Tensor-Based Possibilistic C-Means Clustering

The current data acquisition techniques enable the gathering and storage of extensive datasets, encompassing multidimensional arrays. Recent researchers focus on the analysis of large datasets having diverse data points. These multi-dimensional datasets comprise diverse data points and can be represented as tensors or multi-dimensional arrays. Clustering, a data analysis technique, can be used to discover and reveal latent data patterns from these data sets. The traditional clustering algorithms like k-means, fuzzy c-means (FCM), and possibilistic c-means (PCM) pose some drawbacks in efficiently delivering high-quality clustering results for tensor or multi-dimensional array data. This may stem from the fact that these algorithms are primarily designed for single-view or low-array datasets, rendering them less suitable for the complexities of multi-dimensional arrays. In response to this challenge, this paper introduces the Tensor-based Possibilistic C-Means (TPCM) algorithm. TPCM utilizes a Tensor Distance (TD) function as the distance metric, different from the usual Euclidean distance. The TD function evaluates the distance between data points and cluster centers by considering relationships among different coordinates. To further enhance the analysis, the Canonical Polyadic Decomposition (CPD) method and PARAFAC2 decomposition techniques are used to restructure heterogeneous data into low-order tensors. Our experiments consider two types of datasets: multi-view datasets and tensor datasets. CPD is applied for tensor data decomposition, while PARAFAC2, a CPD variant, addresses multi-view data with varying feature space sizes in each view. Through comprehensive illustrations and evaluations using synthetic and real datasets, we demonstrate the superior performance of TPCM. Experimental results reveal that TPCM consistently achieves higher clustering performance compared to most existing clustering algorithms