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We present a set of algorithms implementing multidimensional scaling (MDS) for large data sets. MDS is a family of dimensionality reduction techniques using a $n \times n$ distance matrix as input, where $n$ is the number of individuals,…
Creating low dimensional representations of a high dimensional data set is an important component in many machine learning applications. How to cluster data using their low dimensional embedded space is still a challenging problem in…
We study the problem of applying spectral clustering to cluster multi-scale data, which is data whose clusters are of various sizes and densities. Traditional spectral clustering techniques discover clusters by processing a similarity…
In the Subspace Clustering with Missing Data (SCMD) problem, we are given a collection of n partially observed d-dimensional vectors. The data points are assumed to be concentrated near a union of low-dimensional subspaces. The goal of SCMD…
Classical multidimensional scaling is an important dimension reduction technique. Yet few theoretical results characterizing its statistical performance exist. This paper provides a theoretical framework for analyzing the quality of…
Robust and accurate nuclei centroid detection is important for the understanding of biological structures in fluorescence microscopy images. Existing automated nuclei localization methods face three main challenges: (1) Most of object…
One of the main challenges for hierarchical clustering is how to appropriately identify the representative points in the lower level of the cluster tree, which are going to be utilized as the roots in the higher level of the cluster tree…
We present an accelerated algorithm for hierarchical density based clustering. Our new algorithm improves upon HDBSCAN*, which itself provided a significant qualitative improvement over the popular DBSCAN algorithm. The accelerated HDBSCAN*…
High-dimensional datasets often contain multiple meaningful clusterings in different subspaces. For example, objects can be clustered either by color, weight, or size, revealing different interpretations of the given dataset. A variety of…
Density-based clustering has found numerous applications across various domains. The Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm is capable of finding clusters of varied shapes that are not linearly…
To further utilize the unsupervised features and pairwise information, we propose a general Bilevel Clustering Optimization (BCO) framework to improve the performance of clustering. And then we introduce three special cases on subspace…
A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data into a graph with edges reflecting a…
Sparse subspace clustering (SSC) is an elegant approach for unsupervised segmentation if the data points of each cluster are located in linear subspaces. This model applies, for instance, in motion segmentation if some restrictions on the…
In this paper, we describe versions of triclustering algorithms adapted for efficient calculations in distributed environments with MapReduce model or parallelisation mechanism provided by modern programming languages. OAC-family of…
The problem of estimating the number of clusters (say k) is one of the major challenges for the partitional clustering. This paper proposes an algorithm named k-SCC to estimate the optimal k in categorical data clustering. For the…
DBSCAN is a fundamental density-based clustering technique that identifies any arbitrary shape of the clusters. However, it becomes infeasible while handling big data. On the other hand, centroid-based clustering is important for detecting…
A general scheme for divisive hierarchical clustering algorithms is proposed. It is made of three main steps : first a splitting procedure for the subdivision of clusters into two subclusters, second a local evaluation of the bipartitions…
The problem of clustering noisy and incompletely observed high-dimensional data points into a union of low-dimensional subspaces and a set of outliers is considered. The number of subspaces, their dimensions, and their orientations are…
This paper focuses on density-based clustering, particularly the Density Peak (DP) algorithm and the one based on density-connectivity DBSCAN; and proposes a new method which takes advantage of the individual strengths of these two methods…
Spectral clustering is a fundamental technique in the field of data mining and information processing. Most existing spectral clustering algorithms integrate dimensionality reduction into the clustering process assisted by manifold learning…