A Survey on Soft Subspace Clustering

Subspace clustering (SC) is a promising clustering technology to identify clusters based on their associations with subspaces in high dimensional spaces. SC can be classified into hard subspace clustering (HSC) and soft subspace clustering (SSC). While HSC algorithms have been extensively studied and well accepted by the scientific community, SSC algorithms are relatively new but gaining more attention in recent years due to better adaptability. In the paper, a comprehensive survey on existing SSC algorithms and the recent development are presented. The SSC algorithms are classified systematically into three main categories, namely, conventional SSC (CSSC), independent SSC (ISSC) and extended SSC (XSSC). The characteristics of these algorithms are highlighted and the potential future development of SSC is also discussed.Comment: This paper has been published in Information Sciences Journal in 201

SACOC: A spectral-based ACO clustering algorithm

The application of ACO-based algorithms in data mining is growing over the last few years and several supervised and unsupervised learning algorithms have been developed using this bio-inspired approach. Most recent works concerning unsupervised learning have been focused on clustering, where ACO-based techniques have showed a great potential. At the same time, new clustering techniques that seek the continuity of data, specially focused on spectral-based approaches in opposition to classical centroid-based approaches, have attracted an increasing research interest–an area still under study by ACO clustering techniques. This work presents a hybrid spectral-based ACO clustering algorithm inspired by the ACO Clustering (ACOC) algorithm. The proposed approach combines ACOC with the spectral Laplacian to generate a new search space for the algorithm in order to obtain more promising solutions. The new algorithm, called SACOC, has been compared against well-known algorithms (K-means and Spectral Clustering) and with ACOC. The experiments measure the accuracy of the algorithm for both synthetic datasets and real-world datasets extracted from the UCI Machine Learning Repository

Quantum Hall Ground States, Binary Invariants, and Regular Graphs

Extracting meaningful physical information out of a many-body wavefunction is often impractical. The polynomial nature of fractional quantum Hall (FQH) wavefunctions, however, provides a rare opportunity for a study by virtue of ground states alone. In this article, we investigate the general properties of FQH ground state polynomials. It turns out that the data carried by an FQH ground state can be essentially that of a (small) directed graph/matrix. We establish a correspondence between FQH ground states, binary invariants and regular graphs and briefly introduce all the necessary concepts. Utilizing methods from invariant theory and graph theory, we will then take a fresh look on physical properties of interest, e.g. squeezing properties, clustering properties, etc. Our methodology allows us to `unify' almost all of the previously constructed FQH ground states in the literature as special cases of a graph-based class of model FQH ground states, which we call \emph{accordion} model FQH states

Hierarchical structure-and-motion recovery from uncalibrated images

This paper addresses the structure-and-motion problem, that requires to find camera motion and 3D struc- ture from point matches. A new pipeline, dubbed Samantha, is presented, that departs from the prevailing sequential paradigm and embraces instead a hierarchical approach. This method has several advantages, like a provably lower computational complexity, which is necessary to achieve true scalability, and better error containment, leading to more stability and less drift. Moreover, a practical autocalibration procedure allows to process images without ancillary information. Experiments with real data assess the accuracy and the computational efficiency of the method.Comment: Accepted for publication in CVI