The rational cubic function with three parameters has been extended to rational bi-cubic function to visualize the shape of regular convex surface data. The rational bi-cubic function involves six parameters in each rectangular patch. Data dependent constraints are derived on four of these parameters to visualize the shape of convex surface data while other two are free to refine the shape of s...

This paper investigates the computational complexity of several clustering problems with special objective functions for point sets in the Euclidean plane. Our strongest negative result is that clustering a set of 3k points in the plane into k triangles with minimum total circumference is NP-hard. On the other hand, we identify several special cases that are solvable in polynomial time due to t...

Clustering of data around one seed does not work well if the shape of the cluster is elongated or non-convex. A complex shaped cluster requires several seeds. This study developed a nonparametric multi-seed data clustering approach which splits and merges procedures to handle the complex shapes of clusters. The splitting process utilizes a genetic algorithm to search for the appropriate cluster...

We consider approximating distributions within the framework of optimal mass transport and specialize to the problem of clustering data sets. Distances between distributions are measured in the Wasserstein metric. The main problem we consider is that of approximating sample distributions by ones with sparse support. This provides a new viewpoint to clustering. We propose different relaxations o...

We consider the problem of fitting a convex piecewise-linear function, with some specified form, to given multi-dimensional data. Except for a few special cases, this problem is hard to solve exactly, so we focus on heuristic methods that find locally optimal fits. The method we describe, which is a variation on the K-means algorithm for clustering, seems to work well in practice, at least on d...

We propose a clustering method that considers non-rigid alignment of samples. The motivation for such a clustering is training of object detectors that consist of multiple mixture components. In particular, we consider the deformable part model (DPM) of Felzenszwalb et al., where each mixture component includes a learned deformation model. We show that alignment based clustering distributes the...

Swarm Intelligence (SI) is an innovative artificial intelligence technique for solving complex optimization problems. Data clustering is the process of grouping data into a number of clusters. The goal of data clustering is to make the data in the same cluster share a high degree of similarity while being very dissimilar to data from other clusters. Clustering algorithms have been applied to a ...

clustering technique is one of the most important techniques of data mining and is the branch of multivariate statistical analysis and a method for grouping similar data in to same clusters. with the databases getting bigger, the researchers try to find efficient and effective clustering methods so that they can make fast and real decisions. thus, in this paper, we proposed an improved ant syst...

Clustering high-dimensional data often requires some form of dimensionality reduction, where clustered variables are separated from “noise-looking” variables. We cast this problem as finding a low-dimensional projection of the data which is well-clustered. This yields a one-dimensional projection in the simplest situation with two clusters, and extends naturally to a multi-label scenario for mo...

Convex optimization is one of the most robust tools for automated data analysis. It has widespread applications in fields such as machine learning, computer vision, combinatorial optimization and scientific computing. However, the rapidly increasing volume and complexity of data that needs to be processed often renders general-purpose algorithms unusable. This thesis aims to address this issue ...