Enhancement in Weighted PageRank Algorithm Using VOL

Transcription

1 IOSR Journal of Computer Engeerg (IOSR-JCE) e-issn: , p- ISSN: Volume 14, Issue 5 (Sep. - Oct. 2013), PP Enhancement Weighted PageRank Algorithm Usg VOL Sonal Tuteja 1 1 (Software Engeerg, Delhi Technological University,India) Abstract: There are billions of web pages available on the World Wide Web (WWW). So there are lots of search results correspondg to a user s query out of which only some are relevant. The relevancy of a web page is calculated by search enges usg page rankg algorithms. Most of the page rankg algorithm use web structure mg and web content mg to calculate the relevancy of a web page. In this paper, the standard Weighted PageRank algorithm is beg modified by corporatg Visits of Lks(VOL).The proposed method takes to account the importance of both the number of visits of lks and outlks of the pages and distributes rank scores based on the popularity of the pages. So, the resultant pages are displayed on the basis of user browsg behavior. Keywords: lks, outlks, search enge, web mg, World Wide Web (WWW). I. Introduction WWW has ample number of hyperlked documents and these documents conta heterogeneous formation cludg text, image, audio, video, and metadata. Sce WWW s evolution, it has expanded by 2000% and its size is doublg every six to ten months [1]. For a given query, there are lots of documents returned by a search enge out of which only few of them are relevant for a user. So the rankg algorithms are dispensable to sort the results so that more relevant documents are displayed at the top. Various rankg algorithms have been developed such as PageRank, Weighted PageRank, Page Content Rankg, and HITS etc. These algorithms are based on web structure mg or web content mg or combation of both. But web structure mg only considers lk structure of the web and web content mg is not able to cope up with multimedia such as images, mp3 and videos [2]. The proposed method corporates VOL with Weighed PageRank to calculate the value of page rank. In this way, the algorithm provides better results by mergg web usage mg with web structure mg. The organization of the paper is as follows: In section 2, a brief idea about research background has been given. In Section 3, the proposed work has been described with algorithm and example. Section 4 describes the advantages and disadvantages of proposed work. In section 5, the results of proposed method have been compared with Weighted PageRank and Weighed PageRank usg visits of lks. Conclusion and future work have been given section 6. II. Research Background Data mg can be defed as the process of extractg useful formation from large amount of data. The application of data mg techniques to extract relevant formation from the web is called as web mg [3] [4]. It plays a vital role web search enges for rankg of web pages and can be divided to three categories: web structure mg (WSM), web content mg (WCM) and web usage mg (WUM) [3]. WSM is used to extract formation from the structure of the web, WCM to me the content of web pages and WUM to extract formation from the server logs. Br and Page [5] came up with an idea at Stanford University to use lk structure of the web to calculate rank of web pages. PageRank algorithm is used by Google to prioritize the results produced by keyword based search. The algorithm works on the prciple that if a web page has important lks towards it then the lks of this page to other pages are also considered important. Thus it relies on the backlks to calculate the rank of web pages. The page rank is calculated by the formula given equation 1. PR u = c PR v N v (1) Where u represents a web page, PR u and PR v represents the page rank of web pages u and v respectively, B(u) is the set of web pages potg to u, N v represents the total numbers of outlks of web page v and c is a factor used for normalization. Origal PageRank algorithm was modified by takg to consideration that not all users follow direct lks on WWW. The modified formula for calculatg page rank is given equation Page

2 Enhancement Weighted PageRank Algorithm Usg VOL PR u = 1 d + d PR v N v (2) Where d is a dampeng factor which represent the probability of user usg direct lks and it can be set between 0 and 1. Wenpu Xg and Ali Ghorbani [6] proposed an algorithm called Weighted PageRank algorithm by extendg standard PageRank. It works on the prciple that if a page is important, more lkages from other web pages have to it or are lked to by it. Unlike standard PageRank, it does not evenly distribute the page rank of a page among its outgog lked pages. The page rank of a web page is divided among its outgog lked pages proportional to the importance or popularity (its number of lks and outlks). W (v, u), the popularity from the number of lks, is calculated based on the number of lks of page u and the number of lks of all reference pages of page v as given equation 3. W v, u = I u pɛr v I p (3) Where I u and I p are the number of lks of page u and p respectively. R(v) represents the set of web pages poted by v. W out (v, u), the popularity from the number of outlks, is calculated based on the number of outlks of page u and the number of outlks of all reference pages of page v as given equation. 4. W out v, u = O u O p pɛr v (4) Where O u and O p are the number of outlks of page u and p respectively and R(v) represents the set of web pages poted by v. The page rank usg Weighted PageRank algorithm is calculated by the formula as given equation 5. PR u = 1 d + d PR v W v, u W out v, u Gyanendra Kumar et. al. [7] came up with a new idea to corporate user s broswsg behavior calculatg page rank. Previous algorithms were either based on web structure mg or web content mg but none of them took web usage mg to consideration. A new page rankg algorithm called Page Rankg based on Visits of Lks (VOL) was proposed for search enges. It modifies the basic page rankg algorithm by takg to consideration the number of visits of bound lks of web pages. It helps to prioritize the web pages on the basis of user s browsg behavior. In the origal PageRank algorithm, the rank of a page p is evenly distributed among its outgog lks but this algorithm, rank values are assigned proportional to the number of visits of lks. The more rank value is assigned to the lk which is most visited by user. The Page Rankg based on Visits of Lks (VOL) can be calculated by the formula given equation 6. 5 PR u = 1 d + d L u PR(v) TL(v) (6) Where PR u and PR v represent page rank of web pages u and v respectively, d is dampeng factor, B(u) is the set of web pages potg to u, L u is number of visits of lks potg from v to u, TL(v) is the total number of visits of all lks from v. Neelam Tyagi and Simple Sharma [8] corporated user browsg behavior Weighted PageRank algorithm to develop a new algorithm called Weighted PageRank based on number of visits of lks (VOL). The algorithm assigns more rank to the outgog lks havg high VOL.It only considers the popularity from the number of lks and ignores the popularity from the number of outlks which was corporated Weighted PageRank algorithm. In the origal Weighted PageRank algorithm, the page rank of a web page is divided among its outgog lked pages proportional to the importance or popularity (its number of lks and outlks) but this algorithm, number of visits of bound lks of web pages are also taken to consideration. The rank of web page usg this algorithm can be calculated as given equation Page

3 Enhancement Weighted PageRank Algorithm Usg VOL VOL u = 1 d + d L u VOL (v)w v, u TL(v) (7) Where VOL u and VOL v represent page rank of web page u and v respectively, d is the dampeng factor, B(u) is the set of web pages potg to u, L u is number of visits of lks potg from v to u, TL(v) is the total number of visits of all lks from v, W v, u represents the popularity from the number of lks of u. Table gives a brief description of above algorithm usg some parameters from [9]. Table 1: Comparison of Rankg Algorithms Algorithm PageRank Weighted PageRank PageRank with VOL Web mg technique used Web structure mg Web structure mg Web structure mg, web usage mg Weighted PageRank with VOL Web structure mg, web usage mg Input Parameters Backlks Backlks, Forward lks Backlks and VOL Backlks and VOL Importance More More More More Relevancy Less Less More More III. Proposed work The origal Weighted PageRank algorithm distributes the rank of a web page among its outgog lked pages proportional to their importance or popularity. W (v, u), the popularity from the number of lks and W out (v, u), the popularity from the number of outlks does not clude usage trends. It does not give more popularity to the lks most visited by the users. The weighted PageRank usg VOL makes use of web structure mg and web usage mg but it neglects the popularity from the number of outlks i.e., W out (v, u). In proposed algorithm,w VOL (v, u), the popularity from the number of visits of lks and W out VOL (v, u), the popularity from the number of visits of outlks are used to calculate the value of page rank. W VOL (v, u) is the weight of lk(v, u) which is calculated based on the number of visits of lks of page u and the number of visits of lks of all reference pages of page v as given equation 8. W VOL v, u = I u VOL (8) pɛr v I p VOL Where I u(vol) and I p(vol ) represents the comg visits of lks of page u and p respectively and R(v) represents the set of reference pages of page v. W out VOL (v, u) is the weight of lk(v, u) which is calculated based on the number of visits of outlks of page u and the number of visits of outlks of all reference pages of page v as given equation 9. O out u VOL W VOL v, u = (9) pɛr v O p VOL Where O u (VOL) and O p(vol ) represents the outgog visits of lks of page u and respectively and R(v) represents the set of reference pages of page v. Now these values are used to calculate page rank usg equation 10. E VOL u = 1 d + d out VOL W VOL v, u W VOL v, u (10) Where d is a dampeng factor, B(u) is the set of pages that pot to u, VOL (u) and VOL (v) are the rank scores of page u and v respectively, W VOL (v, u) represents the popularity from the number of visits of lks and W out VOL (v, u) represents the popularity from the number of visits of outlks Algorithm to calculate E VOL 1. Fdg a website: The website with rich hyperlks is to be selected because the algorithm depends on the hyper structure of website. 2. Generatg a web graph: For selected website, web graph a generated which nodes represent web pages and edges represent hyperlks between web pages. 137 Page

4 Enhancement Weighted PageRank Algorithm Usg VOL 3. Calculatg number of visits of hyperlks: Client side script is used to monitor the hits of hyperlks and formation is sent to the web server and this formation is accessed by crawlers. 4. Calculate page rank of each web page: The values of W VOL (v, u), the popularity from the number of visits of lks and W out VOL (v, u), the popularity from the number of visits of outlks are calculated for each node usg formulae given equation 8 and 9 and these values are substituted equation 10 to calculate values of page rank. 5. Repetition of step 4: The step 4 is used recursively until a stable value of page rank is obtaed. The Fig. 1 shown below explas the steps required to calculate page rank usg proposed algorithm. Fdg a website Genaratg a web graph Calculatg number of visits of hyperlks calculalete page rank of each web page Repitition of previous step until stabilized Fig 1: Algorithm to calculate E VOL 3.2. Example to illustrate the workg of proposed algorithm The workg of proposed algorithm has been illustrated via takg a hypothetical web graph havg web pages A, B and C and lks representg hyperlks between pages marked with their number of visits shown Fig. 2. A B 2 C Fig. 2: A web graph The value of pagerank for web pages A, B and C are calculated usg equation 10 as: E VOL (A) = 1 d + d VOL C W VOL C, A W out VOL (C, A) E VOL B = 1 d + d VOL A W VOL A, B W out VOL (A, B) out E VOL C = 1 d + d( VOL A W VOL A, C W VOL A, C + VOL B W VOL B, C W out VOL (B, C) Each termediate values W VOL v, u and W out VOL (v, u) are calculated usg equation 8 and 9. W VOL C, A = I A(VOL) = 2 I A(VOL) 2 = 1 out W VOL C, A = O A(VOL) = 3 O A(VOL) 3 = 1 W VOL A, B = out W VOL A, B = W VOL A, C = out W VOL A, C = I B(VOL) = 1 I B(VOL) + I C(VOL) = 1 3 O B(VOL) = 2 O B(VOL) + O C(VOL) = 2 4 I C(VOL ) = 4 I C(VOL) + I B(VOL) = 4 5 O C(VOL) = 2 O C(VOL) + O B(VOL) = Page

5 Enhancement Weighted PageRank Algorithm Usg VOL W VOL B, C = I C(VOL) = 4 I C(VOL) 4 = 1 W VOL B, C = O C(VOL) = 2 O C(VOL) 2 = 1 The calculated values are put above equations to calculate the values of page ranks. For d = 0.35, page rank values for A, B and C can be calculated as: E VOL A = = 1 E VOL B = = E VOL C = = These values are calculated iteratively until the values get stabilized and the fal values of page ranks are: A= , B= and C= For d = 0.50, page rank values for A, B and C can be calculated as: E VOL A = = 1 E VOL B = = E VOL C = = These values are calculated iteratively until the values get stabilized and the fal values of page ranks are: A= , B= and C= For d = 0.85, page rank values for A, B and C can be calculated as: E VOL A = = 1 E VOL B = = E VOL C = = These values are calculated iteratively until the values get stabilized and the fal values of page ranks are: A= , B=0.24 and C= The value of page rank at various values of d has been given Table. Table 2: Value of page ranks at different d values d A B C IV. Advantages and Disadvantages The proposed method cludes web usage mg to calculate the page ranks of web pages and has followg advantages. The page rank usg origal remas unaffected whether the page has been accessed by the users or not. i.e.; the relevancy of a web page is ignored. But the page rank usg proposed method E VOL assigns high rank to web pages havg more visits of lks. The page rank usg origal depends only on the lk structure of the web and remas same whether the web page has been accessed by the user or not. Although the algorithm VOL makes use of web structure mg and web usage mg to calculate the value of page rank but it ignores the popularity from the number of outlks W out (v, u). On the other side, our proposed method E VOL makes use 139 Page

6 Enhancement Weighted PageRank Algorithm Usg VOL out of W VOL v, u, the popularity from the number of visits of lks and W VOL A, C, the popularity from the number of visits of outlks to calculate page rank. The proposed method uses number of visits of lks to calculate the rank of web pages. So the resultant pages are popular and more relevant to the users need. The proposed method cludes number of visits of lks of web pages to calculate page ranks. Suppose there is a junk page whose itial page rank is high then the users will access it and it will lead to crease VOL which will further improve page rank. So the pages which are actually relevant will have less page rank than junk pages. So some other usage behavior factors must be troduced addition to VOL. These factors are: Time spent on web page correspondg to a lk: The algorithm must assign more weight to the lk if more time is spent by the users on the web page correspondg to that lk. Most of the times, the time spent on the junk pages is very less as compared to relevant pages. So this factor will help lowerg the rank of junk pages. Most recent use of lk: The lk which is used most recently by users should have more priority than the lk which has been not used so far. So most recent use of lk can also be used to calculate the page rank. Information about the user: A web page is not equally relevant for all the users. Due to different requirements of different users, a web page may be more important for one but not for other. Some kd of users formation like age, gender, educational background can be used to categorize web pages accordg to different users need. V. Result Analysis This section compares the page rank of web pages usg standard Weighted PageRank (), Weighted PageRank usg VOL ( VOL ) and the proposed algorithm. We have calculated rank value of each page based on, VOL and proposed algorithm i.e. E VOL for a web graph shown Fig. 2. As the value of dampeng factor creases, the page rank decreases. The comparison of results is shown Table which shows the values of page rank usg, VOL and E VOL at different d values of 0.35, 0.50 and E Table 3: Comparison of page ranks usg different algorithms d A B C A B C A B C The values of page rank usg, VOL and E VOL have been compared usg a bar chart. The values retrieved by E VOL are better than origal and VOL. The uses only web structure mg to calculate the value of page rank, VOL uses both web structure mg and web usage mg to calculate value of page rank but it uses popularity only from the number of lks not from the number of outlks. The proposed algorithm E VOL method uses number of visits of lks and outlks to calculate values of page rank and gives more rank to important pages. Fig. 3 compares the page ranks of A, B and C usg, VOL and E VOL for d= A B C E Fig. 3: Comparison of page ranks at d= Page

7 Enhancement Weighted PageRank Algorithm Usg VOL Fig. 4 and Fig. 5 compares the page ranks of A, B and C usg, VOL and E VOL for d= A B C E Fig. 4: Comparison of page ranks at d= A B C E Fig. 5: Comparison of page ranks at d=0.85 VI. Conclusions and Future Work Due to enormous amount of formation present on the web, the users have to spend lot of time to get pages relevant to them. So the proposed algorithm E VOL makes use of number of visits of lks (VOL) to calculate the values of page rank so that more relevant results are retrieved first. In this way, it may help users to get the relevant formation quickly. Some of the future works for the proposed algorithm are: The values of page rank have been calculated on a small web graph only. A web graph with large number of websites and hyperlks should be used to check the accuracy and importance of method. We need some other measures like most recent use of lk, formation about the user and time spent on web page correspondg to a lk. So the future work cludes derivg a formula for page rank usg these parameters also. References [1] Sergey Br and Lawrence Page, The Anatomy of a Large-Scale Hypertextual Web Search Enge, Computer Science Department, Stanford University, Stanford, CA [2] Wenpu Xg and Ali Ghorbani, Weighted PageRank Algorithm, Faculty of Computer Science, University of New Brunswick,Fredericton, NB, E3B 5A3, Canada. [3] Gyanendra Kumar, Neelam Duhan, A. K. Sharma, Page Rankg Based on Number of Visits of Lks of Web Page, Department of Computer Engeerg, YMCA University of Science & Technology, Faridabad, India. [4] Naresh Barsagade, "Web Usage Mg And Pattern Discovery: A Survey Paper", CSE 8331, Dec.8, [5] Dell Zhang, Yisheng Dong, A novel Web usage mg approach for search enges, Computer Networks 39 (2002) [6] Neelam Duhan, A. K. Sharma, Komal Kumar Bhatia, Page Rankg Algorithms: A Survey Advance Computg Conference, IACC 2009 IEEE International. [7] R.Cooley, B.Mobasher and J.Srivastava, "Web Mg: Information and Pattern Discovery on the World Wide Web". In Proceedgs of the 9 th IEEE International Conference on Tools with Artificial Intelligence (ICTAI'97), [8] Companion slides for the text by Dr. M. H. Dunham, "Data Mg: Introductory and Advanced Topics", Prentice Hall, [9] Neelam tyagi, Simple Sharma, Weighted Page Rank Algorithm Based on Number of Visits of Lks of Web Page, International Journal of Soft Computg and Engeerg (IJSCE) ISSN: , Volume-2, Issue-3, July Page