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Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a…

Subspace clustering methods based on expressing each data point as a linear combination of all other points in a dataset are popular unsupervised learning techniques. However, existing methods incur high computational complexity on…

In this paper, we address the problem of learning compact similarity-preserving embeddings for massive high-dimensional streams of data in order to perform efficient similarity search. We present a new online method for computing binary…

Clustering is a crucial tool for analyzing data in virtually every scientific and engineering discipline. There are more scalable solutions framed to enable time and space clustering for the future large-scale data analyses. As a result,…

The computational complexity of internal diffusion-limited aggregation (DLA) is examined from both a theoretical and a practical point of view. We show that for two or more dimensions, the problem of predicting the cluster from a given set…

Recent advancement of the WWW, IOT, social network, e-commerce, etc. have generated a large volume of data. These datasets are mostly represented by high dimensional and sparse datasets. Many fundamental subroutines of common data analytic…

Subsampling from a large data set is useful in many supervised learning contexts to provide a global view of the data based on only a fraction of the observations. Diverse (or space-filling) subsampling is an appealing subsampling approach…

Deep multi-view subspace clustering (DMVSC) has recently attracted increasing attention due to its promising performance. However, existing DMVSC methods still have two issues: (1) they mainly focus on using autoencoders to nonlinearly…

Fixed-radius near neighbor search is a fundamental data operation that retrieves all data points within a user-specified distance to a query point. There are efficient algorithms that can provide fast approximate query responses, but they…

In this paper we consider the problem of clustering collections of very short texts using subspace clustering. This problem arises in many applications such as product categorisation, fraud detection, and sentiment analysis. The main…

In this paper, we present a deep extension of Sparse Subspace Clustering, termed Deep Sparse Subspace Clustering (DSSC). Regularized by the unit sphere distribution assumption for the learned deep features, DSSC can infer a new data…

Cluster analysis faces two problems in high dimensions: first, the `curse of dimensionality' that can lead to overfitting and poor generalization performance; and second, the sheer time taken for conventional algorithms to process large…

In this paper we present novel algorithms for several multidimensional data processing problems. We consider problems related to the computation of restricted clusters and of the diameter of a set of points using a new distance function. We…

Density-based cluster mining is known to serve a broad range of applications ranging from stock trade analysis to moving object monitoring. Although methods for efficient extraction of density-based clusters have been studied in the…

Approximate Nearest Neighbor Search (ANNS) in high-dimensional space is an essential operator in many online services, such as information retrieval and recommendation. Indices constructed by the state-of-the-art ANNS algorithms must be…

We develop a new density-based clustering algorithm named CRAD which is based on a new neighbor searching function with a robust data depth as the dissimilarity measure. Our experiments prove that the new CRAD is highly competitive at…

The minimum sum-of-squares clustering problem (MSSC), also known as $k$-means clustering, refers to the problem of partitioning $n$ data points into $k$ clusters, with the objective of minimizing the total sum of squared Euclidean distances…

$k$-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 use of brain images as markers for diseases or behavioral differences is challenged by the small effects size and the ensuing lack of power, an issue that has incited researchers to rely more systematically on large cohorts. Coupled…

The success of deep learning hinges on enormous data and large models, which require labor-intensive annotations and heavy computation costs. Subset selection is a fundamental problem that can play a key role in identifying smaller portions…