Non-Parametric Probabilistic Image Segmentation

We propose a simple probabilistic generative model for image segmentation. Like other probabilistic algorithms (such as EM on a Mixture of Gaussians) the proposed model is principled, provides both hard and probabilistic cluster assignments, as well as the ability to naturally incorporate prior knowledge. While previous probabilistic approaches are restricted to parametric models of clusters (e.g., Gaussians) we eliminate this limitation. The suggested approach does not make heavy assumptions on the shape of the clusters and can thus handle complex structures. Our experiments show that the suggested approach outperforms previous work on a variety of image segmentation tasks

On the Equivalence of Nonnegative Matrix Factorization and K-means- Spectral Clustering

We provide a systematic analysis of nonnegative matrix factorization (NMF) relating to data clustering. We generalize the usual X = FG{sup T} decomposition to the symmetric W = HH{sup T} and W = HSH{sup T} decompositions. We show that (1) W = HH{sup T} is equivalent to Kernel K-means clustering and the Laplacian-based spectral clustering. (2) X = FG{sup T} is equivalent to simultaneous clustering of rows and columns of a bipartite graph. We emphasizes the importance of orthogonality in NMF and soft clustering nature of NMF. These results are verified with experiments on face images and newsgroups

Fuzzy Sets in Business Management, Finance, and Economics

This book collects fifteen papers published in s Special Issue of Mathematics titled “Fuzzy Sets in Business Management, Finance, and Economics”, which was published in 2021. These paper cover a wide range of different tools from Fuzzy Set Theory and applications in many areas of Business Management and other connected fields. Specifically, this book contains applications of such instruments as, among others, Fuzzy Set Qualitative Comparative Analysis, Neuro-Fuzzy Methods, the Forgotten Effects Algorithm, Expertons Theory, Fuzzy Markov Chains, Fuzzy Arithmetic, Decision Making with OWA Operators and Pythagorean Aggregation Operators, Fuzzy Pattern Recognition, and Intuitionistic Fuzzy Sets. The papers in this book tackle a wide variety of problems in areas such as strategic management, sustainable decisions by firms and public organisms, tourism management, accounting and auditing, macroeconomic modelling, the evaluation of public organizations and universities, and actuarial modelling. We hope that this book will be useful not only for business managers, public decision-makers, and researchers in the specific fields of business management, finance, and economics but also in the broader areas of soft mathematics in social sciences. Practitioners will find methods and ideas that could be fruitful in current management issues. Scholars will find novel developments that may inspire further applications in the social sciences

A Probabilistic Approach for Optimizing Spectral Clustering

Spectral clustering enjoys its success in both data clustering and semisupervised learning. But, most spectral clustering algorithms cannot handle multi-class clustering problems directly. Additional strategies are needed to extend spectral clustering algorithms to multi-class clustering problems. Furthermore, most spectral clustering algorithms employ hard cluster membership, which is likely to be trapped by the local optimum. In this paper, we present a new spectral clustering algorithm, named “Soft Cut”. It improves the normalized cut algorithm by introducing soft membership, and can be efficiently computed using a bound optimization algorithm. Our experiments with a variety of datasets have shown the promising performance of the proposed clustering algorithm.