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Comparison of three kind of the clustering and find cost function and loss function and calculate them. Error rate of the clustering methods and how to calculate the error percentage always be one on the important factor for evaluating the…

In the context of clustering, we consider a generative model in a Euclidean ambient space with clusters of different shapes, dimensions, sizes and densities. In an asymptotic setting where the number of points becomes large, we obtain…

Clustering is a fundamental problem in data analysis. In differentially private clustering, the goal is to identify $k$ cluster centers without disclosing information on individual data points. Despite significant research progress, the…

This paper proposes a Mixed-Integer Linear Programming approach for the Soft Graph Clustering Problem. This is the first method that simultaneously allocates membership proportion for vertices that lie in multiple clusters, and that…

Bayesian nonparametrics are a class of probabilistic models in which the model size is inferred from data. A recently developed methodology in this field is small-variance asymptotic analysis, a mathematical technique for deriving learning…

The nonparametric formulation of density-based clustering, known as modal clustering, draws a correspondence between groups and the attraction domains of the modes of the density function underlying the data. Its probabilistic foundation…

We present a hierarchical maximum-margin clustering method for unsupervised data analysis. Our method extends beyond flat maximum-margin clustering, and performs clustering recursively in a top-down manner. We propose an effective greedy…

The Bayesian approach to inference stands out for naturally allowing borrowing information across heterogeneous populations, with different samples possibly sharing the same distribution. A popular Bayesian nonparametric model for…

Clustering is one of the most fundamental and wide-spread techniques in exploratory data analysis. Yet, the basic approach to clustering has not really changed: a practitioner hand-picks a task-specific clustering loss to optimize and fit…

The goal of data clustering is to partition data points into groups to minimize a given objective function. While most existing clustering algorithms treat each data point as vector, in many applications each datum is not a vector but a…

Identification of clusters of co-expressed genes in transcriptomic data is a difficult task. Most algorithms used for this purpose can be classified into two broad categories: distance-based or model-based approaches. Distance-based…

Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph. This non-linear transformation of the data is both the key of…

A novel framework for consensus clustering is presented which has the ability to determine both the number of clusters and a final solution using multiple algorithms. A consensus similarity matrix is formed from an ensemble using multiple…

This paper proposes a centroid-based clustering algorithm which is capable of clustering data-points with n-features, without having to specify the number of clusters to be formed. The core logic behind the algorithm is a similarity…

Gaussian mixture model is very useful in many practical problems. Nevertheless, it cannot be directly generalized to non Euclidean spaces. To overcome this problem we present a spherical Gaussian-based clustering approach for partitioning…

Clustering under pairwise constraints is an important knowledge discovery tool that enables the learning of appropriate kernels or distance metrics to improve clustering performance. These pairwise constraints, which come in the form of…

Density based spatial clustering of points in $\mathbb{R}^n$ has a myriad of applications in a variety of industries. We generalise this problem to the density based clustering of lines in high-dimensional spaces, keeping in mind there…

The problem of clustering is considered, for the case when each data point is a sample generated by a stationary ergodic process. We propose a very natural asymptotic notion of consistency, and show that simple consistent algorithms exist,…

The problem of clustering is considered, for the case when each data point is a sample generated by a stationary ergodic process. We propose a very natural asymptotic notion of consistency, and show that simple consistent algorithms exist,…

This paper considers a canonical clustering problem where one receives unlabeled samples drawn from a balanced mixture of two elliptical distributions and aims for a classifier to estimate the labels. Many popular methods including PCA and…