# A STUDY REGARDING INTER DOMAIN LINKED DOCUMENTS SIMILARITY AND THEIR CONSEQUENT BOUNCE RATE

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4 86 DIANA HALIŢĂ AND DARIUS BUFNEA matrix and precision-recall matrix [7]. That was a key challenge for search engine industry, so spamdexing was cast into a machine learning problem of classification on directed graphs [9]. 4. Predicting bounce rate using external linked documents similarity 4.1. Ideal similarity. Based on the above observations, that high content related web pages are less susceptible for generating a high bounce rate and poor content related pages can lead to a higher percent of visitors that bounce, we intend in this section to study the possible correlation between bounce rate and several similarities functions. In the case of an ideal similarity function, depicted in figure 1, the bounce rate will follow a linear regression path. By using a properly chosen similarity function, one could estimate the bounce rate of a third party external link based only on content of linked documents similarity (currently, bounce rate may only be obtain by a site s owner using web analytics tools such a Google Analytics). Such a method could be used by a third party (for e.g. the search engine) to identify improper placed and abusive links such as ads or spam links. Consequently, a web site that relies on a large number of links that fall in the above categories could be fined by a search engine. Figure 1. Ideal similarity

5 INTER DOMAIN LINKED DOCUMENTS: SIMILARITY AND BOUNCERATE 87 The perfect correlation between bounce rate and similarity of inter domain linked documents, shown in an ideal case [fig:1], is not always found, especially considering usual mathematical similarity functions. We choose to take into consideration more similarity functions in order to determine which one fits better our goal. Intuitively, we say that a similarity function is better than other if the pairs (similarity, bounce rate) obtained from each link between two inter domain linked pages are closer to the diagonal (as we can see in the an ideal case [fig:1]). In our case, similarity represents the horizontal coordinate (abscissa) of the point in a two-dimensional rectangular Cartesian coordinate system and bounce rate represents the vertical coordinate (ordinate) of the above considered system. Taking into consideration the line which is parallel with the secondary bisector of the Cartesian coordinate system and passes through the points (100, 0) and (0, 100), a similarity function is the best if the sum of all distances, from the graphical representation points, represented by the above named pairs, to that line is minimal, i.e. if xi + y i is minimal, where x i and y i are the coordinates of a point on the graphical representation Experimental results. Various similarity functions can be used for determining whether two strings are similar. In this paper, we have tested all gathered data against the following similarity functions: Cosine Similarity, Jaro-Winkler Similarity, Sorensen Similarity and Jaccard Similarity. The Cosine Similarity measures the angle between two vectors, but it does not take into consideration the order of the strings. Jaro-Winkler similarity is a lot more accurate especially because it takes into consideration the order of the strings, but it is designed and best suited for short strings. The Jaccard coefficient is defined as the length of the intersection divided by the length of the union of the two sets of strings. An important class of problems, that Jaccard similarity addresses well, is finding textually similar documents in a large corpus, such as the Web. Sorensen similarity coefficient is similar to Jaccard coefficient, but it has some different properties, including retaining sensitivity in more heterogeneous data sets and gives less weight to outliers. In order to have the best possible accuracy of the results and for reducing the noise induced in the similarity algorithm by the master pages HTML code, we have tested all the similarity functions for the absolute content of the documents (i.e. we ignore all the content that falls within the footer, header or menu).

6 88 DIANA HALIŢĂ AND DARIUS BUFNEA The absolute content of a web page was completely determined using a Java library named boilerpipe, which is able to remove or extract full text from HTML pages. This library provides algorithms which detects and removes the master page template around the main content of a web page. This library was released under Apache License 2.0. In order to follow our ideas we took for experimental purpose, an educational website http : // (Computer Science Faculty website), and we generated all the triplets (landingpage, ref f erer, bounce rate) through two methods: a client side tool provided by Google, named Google Analytics; a server side tool, integrated in the website s master page template, developed by us. We have chosen to experiment on the above website because we have administrator rights on the faculty website and we may properly measure for each external incoming link the generated bounce rate. Figure 2. Cosine similarity

7 INTER DOMAIN LINKED DOCUMENTS: SIMILARITY AND BOUNCERATE 89 Figure 3. Jaccard Similarity Figure 4. Sorensen similarity As we can see in the above figures, the best similarity function which gives us the expected results is Jaccard distance applied only to the absolute

8 90 DIANA HALIŢĂ AND DARIUS BUFNEA Figure 5. Jaro-Winkler Similarity contents of the web pages. Given this, we will use this similarity function for our future graphical representations. We also can prove that Jaccard is the best similarity function in our case, by calculating for each similarity function used and for both absolute content and full content comparison, the distance from all points which are represented on the figure to the line of equation y = x 100. Similarity function Method Value of the Sum Cosine absolute content Jaccard absolute content Sorensen absolute content Jaro-Winkler absolute content Table 1. Sum of the distances from all points to the line of equation y = x Conclusions and Future work In this paper we have advanced a series of experiments in order to see whether the bounce rate correlates with different similarity functions. A high content similarity between linked and source content may imply future visitor

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