Membership Optimization for Clustering Process in Machine Intelligence-A Practical Approach

Asrar Ahmad, V.M. Thakare, M.A. Atique


Clustering is an unsupervised method to divide data into disjoint subsets with high intra-cluster similarity and low inter-cluster similarity. Most of the approaches perform hard clustering, i.e., they assign each item to a single cluster. This works well when clustering compact and well-separated groups of data, but in many real-world situations, clusters overlap. Thus, for items that belong to two or more clusters, it may be more appropriate to assign them with gradual memberships to avoid coarse-grained assignments of data. The objective of k-means clustering is formulated as a Rayleigh quotient function of the between-cluster scatter and the cluster membership matrix and further combined with nonlinear dimensionality reduction in Hilbert space, where heterogeneous data sources can be easily combined as kernel matrices. The objective to optimizing the kernel combination and the cluster memberships on unlabeled data is non-convex. To solve it, minimization method to optimize the cluster memberships and the kernel coefficients iteratively to convergence is to be applied. Instead of a single fixed kernel, multiple kernels may be used. Recent developments in multiple kernel learning have shown that the construction of a kernel from a number of basis kernels allows for more flexible encoding of domain knowledge from different sources or cues. We here extend the multiple kernel-learning paradigm to fuzzy clustering. The proposed algorithm simultaneously finds the best degrees of membership and the optimal kernel weights for a nonnegative combination of a set of kernels. We also embed the feature weight computation into the clustering procedure. The incorporation of multiple kernels and the automatic adjustment of kernel weights render MKFC more immune to unreliable features or kernels. It also makes combining kernels more practical, since appropriate weights are assigned automatically.

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