1 Text categorization Feature selection: chi square test.
26
1 Text categorization Feature selection: chi square test
-
Upload
alaina-dickerson -
Category
Documents
-
view
227 -
download
0
Transcript of 1 Text categorization Feature selection: chi square test.
1
Text categorization
Feature selection: chi square test
2Slides adapted from Mary Ellen Califf
Joint Probability Distribution
The joint probability distribution for a set of random variables X1…Xn gives the probability of every combination of values
P(X1,...,Xn)
Sneeze ¬Sneeze Cold 0.08 0.01 ¬Cold 0.01 0.9
The probability of all possible cases can be calculated by summing the appropriate subset of values from the joint distribution. All conditional probabilities can therefore also be calculated
P(Cold | ¬Sneeze)
BUT it’s often very hard to obtain all the probabilities for a joint distribution
3Slides adapted from Mary Ellen Califf
Bayes Independence Example
Imagine there are diagnoses ALLERGY, COLD, and WELL and symptoms SNEEZE, COUGH, and FEVER Can these be correct numbers?
Prob Well Cold Allergy P(d) 0.9 0.05 0.05 P(sneeze|d) 0.1 0.9 0.9 P(cough | d) 0.1 0.8 0.7
P(fever | d) 0.01 0.7 0.4
4
KL divergence (relative entropy)
x xQ
xPxPQPD
)(
)(log)()||(
Basis of comparing two probability distributions
5Slide adapted from Paul Bennet
Text Categorization Applications
Web pages organized into category hierarchiesJournal articles indexed by subject categories (e.g., the Library of Congress, MEDLINE, etc.)Responses to Census Bureau occupationsPatents archived using International Patent ClassificationPatient records coded using international insurance categoriesE-mail message filteringNews events tracked and filtered by topicsSpam
6
Yahoo News Categories
7
Text Topic categorization
Topic categorization: classify the document into semantics topics
The U.S. swept into the Davis Cup final on Saturday when twins Bob and Mike Bryan defeated Belarus's Max Mirnyi and Vladimir Voltchkov to give the Americans an unsurmountable 3-0 lead in the best-of-five semi-final tie.
One of the strangest, most relentless hurricane seasons on record reached new bizarre heights yesterday as the plodding approach of Hurricane Jeanne prompted evacuation orders for hundreds of thousands of Floridians and high wind warnings that stretched 350 miles from the swamp towns south of Miami to the historic city of St. Augustine.
8
The Reuters collection
A gold standardCollection of (21,578) newswire documents. For research purposes: a standard text collection to compare systems and algorithms135 valid topics categories
9
Reuters
Top topics in Reuters
10
Reuters Document Example<REUTERS TOPICS="YES" LEWISSPLIT="TRAIN" CGISPLIT="TRAINING-SET" OLDID="12981" NEWID="798">
<DATE> 2-MAR-1987 16:51:43.42</DATE>
<TOPICS><D>livestock</D><D>hog</D></TOPICS>
<TITLE>AMERICAN PORK CONGRESS KICKS OFF TOMORROW</TITLE>
<DATELINE> CHICAGO, March 2 - </DATELINE><BODY>The American Pork Congress kicks off
tomorrow, March 3, in Indianapolis with 160 of the nations pork producers from 44 member states determining industry positions on a number of issues, according to the National Pork Producers Council, NPPC.
Delegates to the three day Congress will be considering 26 resolutions concerning various issues, including the future direction of farm policy and the tax law as it applies to the agriculture sector. The delegates will also debate whether to endorse concepts of a national PRV (pseudorabies virus) control and eradication program, the NPPC said.
A large trade show, in conjunction with the congress, will feature the latest in technology in all areas of the industry, the NPPC added. Reuter
</BODY></TEXT></REUTERS>
11
Classification vs. Clustering
Classification assumes labeled data: we know how many classes there are and we have examples for each class (labeled data). Classification is supervisedIn Clustering we don’t have labeled data; we just assume that there is a natural division in the data and we may not know how many divisions (clusters) there areClustering is unsupervised
12
Categories (Labels, Classes)
Labeling data2 problems: Decide the possible classes (which ones, how many)
Domain and application dependent
Label textDifficult, time consuming, inconsistency between annotators
13
Reuters Example, revisited
<REUTERS TOPICS="YES" LEWISSPLIT="TRAIN" CGISPLIT="TRAINING-SET" OLDID="12981" NEWID="798">
<DATE> 2-MAR-1987 16:51:43.42</DATE>
<TOPICS><D>livestock</D><D>hog</D></TOPICS>
<TITLE>AMERICAN PORK CONGRESS KICKS OFF TOMORROW</TITLE>
<DATELINE> CHICAGO, March 2 - </DATELINE><BODY>The American Pork Congress kicks off
tomorrow, March 3, in Indianapolis with 160 of the nations pork producers from 44 member states determining industry positions on a number of issues, according to the National Pork Producers Council, NPPC.
Delegates to the three day Congress will be considering 26 resolutions concerning various issues, including the future direction of farm policy and the tax law as it applies to the agriculture sector. The delegates will also debate whether to endorse concepts of a national PRV (pseudorabies virus) control and eradication program, the NPPC said.
A large trade show, in conjunction with the congress, will feature the latest in technology in all areas of the industry, the NPPC added. Reuter
</BODY></TEXT></REUTERS>
Why not topic = policy ?
14
Binary vs. multi-way classification
Binary classification: two classes
Multi-way classification: more than two classes
Sometime it can be convenient to treat a multi-way problem like a binary one: one class versus all the others, for all classes
15
Features
>>> text = "Seven-time Formula One champion Michael Schumacher took on the Shanghai circuit Saturday in qualifying for the first Chinese Grand Prix."
>>> label = “sport”
>>> labeled_text = LabeledText(text, label)
Here the classification takes as input the whole stringWhat’s the problem with that?What are the features that could be useful for this example?
16
Feature terminology
Feature: An aspect of the text that is relevant to the task Some typical features
Words present in text Frequency of words CapitalizationAre there NE?WordNet Others?
17
Feature terminology
Feature: An aspect of the text that is relevant to the task
Feature value: the realization of the feature in the text
Words present in text Frequency of wordAre there dates? Yes/noAre there PERSONS? Yes/noAre there ORGANIZATIONS? Yes/noWordNet: Holonyms (China is part of Asia), Synonyms(China, People's Republic of China, mainland China)
18
Feature Types
Boolean (or Binary) FeaturesFeatures that generate boolean (binary) values. Boolean features are the simplest and the most common type of feature.
f1(text) = 1 if text contain “elections”
0 otherwise
f2(text) = 1 if text contain PERSON
0 otherwise
19
Feature Types
Integer FeaturesFeatures that generate integer values. Integer features can be used to give classifiers access to more precise information about the text.
f1(text) = Number of times “elections” occurs
f2(text) = Number of times PERSON occurs
20
2 statistic (pronounced “kai square”) A commonly used method of comparing proportions. Measures the lack of independence between a term and
a category
2 statistic (CHI)
21
Is “jaguar” a good predictor for the “auto” class?
We want to compare: the observed distribution above; and null hypothesis: that jaguar and auto are independent
2 statistic (CHI)
Term = jaguar Term jaguar
Class = auto 2 500
Class auto 3 9500
22
Under the null hypothesis: (jaguar and auto independent): How many co-occurrences of jaguar and auto do we expect?
If independent: Pr(j,a) = Pr(j) Pr(a)
So, there would be N Pr(j,a), i.e. N Pr(j) Pr(a) occurances of “jaguar”
Pr(j) = (2+3)/N;
Pr(a) = (2+500)/N;
N=2+3+500+9500
N(5/N)(502/N)=2510/N=2510/10005 0.25
2 statistic (CHI)
Term = jaguar Term jaguar
Class = auto 2 500
Class auto 3 9500
23
Under the null hypothesis: (jaguar and auto independent): How many co-occurrences of jaguar and auto do we expect?
2 statistic (CHI)
Term = jaguar Term jaguar
Class = auto 2 (0.25) 500
Class auto 3 9500
expected: fe
observed: fo
24
Under the null hypothesis: (jaguar and auto – independent): How many co-occurrences of jaguar and auto do we expect?
2 statistic (CHI)
Term = jaguar Term jaguar
Class = auto 2 (0.25) 500 (502)
Class auto 3 (4.75) 9500 (9498)
expected: fe
observed: fo
25
2 is interested in (fo – fe)2/fe summed over all table entries:
The null hypothesis is rejected with confidence .999, since 12.9 > 10.83 (the value for .999 confidence).
2 statistic (CHI)
)001.(9.129498/)94989500(502/)502500(
75.4/)75.43(25./)25.2(/)(),(22
2222
p
EEOaj
Term = jaguar Term jaguar
Class = auto 2 (0.25) 500 (502)
Class auto 3 (4.75) 9500 (9498)
expected: fe
observed: fo
26
There is a simpler formula for 2:
2 statistic (CHI)
N = A + B + C + D
A = #(t,c) C = #(¬t,c)
B = #(t,¬c) D = #(¬t, ¬c)
