Related papers: Randomized Clustered Nystrom for Large-Scale Kerne…
Clustering samples according to an effective metric and/or vector space representation is a challenging unsupervised learning task with a wide spectrum of applications. Among several clustering algorithms, k-means and its kernelized version…
The essential difficulty of gradient-based bilevel optimization using implicit differentiation is to estimate the inverse Hessian vector product with respect to neural network parameters. This paper proposes to tackle this problem by the…
Clustering is an effective technique in data mining to generate groups that are the matter of interest. Among various clustering approaches, the family of k-means algorithms and min-cut algorithms gain most popularity due to their…
One of the major limits of kernel ridge regression (KRR) is that storing and manipulating the kernel matrix K_n for n samples requires O(n^2) space, which rapidly becomes unfeasible for large n. Nystrom approximations reduce the space…
Markov state models (MSMs) have become a popular approach for investigating the conformational dynamics of proteins and other biomolecules. MSMs are typically built from numerous molecular dynamics simulations by dividing the sampled…
We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…
Despite the growing popularity of explainable and interpretable machine learning, there is still surprisingly limited work on inherently interpretable clustering methods. Recently, there has been a surge of interest in explaining the…
Existing approaches remain largely constrained by traditional distance metrics, limiting their effectiveness in handling random data. In this work, we introduce the first k-means variant in the literature that operates within a…
This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of…
This work considers the low-rank approximation of a matrix $A(t)$ depending on a parameter $t$ in a compact set $D \subset \mathbb{R}^d$. Application areas that give rise to such problems include computational statistics and dynamical…
The bilateral and nonlocal means filters are instances of kernel-based filters that are popularly used in image processing. It was recently shown that fast and accurate bilateral filtering of grayscale images can be performed using a…
We investigate how to train kernel approximation methods that generalize well under a memory budget. Building on recent theoretical work, we define a measure of kernel approximation error which we find to be more predictive of the empirical…
We provide the first mathematically complete derivation of the Nystr\"om method for low-rank approximation of indefinite kernels and propose an efficient method for finding an approximate eigendecomposition of such kernel matrices. Building…
This paper introduces a novel K-means clustering algorithm, an advancement on the conventional Big-means methodology. The proposed method efficiently integrates parallel processing, stochastic sampling, and competitive optimization to…
Clustering is a widely used and powerful machine learning technique, but its effectiveness is often limited by the need to specify the number of clusters, k, or by relying on thresholds that implicitly determine k. We introduce k*-means, a…
A new maximum approximate likelihood (ML) estimation algorithm for the mixture of Kent distribution is proposed. The new algorithm is constructed via the BSLM (block successive lower-bound maximization) framework and incorporates manifold…
We develop an accelerated algorithm for computing an approximate eigenvalue decomposition of bistochastic normalized kernel matrices. Our approach constructs a low rank approximation of the original kernel matrix by the pivoted partial…
K-Means algorithm is a popular clustering method. However, it has two limitations: 1) it gets stuck easily in spurious local minima, and 2) the number of clusters k has to be given a priori. To solve these two issues, a multi-prototypes…
This paper concerns the distributed training of nonlinear kernel machines on Map-Reduce. We show that a re-formulation of Nystr\"om approximation based solution which is solved using gradient based techniques is well suited for this,…
This thesis aims to invent new approaches for making inferences with the k-means algorithm. k-means is an iterative clustering algorithm that randomly assigns k centroids, then assigns data points to the nearest centroid, and updates…