Unsupervised learning is becoming an essential tool to analyze the increasingly large
amounts of data produced by atomistic and molecular simulations, in material science, solid …

Clustering, as an unsupervised learning, is aimed at discovering the natural grou**s of a
set of patterns, points, or objects. In clustering algorithms, a significant problem is the …

K-means is one of the most simple and popular clustering algorithms, which implemented as
a standard clustering method in most of machine learning researches. The goal of K-means …

Quantum information is a promising new paradigm for fast computations that can provide
substantial speedups for many algorithms we use today. Among them, quantum machine …

Hypergraphs, which belong to the family of higher-order networks, are a natural and
powerful choice for modeling group interactions in the real world. For example, when …

We design a new distribution over m× n matrices S so that, for any fixed n× d matrix A of rank
r, with probability at least 9/10,∥ SAx∥ 2=(1±ε)∥ Ax∥ 2 simultaneously for all x∈ R d …

Low-rank matrix approximations, such as the truncated singular value decomposition and
the rank-revealing QR decomposition, play a central role in data analysis and scientific …

Randomized algorithms for very large matrix problems have received a great deal of
attention in recent years. Much of this work was motivated by problems in large-scale data …

We develop and analyze a method to reduce the size of a very large set of data points in a
high-dimensional Euclidean space R^d to a small set of weighted points such that the result …

Principal components analysis (PCA) is a well-known technique for approximating a tabular
data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets …