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Rainbow Tool Kit
Matt PerryGlobal Information Systems Spring 2003
Outline1. Introduction to Rainbow2. Description of Bow Library3. Description of Rainbow methods
1. Naïve Bayes2. TFIDF/Rocchio3. K Nearest Neighbor4. Probabilistic Indexing
4. Demonstration of Rainbow1. 20 newsgroups example
What is Rainbow?
Publicly available executable program that performs document classification
Part of the Bow (or libbow) library A library of C code useful for writing statistical text
analysis, language modeling and information retrieval programs
Developed by Andrew McCallum of Carnegie Mellon University
About Bow Library
Provides facilities for Recursively descending directories, finding text files. Finding `document' boundaries when there are multiple
documents per file. Tokenizing a text file, according to several different
methods. Including N-grams among the tokens. Mapping strings to integers and back again, very efficiently. Building a sparse matrix of document/token counts. Pruning vocabulary by word counts or by information gain. Building and manipulating word vectors.
About Bow Library Provides facilities for
Setting word vector weights according to Naive Bayes, TFIDF, and several other methods.
Smoothing word probabilities according to Laplace (Dirichlet uniform), M-estimates, Witten-Bell, and Good-Turning.
Scoring queries for retrieval or classification. Writing all data structures to disk in a compact format. Reading the document/token matrix from disk in an
efficient, sparse fashion. Performing test/train splits, and automatic classification
tests. Operating in server mode, receiving and answering queries
over a socket.
About Bow Library
Does Not Have English parsing or part-of-speech tagging
facilities. Do smoothing across N-gram models. Claim to be finished. Have good documentation. Claim to be bug-free. Run on a Windows Machine.
About Bow Library
In Addition to Rainbow, Bow contains 3 other executable programs Crossbow - does document clustering Arrow - does document retrieval – TFIDF Archer - does document retrieval
Supports AltaVista-type queries +, -, “”, etc.
Back to Rainbow
Classification Methods used by Rainbow Naïve Bayes (mostly designed for this)
TFIDF/Rocchio
K-Nearest Neighbor
Probabilistic Indexing
Description of Naïve Bayes
Bayesian reasoning provides a probabilistic approach to learning.
Idea of Naïve Bayes Classification is to assign a new instance the most probable target value, given the attribute values of the new instance.
How?
Description of Naïve Bayes
Based on Bayes Theorem Notation
P(h) = probability that a hypothesis h holds Ex. Pr (document1 fits the sports category)
P(D) = probability that training data D will be observed
Ex. Pr (we will encounter document1)
Description of Naïve Bayes
Notation Continued P(D|h) probability of observing data D given that
hypothesis h holds. Ex. Probability that we will observe document 1 given
that document 1 is about sports P(h|D) probability that h holds given training data
D. This is what we want Probability that document 1 is a sports document given
the training data D
Description of Naïve Bayes
Bayes Theorem
)()()|()|(
DPhPhDPDhP
Description of Naïve Bayes
Bayes Theorem Provides a way to calculate P(h|D) from P(h),
together with P(D) and P(D|h). Increases with P(D|h) and P(h) Decreases with P(D)
Implies that it is more probable to observe D independent of h.
Less evidence D provides in support of h.
Description of Naïve Bayes Approach: Assign the most probable target value
given the attributes
),...,|(1max aav nj
Pv
valj
Description of Naïve Bayes Simplification based on Bayes Theorem
)()|,...,(
),...,(
)()|,...,(
1
1
1
max
max
vvaaaavvaa
jjn
n
jjn
PPv
val
P
PP
vval
j
j
Description of Naïve Bayes Naïve Bayes assumes (incorrectly) that the
attribute values are conditionally independent given the target value
)|()(max vav ji
ijPP
vval
j
Rainbow Algorithm
Let )(viP = probability that a document belongs to class vi
Let
)|( vw jkP = probability that a
randomly drawn word from class will be the word
v jwk
Rainbow Algorithm
Estimate
||1
)|(Vocabularyn
P nvw kjk
Rainbow Algorithm1. Collect all words, punctuation, and other tokens
that occur in examples2. Calculate the required and
probability terms3. Return the estimated target value for the document
Doc
)|( vw jkP)(v jP
)|()(max vav ji
ijPP
vval
j
TFIDF/Rocchio
Most major component of the Rocchio algorithm is the TFIDF (term frequency / inverse document frequency) word weighting scheme.
TF(w,d) (Term Frequency) is the number of times word w occurs in a document d.
DF(w) (Document Frequency) is the number of documents in which the word w occurs at least once.
TFIDF/Rocchio The inverse document frequency is calculated
as
)log()( )(||wDF
DwIDF
TFIDF/Rocchio
Based on word weight heuristics, the word wi is an important indexing term for a document d if it occurs frequently in that document
However, words that occurs frequently in many document spanning many categories are rated less importantly
TFIDF/Rocchio Each document is D is represented as a vector
within a given vector space V:
),...,( |)(|)1( Fddd
TFIDF/Rocchio
Value of d(i) of feature wi for a document d is calculated as the product
d(i) is called the weight of the word wi in the document d.
)(),()(ii
i wIDFdwTFd
TFIDF/Rocchio
Documents that are “close together” in vector space talk about the same things.
t1
d1
d3
d5t2
θ
φ
t3 d2
d4
http://www.stanford.edu/class/cs276a/handouts/lecture4.ppt
TFIDF/Rocchio Distance between vectors d1 and d2 captured
by the cosine of the angle x between them. Note – this is similarity, not distance
t 1
d2
d1
t 3
t 2
θ
http://www.stanford.edu/class/cs276a/handouts/lecture4.ppt
TFIDF/Rocchio
Cosine of angle between two vectors The denominator involves the lengths of the vectors So the cosine measure is also known as the
normalized inner product
n
i kin
i ji
n
i kiji
kj
kjkj
ww
ww
dd
ddddsim
12,1
2,
1 ,,),(
http://www.stanford.edu/class/cs276a/handouts/lecture4.ppt
TFIDF/Rocchio A vector can be normalized (given a length of 1) by
dividing each of its components by the vector's length This maps vectors onto the unit circle: Then, Longer documents don’t get more weight For normalized vectors, the cosine is simply the dot
product:
kjkj dddd
),cos(
http://www.stanford.edu/class/cs276a/handouts/lecture4.ppt
Rainbow Algorithm
Construct a set of prototype vectors One vector for each class This serves as learned model Model is used to classify a new document D D is assigned to the class with the most
similar vector
K Nearest Neighbor
Features All instances correspond to points in an n-
dimensional Euclidean space Classification is delayed until a new instance
arrives Classification done by comparing feature vectors
of the different points Target function may be discrete or real-valued
K Nearest Neighbor
1 Nearest Neighbor
K Nearest Neighbor
An arbitrary instance is represented by (a1(x), a2(x), a3(x),.., an(x)) ai(x) denotes features
Euclidean distance between two instancesd(xi, xj)=sqrt (sum for r=1 to n (ar(xi) - ar(xj))2)
Find the k-nearest neighbors whose distance from your test cases falls within a threshold p.
If x of those k-nearest neighbors are in category ci, then assign the test case to ci, else it is unmatched.
Rainbow Algorithm
Construct a model of points in n-dimensional space for each category
Classify a document D based on the k nearest points
Probabilistic Indexing
Idea Quantitative model for automatic indexing based
on some statistical assumptions about word distribution.
2 Types of words: function words, specialty words Function words = words with no importance for
defining classes (the, it, etc.) Specialty words = words that are important in
defining classes (war, terrorist, etc.)
Probabilistic Indexing
Idea Function words follow a Poisson distribution over
the set of all documents Specialty words do not follow a Poisson
distribution over the set of all documents Specialty word distribution can be described by a
Poisson process within its class Specialty words distinguish more than one class
of documents
Rainbow Method
Goal is to estimate P(C|si, dm) Probability that assignment of term si to the
document dm is correct Once terms have been identified, assign
Form Of Occurrence (FOC) Certainty that term is correctly identified Significance of Term
Rainbow Method
If term t appears in document d and a term descriptor from t to s exists, s an indexing term, then generate a descriptor indictor
Set of generated term descriptors can be evaluated and a probability calculated that document d lies in class c
Rainbow Demonstration
20 newsgroups example References
http://www.stanford.edu/class/cs276a/handouts/lecture4.ppt http://www-2.cs.cmu.edu/~mccallum/bow/ http://webster.cs.uga.edu/~miller/SemWeb/Project/ApMlPresent.ppt http://citeseer.nj.nec.com/vanrijsbergen79information.html http://citeseer.nj.nec.com/54920.html Mitchell, Tom M. Machine Learning. 1997
http://www-2.cs.cmu.edu/~tom/book.html
Rainbow Commands Create a model for the classes:
rainbow -d ~/model --index training directory Classifying Documents:
Pick Method (naivebayes, knn, tfidf, prind ) rainbow -d ~/model --method=tfidf --test=1
Automatic Test: rainbow -d ~/model --test-set=0.4 --test=3
Test 1 at a time: rainbow -d ~/model –query test file
Rainbow Demonstration Can also run as a server:
rainbow -d ~/model --query-server=port Use telnet to classify new documents
Diagnostics: List the words with the highest mutual info:
rainbow -d ~/model -I 10 Perl script for printing stats:
rainbow -d ~/model --test-set=0.4 --test=2 | rainbow-stats.pl