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Figure from:A survey of clustering ensemble algorithms

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Fig. 2. Diagram of the principal clustering ensemble generation mechanisms.

Figure 2 Diagram of the principal clustering ensemble generation mechanisms.

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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. 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).
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:
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:
Table 1. Comparison of consensus functions.
Table 1. Comparison of consensus functions.