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| '''SimRank''' is a general [[Semantic similarity|similarity measure]], based on a simple and intuitive [[Graph theory|graph-theoretic model]].
| | It involves expertise and knowledge of various tools and technologies used for creating websites. Also, you may want to opt for a more professioanl theme if you are planning on showing your site off to a high volume of potential customers each day. * A community forum for debate of the product together with some other customers in the comments spot. Keep reading for some great Word - Press ideas you can start using today. You can customize the appearance with PSD to Word - Press conversion ''. <br><br> |
| SimRank is applicable in any [[Domain model|domain]] with object-to-object [[Relation (mathematics)|relationships]], that measures similarity of the structural context in which objects occur, based on their relationships with other objects.
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| Effectively, SimRank is a measure that says "'''two objects are similar if they are related to similar objects'''."
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| == Introduction ==
| | As you know today Word - Press has turn out to be a tremendously popular open source publishing and blogging display place. You may either choose to link only to the top-level category pages or the ones that contain information about your products and services. There are number of web services that offer Word press development across the world. Furthermore, with the launch of Windows 7 Phone is the smart phone market nascent App. Many times the camera is following Mia, taking in her point of view in almost every frame. <br><br>The entrepreneurs can easily captivate their readers by using these versatile themes. After sending these details, your Word - Press blog will be setup within a few days. This platform can be customizedaccording to the requirements of the business. These frequent updates have created menace in the task of optimization. Premium vs Customised Word - Press Themes - Premium themes are a lot like customised themes but without the customised price and without the wait. <br><br>Word - Press has plenty of SEO benefits over Joomla and Drupal. In case you need to hire PHP developers or hire Offshore Code - Igniter development services or you are looking for Word - Press development experts then Mindfire Solutions would be the right choice for a Software Development partner. Exacting subjects in reality must be accumulated in head ahead of planning on your high quality theme. Giant business organizations can bank on enterprise solutions to incorporate latest web technologies such as content management system etc, yet some are looking for economical solutions. See a product, take a picture, and it gives you an Amazon price for that product, or related products. <br><br>Under Settings —> Reading, determine if posts or a static page will be your home page, and if your home page is a static page, what page will contain blog posts. By using Word - Press MLM websites or blogs, an online presence for you and your MLM company can be created swiftly and simply. Must being, it's beneficial because I don't know about you, but loading an old website on a mobile, having to scroll down, up, and sideways' I find links being clicked and bounced around like I'm on a freaking trampoline. And, it is better that you leave it on for the duration you are writing plugin code. Verify whether your company has a team of developers or programmers having hands-on experience and knowledge about all Word - Press concepts If you cherished this write-up and you would like to obtain more facts about [http://ad4.fr/wordpress_backup_plugin_7440872 wordpress backup plugin] kindly check out our webpage. . |
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| Many [[Application software|applications]] require a measure of "similarity" between objects.
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| One obvious example is the "find-similar-document" query,
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| on traditional text corpora or the [[World Wide Web|World-Wide Web]].
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| More generally, a similarity measure can be used to [[Cluster analysis|cluster objects]], such as for [[collaborative filtering]] in a [[recommender system]], in which “similar” users and items are grouped based on the users’ preferences.
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| Various aspects of objects can be used to determine similarity, usually depending on the domain and the appropriate definition of similarity for that domain.
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| In a [[Text corpus|document corpus]], matching text may be used, and for collaborative filtering, similar users may be identified by common preferences.
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| SimRank is a general approach that exploits the object-to-object relationships found in many domains of interest.
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| On the [[World Wide Web|Web]], for example, two pages are related if there are [[hyperlink]]s between them.
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| A similar approach can be applied to scientific papers and their citations, or to any other document corpus with [[cross-reference]] information.
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| In the case of recommender systems, a user’s preference for an item constitutes a relationship between the user and the item.
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| Such domains are naturally modeled as [[Graph (mathematics)|graphs]], with [[Vertex (graph theory)|nodes]] representing objects and [[Edge_(graph_theory)#Graph|edges]] representing relationships.
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| The intuition behind the SimRank algorithm is that, in many domains, '''similar objects are related to similar objects'''.
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| More precisely, objects <math>a</math> and <math>b</math> are similar if they are related to objects <math>c</math> and <math>d</math>, respectively, and <math>c</math> and <math>d</math> are themselves similar.
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| The [[Recursion (computer science)#Recursive_programming|base case]] is that objects are similar to themselves | |
| .<ref name=jeh_widom>G. Jeh and J. Widom. SimRank: a measure of structural-context similarity. In [[SIGKDD|KDD'02]]: Proceedings of the eighth ACM SIGKDD international conference on Knowledge discovery and data mining, pages 538-543. [[Association for Computing Machinery|ACM Press]], 2002. [http://www-cs-students.stanford.edu/~glenj/simrank.pdf]</ref> | |
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| It is important to note that SimRank is a general algorithm that determines only the similarity of structural context.
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| SimRank applies to any domain where there are enough relevant relationships between objects to base at least some notion of similarity on relationships.
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| Obviously, similarity of other domain-specific aspects are important as well; these can — and should be combined with relational structural-context similarity for an overall similarity measure.
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| For example, for [[Web page]]s SimRank can be combined with traditional textual similarity; the same idea applies to scientific papers or other document corpora.
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| For recommender systems, there may be built-in known similarities between items (e.g., both computers, both clothing, etc.), as well as similarities between users (e.g., same gender, same spending level).
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| Again, these similarities can be combined with the similarity scores that are computed based on preference patterns, in order to produce an overall similarity measure.
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| == Basic SimRank equation ==
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| For a node <math>v</math> in a graph, we denote by <math>I(v)</math> and <math>O(v)</math> the set of in-neighbors and out-neighbors of <math>v</math>, respectively.
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| Individual in-neighbours are denoted as <math>I_i(v)</math>, for <math>1 \le i \le \left|I(v)\right|</math>, and individual
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| out-neighbors are denoted as <math>O_i(v)</math>, for <math>1 \le i \le \left|O(v)\right|</math>.
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| Let us denote the similarity between objects <math>a</math> and <math>b</math> by <math>s(a, b) \in [0, 1]</math>.
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| Following the earlier motivation, a recursive equation is written for <math>s(a, b)</math>.
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| If <math>a = b</math> then <math>s(a, b)</math> is defined to be <math>1</math>.
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| Otherwise,
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| :<math>s(a, b) = \frac{C}{\left|I(a)\right| \left|I(b)\right|}
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| \sum_{i=1}^{\left|I(a)\right|}\sum_{j=1}^{\left|I(b)\right|}
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| s(I_i(a), I_j(b))</math>
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| where <math>C</math> is a constant between <math>0</math> and <math>1</math>.
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| A slight technicality here is that either <math>a</math> or <math>b</math> may not have any in-neighbors.
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| Since there is no way to infer any similarity between <math>a</math> and <math>b</math> in this case, similarity is set to <math>s(a, b) = 0</math>, so the summation in the above equation is defined to be <math>0</math> when <math>I(a) = \emptyset</math> or <math>I(b) = \emptyset</math>.
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| == Computing SimRank ==
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| A solution to the SimRank equations for a graph <math>G</math> can be reached by [[Iterative method|iteration]] to a [[Fixed point (mathematics)|fixed-point]].
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| Let <math>n</math> be the number of nodes in <math>G</math>.
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| For each iteration <math>k</math>, we can keep <math>n^2</math> entries <math>R_k(*, *)</math> of length <math>n^2</math>, where <math>R_k(a, b)</math> gives the score between <math>a</math> and <math>b</math> on iteration <math>k</math>.
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| We successively compute <math>R_{k+1}(*, *)</math> based on <math>R_k(*, *)</math>.
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| We start with <math>R_0(*, *)</math> where each <math>R_0(a, b)</math> is a lower bound on the actual SimRank score <math>s(a, b)</math>:
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| :<math> R_0(a, b) =
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| \begin{cases}
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| 1 \mbox{ } , \mbox{ } \mbox{if } a = b \mbox{ } , \\
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| 0 \mbox{ } , \mbox{ } \mbox{if } a \neq b \mbox{ } .
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| \end{cases}</math>
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| To compute <math>R_{k+1}(a, b)</math> from <math>R_k(*, *)</math>, we use the basic SimRank equation to get:
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| :<math>R_{k + 1}(a, b) =
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| \frac{C}{\left|I(a)\right| \left|I(b)\right|}
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| \sum_{i=1}^{\left|I(a)\right|}\sum_{j=1}^{\left|I(b)\right|}
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| R_k(I_i(a), I_j(b))</math>
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| for <math>a \ne b</math>, and <math>R_{k+1}(a, b) = 1</math> for <math>a = b</math>.
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| That is, on each iteration <math>k + 1</math>, we update the similarity of <math>(a, b)</math> using the similarity scores of the neighbours of <math>(a, b)</math> from the previous iteration <math>k</math> according to the basic SimRank equation.
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| The values <math>R_k(*, *)</math> are [[Monotonic function|nondecreasing]] as <math>k</math> increases.
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| It was shown in <ref name="jeh_widom"/> that the values [[Limit of a sequence|converge]] to [[Limit of a sequence|limits]] satisfying the basic SimRank equation, the SimRank scores <math>s(*, *)</math>, i.e., for all <math>a, b \in V</math>, <math>\lim_{k \to \infty} R_k(a, b) = s(a, b)</math>.
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| The original SimRank proposal suggested choosing the decay factor <math>C = 0.8</math> and a fixed number <math>K = 5</math> of iterations to perform.
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| However, the recent research <ref name="lizorkin">D. Lizorkin, P. Velikhov, M. Grinev and D. Turdakov. Accuracy Estimate and Optimization Techniques for
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| SimRank Computation. In [[Very large database|VLDB '08]]: Proceedings of the 34th International Conference on Very Large Data Bases, pages 422--433. [http://modis.ispras.ru/Lizorkin/Publications/simrank_accuracy.pdf]</ref> showed that the given values for <math>C</math> and <math>K</math> generally imply relatively low [[Accuracy and precision|accuracy]] of iteratively computed SimRank scores.
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| For guaranteeing more accurate computation results, the latter paper suggests either using a smaller decay factor (in particular, <math>C = 0.6</math>) or taking more iterations.
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| == Further research on SimRank ==
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| * Fogaras and Racz <ref name="fogaras_racz">D. Fogaras and B. Racz. Scaling link-based similarity search. In [[World Wide Web Conference|WWW '05]]: Proceedings of the 14th international conference on World Wide Web, pages 641--650, New York, NY, USA, 2005. [[Association for Computing Machinery|ACM]]. [http://www2005.org/cdrom/docs/p641.pdf]</ref> suggested speeding up SimRank computation through [[Probability theory|probabilistic]] computation using the [[Monte Carlo method]].
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| * Antonellis et al.<ref name="simrank_plusplus">I. Antonellis, H. Garcia-Molina and C.-C. Chang. Simrank++: Query Rewriting through Link Analysis of the Click Graph. In [[Very large database|VLDB '08]]: Proceedings of the 34th International Conference on Very Large Data Bases, pages 408--421. [http://dbpubs.stanford.edu/pub/showDoc.Fulltext?lang=en&doc=2008-17&format=pdf&compression=&name=2008-17.pdf]</ref> extended SimRank equations to take into consideration (i) evidence factor for [[Graph (mathematics)#Properties of graphs|incident nodes]] and (ii) link weights.
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| * Lizorkin et al.<ref name="lizorkin"/> proposed several [[Optimization (computer science)|optimization]] techniques for speeding up SimRank iterative computation.
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| == See also ==
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| * [[PageRank]]
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| == Citations ==
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| {{reflist|colwidth=30em}}
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| [[Category:Information retrieval]]
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It involves expertise and knowledge of various tools and technologies used for creating websites. Also, you may want to opt for a more professioanl theme if you are planning on showing your site off to a high volume of potential customers each day. * A community forum for debate of the product together with some other customers in the comments spot. Keep reading for some great Word - Press ideas you can start using today. You can customize the appearance with PSD to Word - Press conversion .
As you know today Word - Press has turn out to be a tremendously popular open source publishing and blogging display place. You may either choose to link only to the top-level category pages or the ones that contain information about your products and services. There are number of web services that offer Word press development across the world. Furthermore, with the launch of Windows 7 Phone is the smart phone market nascent App. Many times the camera is following Mia, taking in her point of view in almost every frame.
The entrepreneurs can easily captivate their readers by using these versatile themes. After sending these details, your Word - Press blog will be setup within a few days. This platform can be customizedaccording to the requirements of the business. These frequent updates have created menace in the task of optimization. Premium vs Customised Word - Press Themes - Premium themes are a lot like customised themes but without the customised price and without the wait.
Word - Press has plenty of SEO benefits over Joomla and Drupal. In case you need to hire PHP developers or hire Offshore Code - Igniter development services or you are looking for Word - Press development experts then Mindfire Solutions would be the right choice for a Software Development partner. Exacting subjects in reality must be accumulated in head ahead of planning on your high quality theme. Giant business organizations can bank on enterprise solutions to incorporate latest web technologies such as content management system etc, yet some are looking for economical solutions. See a product, take a picture, and it gives you an Amazon price for that product, or related products.
Under Settings —> Reading, determine if posts or a static page will be your home page, and if your home page is a static page, what page will contain blog posts. By using Word - Press MLM websites or blogs, an online presence for you and your MLM company can be created swiftly and simply. Must being, it's beneficial because I don't know about you, but loading an old website on a mobile, having to scroll down, up, and sideways' I find links being clicked and bounced around like I'm on a freaking trampoline. And, it is better that you leave it on for the duration you are writing plugin code. Verify whether your company has a team of developers or programmers having hands-on experience and knowledge about all Word - Press concepts If you cherished this write-up and you would like to obtain more facts about wordpress backup plugin kindly check out our webpage. .