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Clustering is a common technique for statistical data analysis, which is used in many fields, including machine learning, data mining, pattern recognition, image analysis and bioinformatics. Clustering is the process of grouping similar…
Most convex and nonconvex clustering algorithms come with one crucial parameter: the $k$ in $k$-means. To this day, there is not one generally accepted way to accurately determine this parameter. Popular methods are simple yet theoretically…
Extended Vision techniques are ubiquitous in physics. However, the data cubes steaming from such analysis often pose a challenge in their interpretation, due to the intrinsic difficulty in discerning the relevant information from the…
The problem of dimension reduction is of increasing importance in modern data analysis. In this paper, we consider modeling the collection of points in a high dimensional space as a union of low dimensional subspaces. In particular we…
Biclustering algorithms play a central role in the biotechnological and biomedical domains. The knowledge extracted supports the extraction of putative regulatory modules, essential to understanding diseases, aiding therapy research, and…
Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior…
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…
Mining Time Series data has a tremendous growth of interest in today's world. To provide an indication various implementations are studied and summarized to identify the different problems in existing applications. Clustering time series is…
With the advancement in image capturing device, the image data been generated at high volume. If images are analyzed properly, they can reveal useful information to the human users. Content based image retrieval address the problem of…
Clustering is one of the most fundamental problems in unsupervised learning with a large number of applications. However, classical clustering algorithms assume that the data is static, thus failing to capture many real-world applications…
Clustering is one of the most fundamental tools in data science and machine learning, and k-means clustering is one of the most common such methods. There is a variety of approximate algorithms for the k-means problem, but computing the…
Machine learning algorithms perform well on identifying patterns in many different datasets due to their versatility. However, as one increases the size of the dataset, the computation time for training and using these statistical models…
Given a set of points $P \subset \mathbb{R}^d$, the $k$-means clustering problem is to find a set of $k$ {\em centers} $C = \{c_1,...,c_k\}, c_i \in \mathbb{R}^d,$ such that the objective function $\sum_{x \in P} d(x,C)^2$, where $d(x,C)$…
The $k$-means algorithm is arguably the most popular nonparametric clustering method but cannot generally be applied to datasets with incomplete records. The usual practice then is to either impute missing values under an assumed…
We propose an algorithm for clustering high dimensional data. If $P$ features for $N$ objects are represented in an $N\times P$ matrix ${\bf X}$, where $N\ll P$, the method is based on exploiting the cluster-dependent structure of the…
Kernel-based K-means clustering has gained popularity due to its simplicity and the power of its implicit non-linear representation of the data. A dominant concern is the memory requirement since memory scales as the square of the number of…
Random restart of a given algorithm produces many partitions to yield a consensus clustering. Ensemble methods such as consensus clustering have been recognized as more robust approaches for data clustering than single clustering…
Clustering, or grouping, dataset elements based on similarity can be used not only to classify a dataset into a few categories, but also to approximate it by a relatively large number of representative elements. In the latter scenario,…
Spectral clustering is a popular clustering method. It first maps data into the spectral embedding space and then uses Kmeans to find clusters. However, the two decoupled steps prohibit joint optimization for the optimal solution. In…
Coupled cluster theory is a vital cornerstone of electronic structure theory and is being applied to ever-larger systems. Stochastic approaches to quantum chemistry have grown in importance and offer compelling advantages over traditional…