Number Of Clusters In Data Research Articles

Minimum sum-squared residue for fuzzy co-clustering

Clustering is often seen as a more practical but very challenging answer to the task of categorizing objects. Minimum Sum-squared Residue for Fuzzy Co-Clustering (MSR-FCC) is proposed to address two issues faced by many existing clustering algorithms, namely the high-dimensionality and the inherent fuzziness found in most real-world data. MSR-FCC is able to simultaneously cluster data and features using fuzzy techniques. It suggests a new partitioning fuzzy co-clustering algorithm based on the mean squared residue approach. Besides handling overlap clusters, MSR-FCC offers the flexibility that allows the number of data clusters to be different from the number of feature clusters, which reflects the distribution characteristic inherited in real-world data. In this paper, mathematical formulation of MSR-FCC is derived and explained. Experiments were conducted on standard datasets to demonstrate that the proposed algorithm is able to cluster high-dimensional data with overlaps feasibly and at the same time, it provides a new and promising mechanism for improving the interpretability of the co-clusters through the fuzzy membership function.

On finding the number of clusters

We present a novel approach to finding the number of clusters in data based on the minimization of a regularized cost function. Minimization of the proposed cost function results in the minimization of the sum-of-squared distances of the data points from the respective nearest cluster center as well as the sum-of-squared distances of the individual cluster centers from neighborhood cluster centers. Smaller values of the neighborhood encourage the formation of more distinct cluster centers, while larger values of the neighborhood encourage the formation of fewer distinct cluster centers. We identify the neighborhood as a scale parameter and obtain the number of cluster centers at varying values of the scale parameter. The number of cluster centers in the data is then obtained based on persistence over the largest range of the scale parameter. Four simulations are presented to illustrate the efficacy of the proposed algorithm.