Related papers: Phase Transitions for High Dimensional Clustering …
In this paper, we study a new type of clustering problem, called {\em Chromatic Clustering}, in high dimensional space. Chromatic clustering seeks to partition a set of colored points into groups (or clusters) so that no group contains…
We propose a new approach for clustering DNA features using array CGH data from multiple tumor samples. We distinguish data-collapsing: joining contiguous DNA clones or probes with extremely similar data into regions, from clustering:…
As data sets continue to grow in size and complexity, effective and efficient techniques are needed to target important features in the variable space. Many of the variable selection techniques that are commonly used alongside clustering…
We study constrained clustering, where constraints guide the clustering process. In existing works, two categories of constraints have been widely explored, namely pairwise and cardinality constraints. Pairwise constraints enforce the…
To cluster data is to separate samples into distinctive groups that should ideally have some cohesive properties. Today, numerous clustering algorithms exist, and their differences lie essentially in what can be perceived as ``cohesive…
Principal component analysis (PCA) is one of the most widely used dimension reduction and multivariate statistical techniques. From a probabilistic perspective, PCA seeks a low-dimensional representation of data in the presence of…
We propose a change-point detection method for large scale multiple testing problems with data having clustered signals. Unlike the classic change-point setup, the signals can vary in size within a cluster. The clustering structure on the…
Principal component analysis (PCA) is often used to analyze multivariate data together with cluster analysis, which depends on the number of principal components used. It is therefore important to determine the number of significant…
Evaluation of clinical prediction models across multiple clusters, whether centers or datasets, is becoming increasingly common. A comprehensive evaluation includes an assessment of the agreement between the estimated risks and the observed…
Motivated by the possibility of universal quantum computation under noise perturbations, we compute the phase diagram of the 2d cluster state Hamiltonian in the presence of Ising terms and magnetic fields. Unlike in previous analysis of…
We define the notion of a well-clusterable data set combining the point of view of the objective of $k$-means clustering algorithm (minimising the centric spread of data elements) and common sense (clusters shall be separated by gaps). We…
Ensuring that predicted probabilities align with observed frequencies is critical in high-stakes domains such as clinical decision support, autonomous driving and financial risk assessment. Existing calibration methods typically apply a…
We consider a group synchronization problem with multiple frequencies which involves observing pairwise relative measurements of group elements on multiple frequency channels, corrupted by Gaussian noise. We study the computational phase…
The critical and multicritical behavior of the simple cubic Ising model with nearest-neighbor, next-nearest-neighbor and plaquette interactions is studied using the cube and star-cube approximations of the cluster variation method and the…
We study the distributed computing setting in which there are multiple servers, each holding a set of points, who wish to compute functions on the union of their point sets. A key task in this setting is Principal Component Analysis (PCA),…
With inspiration from Random Forests (RF) in the context of classification, a new clustering ensemble method---Cluster Forests (CF) is proposed. Geometrically, CF randomly probes a high-dimensional data cloud to obtain "good local…
Factorizing low-rank matrices is a problem with many applications in machine learning and statistics, ranging from sparse PCA to community detection and sub-matrix localization. For probabilistic models in the Bayes optimal setting, general…
We study the clustering problem for mixtures of bounded covariance distributions, under a fine-grained separation assumption. Specifically, given samples from a $k$-component mixture distribution $D = \sum_{i =1}^k w_i P_i$, where each $w_i…
Few-shot learning aims to learn to generalize a classifier to novel classes with limited labeled data. Transductive inference that utilizes unlabeled test set to deal with low-data problem has been employed for few-shot learning in recent…
We introduce the aggregated clustering problem, where one is given $T$ instances of a center-based clustering task over the same $n$ points, but under different metrics. The goal is to open $k$ centers to minimize an aggregate of the…