Related papers: Efficient Uncertainty Minimization for Fuzzy Spect…
Clustering is one of the most crucial problems in unsupervised learning, and the well-known $k$-means clustering algorithm has been shown to be implementable on a quantum computer with a significant speedup. However, many clustering…
Fuzzy clustering has become a widely used data mining technique and plays an important role in grouping, traversing and selectively using data for user specified applications. The deterministic Fuzzy C-Means (FCM) algorithm may result in…
Hyperspectral remote sensing is a prominent research topic in data processing. Most of the spectral unmixing algorithms are developed by adopting the linear mixing models. Nonnegative matrix factorization (NMF) and its developments are used…
In spectral clustering, one defines a similarity matrix for a collection of data points, transforms the matrix to get the Laplacian matrix, finds the eigenvectors of the Laplacian matrix, and obtains a partition of the data using the…
We consider the problem of estimating a consensus community structure by combining information from multiple layers of a multi-layer network using methods based on the spectral clustering or a low-rank matrix factorization. As a general…
Researches in granular modeling produced a variety of mathematical models, such as intervals, (higher-order) fuzzy sets, rough sets, and shadowed sets, which are all suitable to characterize the so-called information granules. Modeling of…
Spectral embedding is a popular technique for the representation of graph data. Several regularization techniques have been proposed to improve the quality of the embedding with respect to downstream tasks like clustering. In this paper, we…
Convex clustering, a convex relaxation of k-means clustering and hierarchical clustering, has drawn recent attentions since it nicely addresses the instability issue of traditional nonconvex clustering methods. Although its computational…
Information-maximization clustering learns a probabilistic classifier in an unsupervised manner so that mutual information between feature vectors and cluster assignments is maximized. A notable advantage of this approach is that it only…
We consider the problem of clustering a set of high-dimensional data points into sets of low-dimensional linear subspaces. The number of subspaces, their dimensions, and their orientations are unknown. We propose a simple and low-complexity…
Patchwork learning arises as a new and challenging data collection paradigm where both samples and features are observed in fragmented subsets. Due to technological limits, measurement expense, or multimodal data integration, such patchwork…
Our previous experiments demonstrated that subsets collections of (short) documents (with several hundred entries) share a common normalized in some way eigenvalue spectrum of combinatorial Laplacian. Based on this insight, we propose a…
In a data matrix, we may distinguish between cases, each represented by a row vector for a statistical unit, and cells, which correspond to single entries of the data matrix. Recent developments in Robust Statistics have introduced the…
Spectral clustering is a popular algorithm that clusters points using the eigenvalues and eigenvectors of Laplacian matrices derived from the data. For years, spectral clustering has been working mysteriously. This paper explains spectral…
We present a new algorithm for spectral clustering based on a column-pivoted QR factorization that may be directly used for cluster assignment or to provide an initial guess for k-means. Our algorithm is simple to implement, direct, and…
The input of most clustering algorithms is a symmetric matrix quantifying similarity within data pairs. Such a matrix is here turned into a quadratic set function measuring cluster score or similarity within data subsets larger than pairs.…
Graph clustering is a fundamental task in unsupervised learning with broad real-world applications. While spectral clustering methods for undirected graphs are well-established and guided by a minimum cut optimization consensus, their…
We propose a new method for clustering based on the local minimization of the \gamma-divergence, which we call the spontaneous clustering. The greatest advantage of the proposed method is that it automatically detects the number of clusters…
This paper focuses on scalability and robustness of spectral clustering for extremely large-scale datasets with limited resources. Two novel algorithms are proposed, namely, ultra-scalable spectral clustering (U-SPEC) and ultra-scalable…
Spectral clustering is discussed from many perspectives, by extending it to rectangular arrays and discrepancy minimization too. Near optimal clusters are obtained with singular value decomposition and with the weighted $k$-means algorithm.…