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Figure from:A survey of clustering ensemble algorithms

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where each entry oF this matrix W;; reflects the similarity average between the objects az, and «;. As the last step, a graph G = (V, E) is built where each vertex v; identifies the object x; and the edge e;; that connects the vertexes v; and v, has a value equal to W,;. The METIS algorithm is used to obtain the consensus partition from this graph. The second consensus function introduced by Domeniconi and Al-Razgan”’ is the Weighty Bipartite Partition Algorithm (WBPA). As its name indicates, it presents a consensus function based on the partitioning of a bipartite graph. Following the steps of the WSPA algorithm, for an object x; and a partition P,, v=1,...,m, the pos- terior probabilities vector p; is computed. With these vectors, the matrix A is built as following:

Figure 4 where each entry oF this matrix W;; reflects the similarity average between the objects az, and «;. As the last step, a graph G = (V, E) is built where each vertex v; identifies the object x; and the edge e;; that connects the vertexes v; and v, has a value equal to W,;. The METIS algorithm is used to obtain the consensus partition from this graph. The second consensus function introduced by Domeniconi and Al-Razgan”’ is the Weighty Bipartite Partition Algorithm (WBPA). As its name indicates, it presents a consensus function based on the partitioning of a bipartite graph. Following the steps of the WSPA algorithm, for an object x; and a partition P,, v=1,...,m, the pos- terior probabilities vector p; is computed. With these vectors, the matrix A is built as following:

Related Figures (4)

Fig. 1. Diagram of the general process of cluster ensemble. NN III II IJ I IIE A EID DDD LER I ES IIA EEEIIEILE DIES ELI MIELE NA IN IO There are clustering ensemble methods like the voting-k-means”? that demand a well-determined generation process, in this case, all the partitions should be obtained by applying the kMeans algorithm with different initializations for the number of clusters parameter. This method uses a big k value (the number of clusters), in order to obtain complex structure in the consensus partition, from the combination of small hyper-spherical structures in the single partitions.
Fig. 1. Diagram of the general process of cluster ensemble. NN III II IJ I IIE A EID DDD LER I ES IIA EEEIIEILE DIES ELI MIELE NA IN IO There are clustering ensemble methods like the voting-k-means”? that demand a well-determined generation process, in this case, all the partitions should be obtained by applying the kMeans algorithm with different initializations for the number of clusters parameter. This method uses a big k value (the number of clusters), in order to obtain complex structure in the consensus partition, from the combination of small hyper-spherical structures in the single partitions.
Fig. 2. Diagram of the principal clustering ensemble generation mechanisms.
Fig. 2. Diagram of the principal clustering ensemble generation mechanisms.
Fig. 3. Diagram of the principal consensus functions techniques. Consensus functions based on object co-occurrence approach are represented by a rectangle (left) and the ones based on the median partition approach are represented by a rounded rectangle (right).
Fig. 3. Diagram of the principal consensus functions techniques. Consensus functions based on object co-occurrence approach are represented by a rectangle (left) and the ones based on the median partition approach are represented by a rounded rectangle (right).
Table 1. Comparison of consensus functions.
Table 1. Comparison of consensus functions.