Related papers: Scalable Kernel K-Means Clustering with Nystrom Ap…
Kernel methods provide a theoretically grounded framework for non-linear and non-parametric learning, with strong analytic foundations and statistical guarantees. Yet, their scalability has long been limited by prohibitive time and memory…
We initiate the study of the following general clustering problem. We seek to partition a given set $P$ of data points into $k$ clusters by finding a set $X$ of $k$ centers and assigning each data point to one of the centers. The cost of a…
We demonstrate that distributed block coordinate descent can quickly solve kernel regression and classification problems with millions of data points. Armed with this capability, we conduct a thorough comparison between the full kernel, the…
In a geometric $k$-clustering problem the goal is to partition a set of points in $\mathbb{R}^d$ into $k$ subsets such that a certain cost function of the clustering is minimized. We present data structures for orthogonal range-clustering…
$k$-Clustering in $\mathbb{R}^d$ (e.g., $k$-median and $k$-means) is a fundamental machine learning problem. While near-linear time approximation algorithms were known in the classical setting for a dataset with cardinality $n$, it remains…
The widely applied k-means algorithm produces clusterings that violate our expectations with respect to high/low similarity/density and is in conflict with Kleinberg's axiomatic system for distance based clustering algorithms that…
The Nystr\"om method is one of the most popular techniques for improving the scalability of kernel methods. However, it has not yet been derived for kernel PCA in line with classical PCA. In this paper we derive kernel PCA with the…
Clustering is a fundamental unsupervised learning approach. Many clustering algorithms -- such as $k$-means -- rely on the euclidean distance as a similarity measure, which is often not the most relevant metric for high dimensional data…
We propose a simple yet effective multiple kernel clustering algorithm, termed simple multiple kernel k-means (SimpleMKKM). It extends the widely used supervised kernel alignment criterion to multi-kernel clustering. Our criterion is given…
The k-means clustering algorithm is a popular algorithm that partitions data into k clusters. There are many improvements to accelerate the standard algorithm. Most current research employs upper and lower bounds on point-to-cluster…
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…
Bateni et al. has recently introduced the weak-strong distance oracle model to study clustering problems in settings with limited distance information. Given query access to the strong-oracle and weak-oracle in the weak-strong oracle model,…
This paper studies the optimality of kernel methods in high-dimensional data clustering. Recent works have studied the large sample performance of kernel clustering in the high-dimensional regime, where Euclidean distance becomes less…
The classical center based clustering problems such as $k$-means/median/center assume that the optimal clusters satisfy the locality property that the points in the same cluster are close to each other. A number of clustering problems arise…
Recent work has focused on combining kernel methods and deep learning to exploit the best of the two approaches. Here, we introduce a new architecture of neural networks in which we replace the top dense layers of standard convolutional…
As a promising step, the performance of data analysis and feature learning are able to be improved if certain pattern matching mechanism is available. One of the feasible solutions can refer to the importance estimation of instances, and…
\textit{Clustering problems} often arise in the fields like data mining, machine learning etc. to group a collection of objects into similar groups with respect to a similarity (or dissimilarity) measure. Among the clustering problems,…
K-means is an effective clustering technique used to separate similar data into groups based on initial centroids of clusters. In this paper, Normalization based K-means clustering algorithm(N-K means) is proposed. Proposed N-K means…
We consider the classical $k$-means clustering problem in the setting bi-criteria approximation, in which an algoithm is allowed to output $\beta k > k$ clusters, and must produce a clustering with cost at most $\alpha$ times the to the…
Scalable kernel methods, including kernel ridge regression, often rely on low-rank matrix approximations using the Nystrom method, which involves selecting landmark points from large data sets. The existing approaches to selecting landmarks…