Data Mining in Bioinformatics Day 4: Text Mining

Transcription

1 Data Mining in Bioinformatics Day 4: Text Mining Karsten Borgwardt February 25 to March 10 Bioinformatics Group MPIs Tübingen Karsten Borgwardt: Data Mining in Bioinformatics, Page 1

2 What is text mining? Definition Text mining is the use of automated methods for exploiting the enormous amount of knowledge available in the (biomedical) literature. Motivation Most knowledge is stored in terms of texts, both in industry and in academia This alone makes text mining an integral part of knowledge discovery! Furthermore, to make text machine-readable, one has to solve several recognition (mining) tasks on text Karsten Borgwardt: Data Mining in Bioinformatics, Page 2

3 What is text mining? Common tasks Information retrieval: Find documents that are relevant to a user, or to a query in a collection of documents Document ranking: rank all documents in the collection Document selection: classify documents into relevant and irrelevant Information filtering: Search newly created documents for information that is relevant to a user Document classification: Assign a document to a category that describes its content Keyword co-occurrence: Find groups of keywords that co-occur in many documents Karsten Borgwardt: Data Mining in Bioinformatics, Page 3

4 Evaluating text mining Precision and Recall Let the set of documents that are relevant to a query be denoted as {Relevant} and the set of retrieved documents as {Retrieved}. The precision is the percentage of retrieved documents that are relevant to the query precision = {Relevant} {Retrieved} {Retrieved} The recall is the percentage of relevant documents that were retrieved by the query: recall = {Relevant} {Retrieved} {Relevant} (1) (2) Karsten Borgwardt: Data Mining in Bioinformatics, Page 4

5 Text representation Tokenization Process of identifying keywords in a document Not all words in a text are relevant Text mining ignores stop words Stop words form the stop list Stop lists are context-dependent Karsten Borgwardt: Data Mining in Bioinformatics, Page 5

6 Text representation Vector space model Given #d documents and #t terms Model each document as a vector v in a t-dimensional space Weighted Term-frequency matrix Matrix T F of size #d #t Entries measure association of term and document If a term t does not occur in a document d, then T F (d, t) = 0 If a term t does occur in a document d, then T F (d, t) > 0. Karsten Borgwardt: Data Mining in Bioinformatics, Page 6

7 Text representation If term t occurs in document d, then T F (d, t) = 1 T F (d, t) = frequency of t in d (freq(d, t)) freq(d,t) T F (d, t) = t T freq(d,t ) T F (d, t) = 1 + log(1 + log(freq(d, t))) Karsten Borgwardt: Data Mining in Bioinformatics, Page 7

8 Text representation Inverse document frequency represents the scaling factor, or importance, of a term A term that appears in many document is scaled down IDF (t) = log 1 + d d t where d is the number of all documents, and d t is the number of documents containing term t TF-IDF measure Product of term frequency and inverse document frequency: (3) T F -IDF (d, t) = T F (d, t)idf (t); (4) Karsten Borgwardt: Data Mining in Bioinformatics, Page 8

9 Measuring similarity Cosine measure Kernels Let v 1 and v 2 be two document vectors. The cosine similarity is defined as sim(v 1, v 2 ) = v 1 v 2 v 1 v 2 depending on how we represent a document, there are many kernels available for measuring similarity of these representations vectorial representation: vector kernels like linear, polynomial, Gaussian RBF kernel one long string: string kernels that count common k- mers in two strings (more on that later in the course) (5) Karsten Borgwardt: Data Mining in Bioinformatics, Page 9

10 Keyword co-occurrence Problem Find sets of keyword that often co-occur Common problem in biomedical literature: find associations between genes, proteins or other entities using co-occurrence search Keyword co-occurrence search is an instance of a more general problem in data mining, called association rule mining. Karsten Borgwardt: Data Mining in Bioinformatics, Page 10

11 Association rules Definitions Let I = {I 1, I 2,..., I m } be a set of items (keywords) Let D be the database of transactions T (collection of documents) A transaction T D is a set of items: T I (a document is a set of keywords) Let A be a set of items: A T. An association rule is an implication of the form where A, B I and A B = A T B T, (6) Karsten Borgwardt: Data Mining in Bioinformatics, Page 11

12 Association rules Support and Confidence The rule A B holds in the transaction set D with support s, where s is the percentage of transactions in D that contain A B: {T D A T B T } support(a B) = (7) {T D} The rule A B has confidence c in the transaction set D, where c is the percentage of transactions in D containing A that also contain B: confidence(a B) = {T D A T B T } {T D A T } (8) Karsten Borgwardt: Data Mining in Bioinformatics, Page 12

13 Association rules Strong rules Rules that satisfy both a minimum support threshold (minsup) and a minimum confidence threshold (minconf) are called strong association rules and these are the ones we are after! Finding strong rules 1. Search for all frequent itemsets (set of items that occur in at least minsup % of all transactions) 2. Generate strong association rules from the frequent itemsets Karsten Borgwardt: Data Mining in Bioinformatics, Page 13

14 Association rules Apriori algorithm Steps Makes use of the Apriori property: If an itemset A is frequent, then any subset B of A (B A) is frequent as well. If B is infrequent, then any superset A of B (A B) is infrequent as well. 1. Determine frequent items = k-itemsets with k = 1 2. Join all pairs of frequent k-itemsets that differ in at most 1 item = candidates C k+1 for being frequent k+1 itemsets 3. Check the frequency of these candidates C k+1 : the frequent ones form the frequent k + 1-itemsets (trick: discard any candidate immediately that contains an infrequent k-itemset) 4. Repeat from Step 2 until no more candidate is frequent Karsten Borgwardt: Data Mining in Bioinformatics, Page 14

15 Transduction Known test set Classification on text databases often means that we know all the data we will work with before training Hence the test set is known apriori This setting is called transductive Can we define classifiers that exploit the known test set? Yes! Transductive SVM (Joachims, ICML 1999) Trains SVM on both training and test set Uses test data to maximise margin Karsten Borgwardt: Data Mining in Bioinformatics, Page 15

16 Inductive vs. transductive Classification Task: predict label y from features x Classic inductive setting Strategy: Learn classifier on (labelled) training data Goal: Classifier shall generalise to unseen data from same distribution Transductive setting Strategy: Learn classifier on (labelled) training data AND a given (unlabelled) test dataset Goal: Predict class labels for this particular dataset Karsten Borgwardt: Data Mining in Bioinformatics, Page 16

17 Why transduction? Really necessary? Classic approach works: train on training dataset, test on test dataset That is what we usually do in practice, for instance, in cross-validation. We usually ignore or neglect that the fact that settings are transductive. The benefits of transductive classification Inductive setting: infinitely many potential classifiers Transductive setting: finite number of equivalence classes of classifiers f and f in same equivalence class f and f classify points from training and test dataset identically Karsten Borgwardt: Data Mining in Bioinformatics, Page 17

18 Why transduction? Idea of Transductive SVMs Risk on Test data Risk on Training data + confidence interval (depends on number of equivalence classes) Theorem by Vapnik(1998): The larger the margin, the lower the number of equivalence classes that contain a classifier with this margin Find hyperplane that separates classes in training data AND in test data with maximum margin. Karsten Borgwardt: Data Mining in Bioinformatics, Page 18

19 Why transduction? Karsten Borgwardt: Data Mining in Bioinformatics, Page 19

20 Transduction on text Karsten Borgwardt: Data Mining in Bioinformatics, Page 20

21 Transductive SVM Linearly separable case 1 min w,b,y 2 w 2 s.t. n i=1 y i [w x i + b] 1 k j=1 y j [w x j + b] 1 Karsten Borgwardt: Data Mining in Bioinformatics, Page 21

22 Transductive SVM Non-linearly separable case 1 min w,b,y,ξ,ξ 2 w 2 + C n ξ i + C i=0 k j=0 ξ j s.t. n i=1 y i [w x i + b] 1 ξ i k j=1 y j [w x j + b] 1 ξ j n i=1 ξ i 0 k j=1 ξ j 0 Karsten Borgwardt: Data Mining in Bioinformatics, Page 22

23 Transductive SVM Optimisation How to solve this OP? Not so nice: combination of integer and convex OP Joachims approach: find approximate solution by iterative application of inductive SVM train inductive SVM on training data, predict on test data, assign labels to test data retrain on all data, with special slack weights for test data (C, C + ) Outer loop: repeat and slowly increase (C, C + ) Inner loop: within each repetition switch pairs of misclassified data points repeatedly Local search with approximate solution to OP Karsten Borgwardt: Data Mining in Bioinformatics, Page 23

24 Inductive SVM for TSVM Variant of inductive SVM 1 min w,b,y,ξ,ξ 2 w 2 + C n k ξ i + C ξj + C+ j:yj = 1 i=0 k j:y j =1 ξ j s.t. n i=1 y i [w x i + b] 1 ξ i k j=1 yj [w x j + b] 1 ξj Three different penalty costs C for points from training dataset C for points from in test dataset currently in class 1 for points from in test dataset currently in class +1 C + Karsten Borgwardt: Data Mining in Bioinformatics, Page 24

25 Experiments Average P/R-breakeven point on the Reuters dataset for different training set sizes and a test size of 3,299 Karsten Borgwardt: Data Mining in Bioinformatics, Page 25

26 Experiments Average P/R-breakeven point on the Reuters dataset for 17 training documents and varying test set size for the TSVM Karsten Borgwardt: Data Mining in Bioinformatics, Page 26

27 Experiments Average P/R-breakeven point on the WebKB category course for different training set sizes Karsten Borgwardt: Data Mining in Bioinformatics, Page 27

28 Experiments Average P/R-breakeven point on the WebKB category project for different training set sizes Karsten Borgwardt: Data Mining in Bioinformatics, Page 28

29 Summary Results Transductive version of SVM Maximizes margin on training and test data Implementation uses variant of classic inductive SVM Solution is approximate and fast Works well on text, in particular on small training samples and large test sets Karsten Borgwardt: Data Mining in Bioinformatics, Page 29

30 References and further reading References [1] T.-Joachims. Transductive Inference for Text Classification using Support Vector Machines ICML, 1999: [2] J. Han and M. Kamber. Data Mining: Concepts and Techniques. Elsevier, Morgan-Kaufmann Publishers, Karsten Borgwardt: Data Mining in Bioinformatics, Page 30

31 The end See you tomorrow! Next topic: Graph Mining Karsten Borgwardt: Data Mining in Bioinformatics, Page 31