Related papers: Clustering, Encoding and Diameter Computation Algo…
In this paper we present novel algorithmic solutions for several resource processing and data transfer multicriteria optimization problems. The results of most of the presented techniques are strategies which solve the considered problems…
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…
DBSCAN is a popular density-based clustering algorithm that has many different applications in practice. However, the running time of DBSCAN in high-dimensional space or general metric space ({\em e.g.,} clustering a set of texts by using…
In cluster analysis, a common first step is to scale the data aiming to better partition them into clusters. Even though many different techniques have throughout many years been introduced to this end, it is probably fair to say that the…
Advances made to the traditional clustering algorithms solves the various problems such as curse of dimensionality and sparsity of data for multiple attributes. The traditional H-K clustering algorithm can solve the randomness and apriority…
Optimization is nothing but a mathematical technique which finds maxima or minima of any function of concern in some realistic region. Different optimization techniques are proposed which are competing for the best solution. Particle Swarm…
A fuzzy clustering algorithm for multidimensional data is proposed in this article. The data is described by vectors whose components are linguistic variables defined in an ordinal scale. The obtained results confirm the efficiency of the…
In general, the clustering problem is NP-hard, and global optimality cannot be established for non-trivial instances. For high-dimensional data, distance-based methods for clustering or classification face an additional difficulty, the…
Clustering is one of the most widely used procedures in the analysis of microarray data, for example with the goal of discovering cancer subtypes based on observed heterogeneity of genetic marks between different tissues. It is well-known…
We provide a rigorous mathematical treatment to the crowding issue in data visualization when high dimensional data sets are projected down to low dimensions for visualization. By properly adjusting the capacity of high dimensional balls,…
We consider the problem of subspace clustering: given points that lie on or near the union of many low-dimensional linear subspaces, recover the subspaces. To this end, one first identifies sets of points close to the same subspace and uses…
In this article, we continue our analysis for a novel recursive modification to the Max $k$-Cut algorithm using semidefinite programming as its basis, offering an improved performance in vectorized data clustering tasks. Using a dimension…
The use of brain images as markers for diseases or behavioral differences is challenged by the small effects size and the ensuing lack of power, an issue that has incited researchers to rely more systematically on large cohorts. Coupled…
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…
We give a simple, local process for nodes in an undirected graph to form non-adjacent clusters that (1) have at most a polylogarithmic diameter and (2) contain at least half of all vertices. Efficient deterministic distributed clustering…
The $k$-Means clustering problem on $n$ points is NP-Hard for any dimension $d\ge 2$, however, for the 1D case there exists exact polynomial time algorithms. Previous literature reported an $O(kn^2)$ time dynamic programming algorithm that…
In this paper we present several novel efficient techniques and multidimensional data structures which can improve the decision making process in many domains. We consider online range aggregation, range selection and range weighted median…
We consider the distributed source coding problem in which correlated data picked up by scattered sensors has to be encoded separately and transmitted to a common receiver, subject to a rate-distortion constraint. Although near-tooptimal…
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…
In the classic circle packing problem, one asks whether a given set of circles can be packed into a given container. Packing problems like this have been shown to be $\mathsf{NP}$-hard. In this paper, we present new sufficient conditions…