A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Convex clustering can only learn convex clusters, with significant gaps between clusters.
CCMM efficiently solves large-scale convex clustering problems.
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 and statistical properties have been recently studied, the performance of convex c…
Paper proposes a new clustering model that preserves cluster recovery with fewer dimensions.
A new algorithm speeds up convex clustering.
Introduces robust convex clustering with Median of Means for better data clustering.
New method recovers clusters in non-convex finite metric spaces with oracle queries.
Convex clustering solves a stable optimization problem for clustering.
Kernelized convex clustering handles non-linear and non-convex data.
Data clustering is a fundamental problem with a wide range of applications. Standard methods, eg the -means method, usually require solving a non-convex optimization problem. Recently, total variation based convex relaxation to the -means model has emerged as an attractive alternative for data clustering. However…
Sparse convex clustering is to cluster observations and conduct variable selection simultaneously in the framework of convex clustering. Although a weighted norm is usually employed for the regularization term in sparse convex clustering, its use increases the dependence on the data and reduces the estimation acc…
New bounds for convex clustering under graph connectivity.
Unified method for simultaneous denoising and clustering.
Convex clustering is a recent stable alternative to hierarchical clustering. It formulates the recovery of progressively coalescing clusters as a regularized convex problem. While convex clustering was originally designed for handling Euclidean distances between data points, in a growing number of applications, the dat…
Co-Clustering, the problem of simultaneously identifying clusters across multiple aspects of a data set, is a natural generalization of clustering to higher-order structured data. Recent convex formulations of bi-clustering and tensor co-clustering, which shrink estimated centroids together using a convex fusion penalt…
Convex clustering is a promising new approach to the classical problem of clustering, combining strong performance in empirical studies with rigorous theoretical foundations. Despite these advantages, convex clustering has not been widely adopted, due to its computationally intensive nature and its lack of compelling v…
We suggest using the max-norm as a convex surrogate constraint for clustering. We show how this yields a better exact cluster recovery guarantee than previously suggested nuclear-norm relaxation, and study the effectiveness of our method, and other related convex relaxations, compared to other clustering approaches.
CDL index improves clustering validation for non-convex data.
Cluster analysis is a fundamental tool for pattern discovery of complex heterogeneous data. Prevalent clustering methods mainly focus on vector or matrix-variate data and are not applicable to general-order tensors, which arise frequently in modern scientific and business applications. Moreover, there is a gap between …
Clustering is a fundamental problem in unsupervised learning. Popular methods like K-means, may suffer from poor performance as they are prone to get stuck in its local minima. Recently, the sum-of-norms (SON) model (also known as the clustering path) has been proposed in Pelckmans et al. (2005), Lindsten et al. (2011)…
Although many convex relaxations of clustering have been proposed in the past decade, current formulations remain restricted to spherical Gaussian or discriminative models and are susceptible to imbalanced clusters. To address these shortcomings, we propose a new class of convex relaxations that can be flexibly applied…
Clustering is a fundamental problem in many scientific applications. Standard methods such as -means, Gaussian mixture models, and hierarchical clustering, however, are beset by local minima, which are sometimes drastically suboptimal. Recently introduced convex relaxations of -means and hierarchical clustering s…
Clustering, like covariate selection for classification, is an important step to compress and interpret the data. However, clustering of covariates is often performed independently of the classification step, which can lead to undesirable clustering results that harm interpretability and compression rate. Therefore, we…
Knowledge of functional groupings of neurons can shed light on structures of neural circuits and is valuable in many types of neuroimaging studies. However, accurately determining which neurons carry out similar neurological tasks via controlled experiments is both labor-intensive and prohibitively expensive on a large…
Traditional nearest points methods use all the samples in an image set to construct a single convex or affine hull model for classification. However, strong artificial features and noisy data may be generated from combinations of training samples when significant intra-class variations and/or noise occur in the image s…
MTLRRC improves MTL by robustly clustering tasks and detecting outliers.
This paper characterizes hierarchical clustering methods that abide by two previously introduced axioms -- thus, denominated admissible methods -- and proposes tractable algorithms for their implementation. We leverage the fact that, for asymmetric networks, every admissible method must be contained between reciprocal …
Efficient algorithm for self-directed learning of convex clusters on graphs.
The paper provides guarantees for clustering validity without distributional assumptions.
Paper proposes ABDR for convex subspace clustering with adaptive block diagonal representation.
Fixed points found in cluster modular groups under specific conditions.
In mixed multi-view data, multiple sets of diverse features are measured on the same set of samples. By integrating all available data sources, we seek to discover common group structure among the samples that may be hidden in individualistic cluster analyses of a single data-view. While several techniques for such int…
This manuscript develops the theory of agglomerative clustering with Bregman divergences. Geometric smoothing techniques are developed to deal with degenerate clusters. To allow for cluster models based on exponential families with overcomplete representations, Bregman divergences are developed for nondifferentiable co…
New algorithms recover clusters with minimal queries, connecting margins to recoverability.
Multilayer graphs are commonly used for representing different relations between entities and handling heterogeneous data processing tasks. Non-standard multilayer graph clustering methods are needed for assigning clusters to a common multilayer node set and for combining information from each layer. This paper present…
Clustering is a fundamental task in data analysis, and spectral clustering has been recognized as a promising approach to it. Given a graph describing the relationship between data, spectral clustering explores the underlying cluster structure in two stages. The first stage embeds the nodes of the graph in real space, …
Unified framework for clustering with sparse convex combinations.
Low-rank matrix is desired in many machine learning and computer vision problems. Most of the recent studies use the nuclear norm as a convex surrogate of the rank operator. However, all singular values are simply added together by the nuclear norm, and thus the rank may not be well approximated in practical problems. …
Multilayer graphs are commonly used for representing different relations between entities and handling heterogeneous data processing tasks. New challenges arise in multilayer graph clustering for assigning clusters to a common multilayer node set and for combining information from each layer. This paper presents a theo…
Proposes a new method for clustering tasks in multi-task learning.
In recent years, spectral clustering has become a standard method for data analysis used in a broad range of applications. In this paper we propose a new class of algorithms for multiway spectral clustering based on optimization of a certain "contrast function" over the unit sphere. These algorithms, partly inspired by…
New spectral clustering method for multi-layer networks improves accuracy.
SCC clusters data with supervising variables for better interpretation.
We study exact recovery conditions for convex relaxations of point cloud clustering problems, focusing on two of the most common optimization problems for unsupervised clustering: -means and -median clustering. Motivations for focusing on convex relaxations are: (a) they come with a certificate of optimality, and…
Develops a tensor mixture model for high-dimensional data clustering.
Spectral clustering has become one of the most widely used clustering techniques when the structure of the individual clusters is non-convex or highly anisotropic. Yet, despite its immense popularity, there exists fairly little theory about performance guarantees for spectral clustering. This issue is partly due to the…
This paper certifies cluster assignments from sum-of-norms clustering algorithms.
Exact partitioning of high-order planted models achieved through convex optimization.