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We combine K-means clustering with the least-squares kernel classification method. K-means clustering is used to extract a set of representative vectors for each class. The least-squares kernel method uses these representative vectors as a…
Cluster analysis plays an important role in decision making process for many knowledge-based systems. There exist a wide variety of different approaches for clustering applications including the heuristic techniques, probabilistic models,…
This paper presents a novel method for clustering surfaces. The proposal involves first using basis functions in a tensor product to smooth the data and thus reduce the dimension to a finite number of coefficients, and then using these…
The classical k-means clustering, based on distances computed from all data features, cannot be directly applied to incomplete data with missing values. A natural extension of k-means to missing data, namely k-POD, uses only the observed…
K-means is an effective clustering technique used to separate similar data into groups based on initial centroids of clusters. In this paper, Normalization based K-means clustering algorithm(N-K means) is proposed. Proposed N-K means…
Count data is becoming more and more ubiquitous in a wide range of applications, with datasets growing both in size and in dimension. In this context, an increasing amount of work is dedicated to the construction of statistical models…
Quantum Clustering is a powerful method to detect clusters in data with mixed density. However, it is very sensitive to a length parameter that is inherent to the Schr\"odinger equation. In addition, linking data points into clusters…
To cluster data that are not linearly separable in the original feature space, $k$-means clustering was extended to the kernel version. However, the performance of kernel $k$-means clustering largely depends on the choice of kernel…
We show that the objective function of conventional k-means clustering can be expressed as the Frobenius norm of the difference of a data matrix and a low rank approximation of that data matrix. In short, we show that k-means clustering is…
Kernel methods are powerful learning methodologies that allow to perform non-linear data analysis. Despite their popularity, they suffer from poor scalability in big data scenarios. Various approximation methods, including random feature…
Clustering is one of the most fundamental problems in data analysis and it has been studied extensively in the literature. Though many clustering algorithms have been proposed, clustering theories that justify the use of these clustering…
Center-based clustering has attracted significant research interest from both theory and practice. In many practical applications, input data often contain background knowledge that can be used to improve clustering results. In this work,…
Clustering is a long-standing research problem and a fundamental tool in AI and data analysis. The traditional k-center problem, a fundamental theoretical challenge in clustering, has a best possible approximation ratio of 2, and any…
Correlation clustering is a technique for aggregating data based on qualitative information about which pairs of objects are labeled 'similar' or 'dissimilar.' Because the optimization problem is NP-hard, much of the previous literature…
A new procedure for simultaneously finding the optimal cluster structure of multivariate functional objects and finding the subspace to represent the cluster structure is presented. The method is based on the $k$-means criterion for…
Scaling clustering algorithms to massive data sets is a challenging task. Recently, several successful approaches based on data summarization methods, such as coresets and sketches, were proposed. While these techniques provide provably…
We study in this paper the problem of jointly clustering and learning representations. As several previous studies have shown, learning representations that are both faithful to the data to be clustered and adapted to the clustering…
Cluster analysis requires many decisions: the clustering method and the implied reference model, the number of clusters and, often, several hyper-parameters and algorithms' tunings. In practice, one produces several partitions, and a final…
In many situations where the interest lies in identifying clusters one might expect that not all available variables carry information about these groups. Furthermore, data quality (e.g. outliers or missing entries) might present a serious…
Pseudo-Centroid Clustering replaces the traditional concept of a centroid expressed as a center of gravity with the notion of a pseudo-centroid (or a coordinate free centroid) which has the advantage of applying to clustering problems where…