

• We define surfaces to delineate classes in the space

### Documents in a Vector Space ### Test Document of what class? ### Test Document = Government ### Aside: 2D/3D graphs can be misleading ### Using Rocchio for text classification

• Relevance feedback methods can be adapted for text categorization

• As noted before, relevance feedback can be viewed as 2-class classification

• Relevant vs. nonrelevant documents

• Use standard tf-idf weighted vectors to represent text documents

• For training documents in each category, compute a prototype vector by summing the vectors of the training documents in the category.

• Prototype = centroid of members of class

• Assign test documents to the category with the closest prototype vector based on cosine similarity.

### Illustration of Rocchio Text Categorization ### Definition of centroid • Where Dc is the set of all documents that belong to class c and v(d) is the vector space representation of d.

• Note that centroid will in general not be a unit vector even when the inputs are unit vectors.

### Rocchio Properties

• Forms a simple generalization of the examples in each class (a prototype).

• Prototype vector does not need to be averaged or otherwise normalized for length since cosine similarity is insensitive to vector length.

• Classification is based on similarity to class prototypes.

• Does not guarantee classifications are consistent with the given training data.

Why not?

### Rocchio Anomaly

• Prototype models have problems with polymorphic (disjunctive) categories. ### Rocchio classification

• Rocchio forms a simple representation for each class: the centroid/prototype

• Classification is based on similarity to / distance from the prototype/centroid

• It does not guarantee that classifications are consistent with the given training data

• It is little used outside text classification

• It has been used quite effectively for text classification

• But in general worse than Naïve Bayes

• Again, cheap to train and test documents

### kNN decision boundaries ### Example: k=6 (6NN) ### Nearest-Neighbor Learning Algorithm

• Learning is just storing the representations of the training examples in D.

• Testing instance x (under 1NN):

• Compute similarity between x and all examples in D.

• Assign x the category of the most similar example in D.

• Does not explicitly compute a generalization or category prototypes.

• Also called:

• Case-based learning

• Memory-based learning

• Lazy learning

• Rationale of kNN: contiguity hypothesis

### kNN Is Close to Optimal

• Cover and Hart (1967)

• Asymptotically, the error rate of 1-nearest-neighbor classification is less than twice the Bayes rate [error rate of classifier knowing model that generated data]

• In particular, asymptotic error rate is 0 if Bayes rate is 0.

• Assume: query point coincides with a training point.

• Both query point and training point contribute error → 2 times Bayes rate

### k Nearest Neighbor

• Using only the closest example (1NN) to determine the class is subject to errors due to:

• A single atypical example.

• Noise (i.e., an error) in the category label of a single training example.

• More robust alternative is to find the k most-similar examples and return the majority category of these k examples.

• Value of k is typically odd to avoid ties; 3 and 5 are most common.

### k Nearest Neighbor Classification

• kNN = k Nearest Neighbor

• To classify a document d into class c:

• Define k-neighborhood N as k nearest neighbors of d

• Count number of documents i in N that belong to c

• Estimate P(c|d) as i/k

• Choose as class argmaxc P(c|d) [ = majority class]

### Similarity Metrics

• Nearest neighbor method depends on a similarity (or distance) metric.

• Simplest for continuous m-dimensional instance space is Euclidean distance.

• Simplest for m-dimensional binary instance space is Hamming distance (number of feature values that differ).

• For text, cosine similarity of tf.idf weighted vectors is typically most effective.

### Illustration of 3 Nearest Neighbor for Text Vector Space ### 3 Nearest Neighbor vs. Rocchio

• Nearest Neighbor tends to handle polymorphic categories better than Rocchio/NB. ### Nearest Neighbor with Inverted Index

• Naively, finding nearest neighbors requires a linear search through |D| documents in collection

• But determining k nearest neighbors is the same as determining the k best retrievals using the test document as a query to a database of training documents.

• Use standard vector space inverted index methods to find the k nearest neighbors.

• Testing Time: O(B|Vt|) where B is the average number of training documents in which a test-document word appears.

• Typically B << |D|

### kNN: Discussion

• No feature selection necessary

• Scales well with large number of classes

• Don’t need to train n classifiers for n classes

• Classes can influence each other

• Small changes to one class can have ripple effect

• Scores can be hard to convert to probabilities

• No training necessary

• Actually: perhaps not true. (Data editing, etc.)

• May be expensive at test time

• In most cases it’s more accurate than NB or Rocchio

### kNN vs. Naive Bayes

• Bias/Variance tradeoff

• Variance ≈ Capacity

• kNN has high variance and low bias.

• Infinite memory

• NB has low variance and high bias.

• Decision surface has to be linear (hyperplane – see later)

• Consider asking a botanist: Is an object a tree?

• Too much capacity/variance, low bias

• Botanist who memorizes

• Will always say “no” to new object (e.g., different # of leaves)

• Not enough capacity/variance, high bias

• Lazy botanist

• Says “yes” if the object is green

• You want the middle ground

(Example due to C. Burges)

### Bias vs. variance: Choosing the correct model capacity ### Linear classifiers and binary and multiclass classification

• Consider 2 class problems

• Deciding between two classes, perhaps, government and non-government

• One-versus-rest classification

• How do we define (and find) the separating surface?

• How do we decide which region a test doc is in?

### Separation by Hyperplanes

• A strong high-bias assumption is linear separability:

• in 2 dimensions, can separate classes by a line

• in higher dimensions, need hyperplanes
• Can find separating hyperplane by linear programming

• (or can iteratively fit solution via perceptron):

• separator can be expressed as ax + by = c ### Linear programming / Perceptron • Find a,b,c, such that
• ax + by > c for red points

• ax + by < c for blue points.

### Which Hyperplane? • In general, lots of possible solutions for a,b,c.

### Which Hyperplane?

• Lots of possible solutions for a,b,c.

• Some methods find a separating hyperplane, but not the optimal one [according to some criterion of expected goodness]

• E.g., perceptron

• Most methods find an optimal separating hyperplane

 Which points should influence optimality?All pointsLinear/logistic regressionNaïve BayesOnly “difficult points” close to decision boundarySupport vector machines ### Linear classifier: Example

• Class: “interest” (as in interest rate)

• Example features of a linear classifier

wi     ti                                              wi     ti

0.70 prime                                        −0.71 dlrs

0.67 rate                                           −0.35 world

0.63 interest                                     −0.33 sees

0.60 rates                                          −0.25 year

0.46 discount                                    −0.24 group

0.43 bundesbank                               −0.24 dlr

• To classify, find dot product of feature vector and weights

### Linear Classifiers

• Many common text classifiers are linear classifiers

• Naïve Bayes

• Perceptron

• Rocchio

• Logistic regression

• Support vector machines (with linear kernel)

• Linear regression with threshold

• Despite this similarity, noticeable performance differences

• For separable problems, there is an infinite number of separating hyperplanes. Which one do you choose?

• What to do for non-separable problems?

• Different training methods pick different hyperplanes

• Classifiers more powerful than linear often don’t perform better on text problems. Why?

### Rocchio is a linear classifier ### Two-class Rocchio as a linear classifier

• Line or hyperplane defined by: • For Rocchio, set: • [Aside for ML/stats people: Rocchio classification is a simplification of the classic Fisher Linear Discriminant where you don’t model the variance (or assume it is spherical).]

### Naive Bayes is a linear classifier

• Two-class Naive Bayes. We compute: • Decide class C if the odds is greater than 1, i.e., if the log odds is greater than 0.

• So decision boundary is hyperplane: ### A nonlinear problem • A linear classifier like Naïve Bayes does badly on this task

• kNN will do very well (assuming enough training data)

### High Dimensional Data

 Pictures like the one at right are absolutely misleading!Documents are zero along almost all axesMost document pairs are very far apart (i.e., not strictly orthogonal, but only share very common words and a few scattered others)In classification terms: often document sets are separable, for most any classificationThis is part of why linear classifiers are quite successful in this domain ### More Than Two Classes

• Any-of or multivalue classification

• Classes are independent of each other.

• A document can belong to 0, 1, or >1 classes.

• Decompose into n binary problems

• Quite common for documents

• One-of or multinomial or polytomous classification

• Classes are mutually exclusive.

• Each document belongs to exactly one class

• E.g., digit recognition is polytomous classification

• Digits are mutually exclusive

### Set of Binary Classifiers: Any of

• Build a separator between each class and its complementary set (docs from all other classes).

• Given test doc, evaluate it for membership in each class.

• Apply decision criterion of classifiers independently

• Done

• Though maybe you could do better by considering dependencies between categories

### Set of Binary Classifiers: One of

• Build a separator between each class and its complementary set (docs from all other classes).

• Given test doc, evaluate it for membership in each class.

• Assign document to class with:

 maximum scoremaximum confidencemaximum probability ### Summary: Representation ofText Categorization Attributes

• Representations of text are usually very high dimensional (one feature for each word)

• High-bias algorithms that prevent overfitting in high-dimensional space should generally work best*

• For most text categorization tasks, there are many relevant features and many irrelevant ones

• Methods that combine evidence from many or all features (e.g. naive Bayes, kNN) often tend to work better than ones that try to isolate just a few relevant features*

*Although the results are a bit more mixed than often thought

### Which classifier do I use for a given text classification problem?

• Is there a learning method that is optimal for all text classification problems?

• No, because there is a tradeoff between bias and variance.

• Factors to take into account:

• How much training data is available?

• How simple/complex is the problem? (linear vs. nonlinear decision boundary)

• How noisy is the data?

• How stable is the problem over time?

• For an unstable problem, it’s better to use a simple and robust classifier.

### Resources for today’s lecture

• IIR 14

• Fabrizio Sebastiani. Machine Learning in Automated Text Categorization. ACM Computing Surveys, 34(1):1-47, 2002.

• Yiming Yang & Xin Liu, A re-examination of text categorization methods. Proceedings of SIGIR, 1999.

• Trevor Hastie, Robert Tibshirani and Jerome Friedman, Elements of Statistical Learning: Data Mining, Inference and Prediction. Springer-Verlag, New York.

• Open Calais: Automatic Semantic Tagging

• Free (but they can keep your data), provided by Thompson/Reuters

• Weka: A data mining software package that includes an implementation of many ML algorithms

Creator: Tgbyrdmc

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