Topic Continuity for Web Document Categorization and Ranking

Transcription

1 Topic Continity for Web ocment Categorization and Ranking B. L. Narayan, C. A. Mrthy and Sankar. Pal Machine Intelligence Unit, Indian Statistical Institte, 03, B. T. Road, olkata , India. bln r, mrthy, Abstract PageRank is primarily based on link strctre analysis. Recently, it has been shown that content information can be tilized to improve link analysis. We propose a novel algorithm that harnesses the information contained in the history of a srfer to determine his topic of interest when he is on a given page. As the history is navailable ntil qery time, we gess it probabilistically so that the operations can be performed offline. This leads to a better web page categorization and, thereby, to a better ranking of web pages.. Introdction Traditional information retrieval in docment analysis has largely focsed on looking at the content of a docment for drawing inferences regarding it. The categorization of the docment is performed on the basis of the terms (or words) present in the docment. The term freqency reflects the significance of the docment with respect to the term whereas the inverse docment freqency acconts for the relevance of a docment. The TFIF measre is a combination of the two and it provides the importance of a docment with respect to a set of terms or qeries. Unlike text docments, a hypertext docment is not selfcontained. There is a wealth of information abot the crrent docment hidden in its neighborhood which is determined throgh the link strctre of the available hypertext data. A hypertext docment has both in-neighbors and otneighbors, and the text associated with its neighbors proves to be sefl in inferring abot the content of the present docment. Chakrabarti, et al [] have performed experiments in this regard and have shown promising reslts. Link strctre, by itself, has been in se for identifying important docments across the web and ranking them. Search engines combine the ranks and the TFIF measres of web pages and present them, in order of their importance, to the ser in response to a given qery. In order to satisfy the ser, it is essential to obtain the best sch ordering. Recently, Richardson and omingos [8], have proposed a directed srfer model which enhances the PageRank by taking into consideration the link strctre as well as the content of the docments in the neighborhood. As the probability of following a link is assmed to be associated to the contents of the two pages that the link connects, it is necessary to have a proper text scoring fnction which shall be sed to jdge how relevant the page is to the given qery. In this article, we describe a methodology for compting the PageRank that combines the link strctre, and the contents of a page and its neighborhood. Thogh the directed srfer model comptes the probability of following a particlar link based on the contents of the crrent page, the history of the srfer is ignored. Since all the comptations are performed offline, the proposed algorithm gesses the history with the help of the contents on the backlinks of the given page. This leads to a better categorization of the web docments and improves their PageRank. The remaining part of this article is organized as follows. First, we shall discss the related work in Section. We describe or proposed methodology in Section 3. This is followed by the experimental reslts, in Section 4. Related work on page ranking and content analysis Simple citation ranking is sed in docment analysis where the nmber of citations of a docment is considered to be a measre of importance of that page. Brin and Page [] and leinberg [7] extended the idea to web page ranking where the nmber of inlinks of a page was taken to be a measre of its importance. We shall se the following notation in this article.,

2 = ] ] International Conference on Web Intelligence, pp October 003, Halifax, Canada and denote hypertext pages and and stand for topics. Let be the link matrix where N is the nmber of web pages, i.e., if and only if page has a link from page. If is a web page, "! $#&%'%&%(#*),+ -$+ is the set of pages points to, and. / "! $#&%'%&%(#*),+ -$+ is the set of pages that point to. ) 0 is the nmber of otlinks from. Let 3 denote the normalized link matrix obtained by dividing each colmn of by its total. leinberg proposed the Hypertext Indced Topic Selection (HITS) algorithm for ranking web pages where he introdced the notion of hbs and athorities. The hb vale of a page is defined to be the sm of the athority vales of the pages that it links to and the athority vale of a page is the sm of the hb vales of the pages that link to it. The hb and athority vales are compted for a sbgraph 4 that consists of only pages deemed relevant to the qery :$;6<>= 67 :$@<?# 5 A(% Rewriting in matrix form and combining the two steps, B C4EGFH C4IJ4 B # FH 4 B C4I4EGF% These steps are performed till convergence. The hb and athority comptations are performed afresh for each qery. This makes it comptationally costly. In the rest of this article, we do not consider HITS and other similar algorithms like PHITS [3]. The PageRank algorithm was introdced by Brin and Page [], and is employed by Google ( Every page is considered to distribte its rank eqally into its otlinks. The rank of a page is recrsively defined as the sm of the ranks conferred on it by its backlinks. Starting with an arbitrary vector, the PageRank vector is compted iteratively by mltiplying with the normalized link matrix 3. To avoid rank sinks and rank leaks, the transition matrix is modified as 3-LM N PO/QRST3VUWQTX ZY \[?. 3 L The PageRank vector trns ot to be the dominant eigenvector of 3^L. The PageRank vector is compted withot considering the content information and is independent of the qery. At qery time, only the relevance of the page to the qery is compted and the reslts are ordered taking both the relevance and the (nconditional) rank into consideration. The PageRank algorithm has another interpretation, known as the random srfer model. It is assmed that a srfer is browsing web pages by clicking on the links at random, never clicking the back btton. The state of the stochastic process is the web page that the srfer is on and the click corresponds to a transition. The matrix 3NL corresponds to the stochastic matrix for the process. Q is the probability that the srfer decides not to follow a link and moves to a new page by typing its URL. Under this model, the PageRank trns ot to be the stationary probability of the process. It can also be interpreted as the nconditional probability of the srfer being on a page. The relevance of a page to a given qery is compted by calclating the TFIF measre of the page for each term in the qery. A page is considered to be significant for a term if the term freqency (TF) is high. If a term appears in almost all the docments, it might not be relevant. So, the term freqency is weighted by the inverse of the docments freqency in which it appears. This provides the TFIF measre for each term. The TFIF measres for each term in the qery are added to provide the TFIF vale of the page for a given qery. When dealing with hypertext data, the TFIF measre often fails to identify some relevant web pages. A celebrated example of sch a sitation is for the qery search engine. Home pages of most search engines do not contain the phrase search engine and, as a reslt, get a low TFIF vale. So, even thogh they have a hge nmber of inlinks, and hence a high PageRank, they do not featre at the top of the reslts. This sort of a problem was overcome by considering text from the neighborhood of a given web page as its own. Chakrabarti, et al [] have stdied varios ways of assigning text to a docment from its neighbors. Richardson and omingos [8] have attempted to rectify the above mentioned problem by combining the content information into the page ranking algorithm itself. The probability of following a link on a page containing the qery is weighted according to the presence or absence of the qery in the page that the link leads to. This is called the directed srfer model which caters to the intition that a srfer wold more likely follow a link to a page that contains the qery rather than to a page that does not. Recently, Haveliwala [5] has proposed to compte a PageRank vector for each distinct topic. As the comptation of PageRank is time consming, it is sggested that the nmber of topics be kept small. For each topic, a different bias vector is sed dring the comptation of PageRank. The topic is decided on the basis of the context of the qery. In each of the mentioned cases, the original assmption of the random srfer model, that each of the links on a page is eqally likely to be followed, has been relaxed. The probability of following a link has been modified or biased in certain ways. There have been other modifications that took

3 International Conference on Web Intelligence, pp October 003, Halifax, Canada into accont the location or the visal characteristics of the content and links on the page. These too can be taken into accont while compting the transition probabilities. The directed srfer model assmes an accrate classification of any given web page into the topics that are contained in it. Simple text based classification does not perform well de to the very natre of a langage where the same words may appear in different topics. The need for context sensitive page categorization, therefore, arises for this reason. In the following section, we describe the problem that we consider here and provide a soltion to it. We also discss how it differs from other related approaches. 3. Methodology for incorporating history into content analysis v w w 3.. Assmptions We assme that every page consists of content on one or more of a set of predefined topics and that pages on similar or same topics are more likely to be linked to each other than pages on totally nrelated topics. We also assme that a srfer wold browse pages not jst randomly, bt with some objective in mind. There is a topic of interest (ToI) for the srfer at any time and he is more likely to be interested in the same topic at time U. With a small probability, he does change his topic of interest, possibly, ot of criosity. Another related assmption is that, if a srfer is on a particlar page, his topic of interest is one of the set of topics available on the page. For the time being, we consider the case where the srfer always follows a link on the crrent page. 3.. Problem nder consideration With the above assmptions in mind, we consider the following example. A page leads to two pages and (see Fig. ). If a srfer is on page at time, what is the probability that he is on page at time7u-? The random srfer model had assigned a probability of % to that (assming the srfer follows one of the links available on page ). If, after analyzing the textal content, it is fond that belongs eqally to topics and, belongs to and belongs to, then what is the above probability? The directed srfer model prescribes a vale of %. However, had it been known that the srfer had followed the link from, wold it still be as likely for the srfer to reach? In sch a sitation, it seems to be more likely that the srfer is interested in and, hence, qite probably, wold visit rather than. From this example, it is evident that both the transition probabilities and the topic categorization depend not jst on the contents of the crrent page bt on the PageRank t - t t + Figre. Given that the srfer is on page at time what is the probability of him being on page at time U? What if it is known that the srfer had followed the link shown by the dotted line? and the contents of the backlinks too. We make se of the information hidden in the srfer s history to compte both the above qantities simltaneosly. Thogh it is evident that the history of the srfer plays an important role in determining the transition probabilities, it is not likely to be obtained before qery time. Or intention being a qick response at qery time, the comptations are reqired to be performed offline. To this end, we probabilistically gess the history of a srfer on a given page. As we consider only the case where the srfer follows a link to reach the crrent page, we apply Bayes Theorem to find the probability of the srfer having reached here from a particlar backlink. The ToI too is determined by a similar approach. It may be noted here that thogh Chakrabarti, et al [] had considered text from neighboring pages, they had not taken into consideration the rank of the pages that lead to the crrent page. A backlink with a low PageRank, althogh with the same content as the crrent page, is not as likely to have been visited as compared to a backlink with a high PageRank Methodology Based on the aforesaid concept we provide here an algorithm to compte the transition probabilities in terms of the ToI. As these two qantities depend on each other, we com- 3

4 < < < International Conference on Web Intelligence, pp October 003, Halifax, Canada pte both the ToI and the transition probabilities recrsively. Once the transition matrix is available, the PageRank vector is obtained in the sal manner as the dominant eigenvector of the transition matrix. We assme that the srfer strays from his crrent ToI with a small probability of. The transition probabilities are compted as follows.? P G # U 8 U 8 X GP # PO ) > # G O A > R? R? Y A R A*# # G A #? )Z > where R R A is taken to be 0 if!6. In this manner, the transition probabilities can be calclated once the qantities T T A are known. They are normalized each time so that 8 R R? ^ The topic of interest of the srfer given that the srfer is on page is calclated as: :$;! R > A R? # A # #"6 G#? >? The denominator can be ignored as it will disappear dring normalization. Now, $ : $ : > # #"6P # R? R #" P C # #"6 # # #"6 # #" 6 # R "% #" P # #"6P 6 Extract Link Strctre Compte Transition Probabilities Raw HTML Extract Text Recategorize pages Calclate PageRank OP ata Extract Text Train Categorize pages Figre. Flowchart of the proposed algorithm $ : # "% #" C # #"6 #"6P R& #" P 6 #"6P The initial vales of? can be estimated by text based scoring. Once the ToI has been calclated accrately, the directed srfer model can be employed to enhance the PageRank. A flowchart of the proposed algorithm is provided in Fig.. It has been shown that the directed srfer model is scalable. The above comptations too, are scalable. The operations are performed in exactly the same manner as for efficiently compting the PageRank [4]. 4. Experimental Reslts To deonstrate the effectiveness of or method, one million pages have been obtained from Stanford s WebBase [6] available online at www-diglib.stanford.ed/' testbed/doc/webbase/. Since most of these pages belong to sites related to Stanford University, we added Stanford to the list of stopwords. The training data for the analysis of the textal content of all these pages has been taken from 4

5 International Conference on Web Intelligence, pp October 003, Halifax, Canada the Open irectory Project (OP) available online at Abot 3.6 million web pages are available nder the seventeen categories in the OP data. We have, however, ignored the categories regional and world de to the high nmber of non-english words that they generate. The classification is performed by manal volnteers and is considered to be of high qality. e to lack of time for training, only the description of each page (and not the content) has been considered. Each word is stemmed with Porter s Stemming Algorithm prior to its se in the analysis. The freqency of a stem for each topic is compted by conting the nmber of times the stem appears nder that particlar topic. Stopwords are ignored at the otset itself. Rare stems, i.e., those appearing fifteen times or less, are treated as spelling mistakes and are ignored. For each page and topic, we compte 5 A. After normalizing, if any of these probabilities is fond to be less than 0., we consider it to be noise and forcibly pt it to zero. If a page does not appear to be significantly related to any of the fifteen topics, we replace the ToI vector by a prior vector which is jst the nconditional probability of a page being on a particlar topic. This vector is estimated from the OP data as the proportion of topics nder each category. The scores are normalized once more. The initial estimates are based on a simple text scoring fnction which ses the freqencies of the stems in each of the fifteen topics to decide the set of topics that are available on the crrent page. Refinements are then made on the basis of the link strctre and an initial estimate of PageRank (the one compted assming eqal probabilities for all otlinks). Once the categorization is performed accrately, the desired transition probability matrix is obtained. The dominant eigenvector of this matrix is taken to be the final PageRank vector. A grop of three volnteers were reqested to stdy the categorizations obtained before and after or algorithm was applied. The distances between the two categorization vectors was compted. Fifteen sch pages were obtained for which the distance trned ot to be larger than 0.7 (Table. These were made available to the volnteers and they were asked to rate the extent of their agreement with each categorization. The ratings (Table ) were analysed and the improvement has been fond to be significant by a t-test (with 4 degrees of freedom) (see Table 3). The nll hypothesis that the proposed method does not provide an improvement in topic categorization was rejected at a confidence level of 97.5%. Table. URLs whose categorization vectors were at a distance greater than 0.7 No. URL. tor.stanford.ed/cgi/search.prl/d/. pangea.stanford.ed/stdents/jobfair.html 3. labrea.stanford.ed/gn/cvs/ 4. cis.stanford.ed/programs/talks/cath/abstract.html 5. w6yx.stanford.ed/ palf/ 6. kzs.stanford.ed/pgide/996spring/page05.html 7. cellwall.stanford.ed/cellwall/species/ arabidopsis atcsla/graphics.shtml 8. cellwall.stanford.ed/cellwall/species/ arabidopsis atcsle/graphics.shtml 9. kzs.stanford.ed/pgide/996winter/page9.html 0. tehran.stanford.ed/literatre/poetry/classic/ hafez.0.html. kzs.stanford.ed/pgide/996winter/page4.html. sloan.stanford.ed/evonline/profiles.htm 3. labrea.stanford.ed/gn/gnrobots/ 4. labrea.stanford.ed/gn/goose/ 5. ass.stanford.ed/speakers/bios/clark.html Table. Ratings of categorizations averaged over all sers Rating URL No. Text Link based based

6 International Conference on Web Intelligence, pp October 003, Halifax, Canada Table 3. Smmary of reslts Mean (s.d.) Mean (s.d.) 5 O 5 Average rating (0.897) (0.64) by each ser (0.446) (0.366) (0.569) (0.334) Overall average 0.37 (0.97) (0.45) (0.3905) t-statistic.56 * & '.4 [4] T. H. Haveliwala. Efficient comptation of pagerank. Technical report, Stanford University, 999. [5] T. H. Haveliwala. Topic-sensitive pagerank. In Proceedings of the Eleventh International World Wide Web Conference, 00. [6] J. Hirai, S. Raghavan, H. Garcia-Molina, and A. Paepcke. Webbase: A repository of web pages. In Proceedings of Ninth International World Wide Web Conference, 000. [7] J. leinberg. Athoritative sorces in a hyperlinked environment. Jornal of the ACM, 46(5):604 63, 999. [8] M. Richardson and P. omingos. The intelligent srfer: Probabilistic combination of link and content information in pagerank,. In Advances in Neral Information Processing Systems, volme 4. MIT Press, Conclsions Page ranking is greatly enhanced by considering the textal content of web pages along with the link strctre. Proper categorization of web pages is reqired to obtain a correct ranking techniqe. However, by its very natre, a langage consists of words that appear in mltiple categories. The confsion that sch words add to categorization of web pages can be redced by considering the context of the web page. We have sggested one sch approach where the context is atomatically obtained from the backlinks of a page. We have also shown how the categorization can be refined starting with an initial classification. The present investigation shows the improvement of categorization of web docments becase of the incorporation of history. this can be sbseqently sed to enhance the page rank sing the algorithm of Richardson and omingos [8]. 6. Acknowledgements We wold like to thank Wang Lam for helping s with retrieving docments from the Stanford Webbase. We are also gratefl to the volnteers for sparing their valable time. The first athor s research is fnded by INSEA, Fontaineblea, France. References [] S. Brin and L. Page. The anatomy of a large-scale hypertextal search engine. Technical report, Stanford University, 998. [] S. Chakrabarti, B. om, and P. Indyk. Enhanced hypertext categorization sing hyperlinks. In Proceedings of SIGMO- 98, ACM International Conference on Management of ata, 998. [3]. Cohn and H. Chang. Learning to probabilistically identify athoritative docments. In Proceedings of the 7th International Conference on Machine Learning,