Có 40+ tài liệu thuộc chủ đề "các thuật toán clustering"
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Given a target graph 𝐺 and a query graph 𝑄, let u = [𝑢 1 , 𝑢 2. 𝑣 𝑛 ] 𝑇 be their corresponding feature vectors, where 𝑢 𝑖 and 𝑣 𝑖 are the frequencies (i.e., the number of embeddings) of feature 𝑓 𝑖 in graphs 𝐺 and 𝑄. As mentioned before, for any feature set, the corresponding feature...
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Consider a se- mantic network that represents people as nodes in the graph and relationships among people as edges in the graph. Here, 𝑢 ↝ 𝑣 returns true if and only if there is a di- rected path in the directed graph 𝐺 from 𝑢 to 𝑣. A reachability query over a directed graph 𝐺 can be answered over a...
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Algorithm 2 Compute-Chain-Cover(𝐺. Input: The DAG 𝐺, and a chain cover { 𝐶 1. 𝐶 𝑘 } Output: The chain cover code for every node in 𝐺. 1: sort all nodes in 𝐺 in topological order;. 18: return the set of chaincode(𝑣 𝑖 ) for every 𝑣 𝑖 ∈ 𝐺;. all chains is the entire set of nodes in 𝐺,...
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minimum 2-hop cover to cover reachability cross 𝐺 𝐴 and 𝐺 𝐷 from the nodes appearing in 𝐸 𝐶 . It is important to note that reachability between the two sub- graphs, 𝐺 𝐴 and 𝐺 𝐷 , are completely covered by the set of 2-hop clusters using the set of nodes 𝑉 𝑤 . Both 𝐺 ⊤ and 𝐺...
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In Proceedings of the 1989 ACM SIGMOD international conference on Management of data (SIGMOD . In Proceedings of the 12th international conference on World Wide Web (WWW . In Proceedings of the 17th international conference on World Wide Web (WWW . In Proceedings of the 2002 ACM SIGMOD international conference on Management of data (SIGMOD . In Proceedings of the...
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In [43] the tree search method for isomorphism is sped up by means of another heuristic derived from Con- straint Satisfaction. The reader is referred to [15] for an exhaustive list of exact graph matching algorithms developed since 1973.. As a matter of fact, subgraph isomorphism is a harder problem than graph isomorphism as one has not only to check...
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Query graphs are more general than common graphs in the sense that don’t care symbol and variables may occur as the values of attributes on the nodes and edges. The purpose of the variables is to define those attributes whose values are to be returned as an answer to a query (we will come back to this point later). According...
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A note on the derivation of maximal common subgraphs of two directed or undirected graphs. Structural graph matching using the EM algo- rithm and singular value decomposition. Pattern Recognition . In Journal of the Society for Industrial and Applied Mathematics, vol- ume 5, pages 32–38, March 1957.. Self-organizing maps for learning the edit costs in graph matching. The Dissimilarity Representation...
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If we remove node C and the two keyword nodes under C, the remaining tree is still an answer to the query. Clearly, this answer is independent of the answer 𝐶 ∈ 𝑆𝐿𝐶𝐴(𝑥, 𝑦), yet it is not represented by the SLCA semantics.. XRank [13], for example, adopts different query semantics for keyword search. 𝑘 𝑛 ) contains the set...
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Given an an- swer tree 𝑇 , for each keyword 𝑘 𝑖 , we use 𝑠(𝑇, 𝑘 𝑖 ) to represent the sum of the edge weights on the path from the root of 𝑇 to the leaf containing key- word 𝑘 𝑖 . Let 𝑁 denote the aggregated score of nodes that contain keywords. 𝐸𝑁 𝜆 to find top-K...
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The first type consists of node clustering algorithms in which we attempt to determine dense regions of the graph based on edge behavior. We will also discuss the applicability of the approach to other kinds of data such as semi-structured data, and the utility of graph mining algorithms to such representations.. Since core graph-mining algorithms can be extended to this...
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Here 𝑁 𝑢𝑚𝐶𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑒𝑑𝑃 𝑎𝑡ℎ𝑠(𝑒, 𝑖, 𝑗) refers to the number of (global) short- est paths between 𝑖 and 𝑗 which pass through 𝑒, and 𝑁 𝑢𝑚𝑆ℎ𝑜𝑟𝑡𝑃 𝑎𝑡ℎ𝑠(𝑖, 𝑗) refers to the number of shortest paths between 𝑖 and 𝑗. Note that the value of 𝑁 𝑢𝑚𝐶𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑒𝑑𝑃 𝑎𝑡ℎ𝑠)(𝑒, 𝑖, 𝑗) may be 0 if none of the shortest paths between 𝑖...
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Similarly, let the average sub-structural self- similarity at the end of the the previous iteration be Φ. In the beginning of the next iteration, the algorithm computes the increase of the average sub- structural self-similarity, Φ − Φ. This is done in order to effectively handle situations in which the threshold 𝜖 is chosen to be too small. Two further...
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If the edges are weighted, then 𝑤(𝑢) is the weight of edge 𝑢. For an undirected graph, 𝐸(𝑆) is the set of induced edges on 𝑆: 𝐸(𝑆. Then, 𝐻 𝑆 is the induced subgraph (𝑆, 𝐸(𝑆. Similarly, 𝐸(𝑆, 𝑇 ) designates the set of edges from 𝑆 to 𝑇. 𝐻 𝑆,𝑇 is the induced subgraph (𝑆, 𝑇, 𝐸(𝑆, 𝑇. this...
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Figure 10.2. Figure 10.3. in the upper part links to some other web pages in the lower part. In order to put some vertices into the same group, we have to measure the similarity of the vertices which denotes to what extent they share common neighbors. With the help of shingling, for each vertex in the upper part, we can...
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Then, the density of 𝐺 𝑙 is no less than half of the density of 𝐺 𝑠. Anderson et al. Anderson et al.. This algorithm runs in 𝑂(𝑚 + 𝑛) and 𝑂(𝑚 + 𝑛 log 𝑛) time for unweighted and weighted graphs, respectively.. Finally, we choose the subgraph 𝐻 𝑘 with maximal density 𝑑(𝐻 𝑘 ) as the resulting dense...
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336 MANAGING AND MINING GRAPH DATA [42] N. A graph theoretic generalization of the clique concept. GRAPH CLASSIFICATION. Abstract Supervised learning on graphs is a central subject in graph data processing. In graph classification and regression, we assume that the target values of a certain number of graphs or a certain part of a graph are available as a training...
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Figure 11.4. Figure 11.5. 𝑟(𝑥 1 , 𝑥 ′ 1 ) can be computed based on the precomputed values of 𝑟(𝑥 2 , 𝑥 ′ 2. of the kernel like (2.11), and reduce the problem to solving a system of simul- taneous linear equations.. Replacing the order of summation in (2.12), we have the following:. Thus we need to compute...
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It is possible to employ other algorithms such as partial least squares regression (PLS) [39] and least angle regression (LARS) [45].. It is due to strong correlation among features corresponding to similar subgraphs. The graph mining version of PLS, gPLS [39], solves this problem by summarizing similar subgraphs into each feature (Figure 11.9). Since only one graph mining call is...
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where 𝑙 and 𝑙 ′ are the labeling functions of 𝑔 and 𝑔. Definition 12.2 (Frequent Graph). 𝐺 𝑛 } and a subgraph 𝑔, the supporting graph set of 𝑔 is 𝐷 𝑔. An important property, called anti-monotonicity, is crucial to confine the search space of frequent subgraph mining.. Definition 12.3 (Anti-Monotonicity). Many frequent graph pattern mining algorithms have been...