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Measuring similarity between two objects is the core operation in existing clustering algorithms in grouping similar objects into clusters. This paper introduces a new similarity measure called point-set kernel which computes the similarity…
Clustering algorithms are one of the main analytical methods to detect patterns in unlabeled data. Existing clustering methods typically treat samples in a dataset as points in a metric space and compute distances to group together similar…
Cluster structure detection is a fundamental task for the analysis of graphs, in order to understand and to visualize their functional characteristics. Among the different cluster structure detection methods, spectral clustering is…
Convex clustering is a well-regarded clustering method, resembling the similar centroid-based approach of Lloyd's $k$-means, without requiring a predefined cluster count. It starts with each data point as its centroid and iteratively merges…
Ensemble methods are known for enhancing the accuracy and robustness of machine learning models by combining multiple base learners. However, standard approaches like greedy or random ensembling often fall short, as they assume a constant…
In fully-dynamic consistent clustering, we are given a finite metric space $(M,d)$, and a set $F\subseteq M$ of possible locations for opening centers. Data points arrive and depart, and the goal is to maintain an approximately optimal…
A low-rank transformation learning framework for subspace clustering and classification is here proposed. Many high-dimensional data, such as face images and motion sequences, approximately lie in a union of low-dimensional subspaces. The…
Recently, a novel family of biologically plausible online algorithms for reducing the dimensionality of streaming data has been derived from the similarity matching principle. In these algorithms, the number of output dimensions can be…
Subspace clustering (SC) algorithms utilize the union of subspaces model to cluster data points according to the subspaces from which they are drawn. To better address separability of subspaces and robustness to noise we propose a wavelet…
Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN) finds meaningful patterns in spatial data by considering density and spatial proximity. As the clustering algorithm is inherently designed for static…
The performance of spectral clustering can be considerably improved via regularization, as demonstrated empirically in Amini et. al (2012). Here, we provide an attempt at quantifying this improvement through theoretical analysis. Under the…
The optimization of the variance supplemented by a budget constraint and an asymmetric $\ell_1$ regularizer is carried out analytically by the replica method borrowed from the theory of disordered systems. The asymmetric regularizer allows…
As in other estimation scenarios, likelihood based estimation in the normal mixture set-up is highly non-robust against model misspecification and presence of outliers (apart from being an ill-posed optimization problem). A robust…
Clustering is essential to many tasks in pattern recognition and computer vision. With the advent of deep learning, there is an increasing interest in learning deep unsupervised representations for clustering analysis. Many works on this…
While traditional research on text clustering has largely focused on grouping documents by topic, it is conceivable that a user may want to cluster documents along other dimensions, such as the authors mood, gender, age, or sentiment.…
One basic requirement of many studies is the necessity of classifying data. Clustering is a proposed method for summarizing networks. Clustering methods can be divided into two categories named model-based approaches and algorithmic…
To further utilize the unsupervised features and pairwise information, we propose a general Bilevel Clustering Optimization (BCO) framework to improve the performance of clustering. And then we introduce three special cases on subspace…
This work deals with a regularization method enforcing solution sparsity of linear ill-posed problems by appropriate discretization in the image space. Namely, we formulate the so called least error method in an $\ell^1$ setting and perform…
Machine learning algorithms typically require abundant data under a stationary environment. However, environments are nonstationary in many real-world applications. Critical issues lie in how to effectively adapt models under an…
Accurate and efficient entity resolution is an open challenge of particular relevance to intelligence organisations that collect large datasets from disparate sources with differing levels of quality and standard. Starting from a…