Improving K-means clustering with enhanced Firefly Algorithms

In this research, we propose two variants of the Firefly Algorithm (FA), namely inward intensified exploration FA (IIEFA) and compound intensified exploration FA (CIEFA), for undertaking the obstinate problems of initialization sensitivity and local optima traps of the K-means clustering model. To enhance the capability of both exploitation and exploration, matrix-based search parameters and dispersing mechanisms are incorporated into the two proposed FA models. We first replace the attractiveness coefficient with a randomized control matrix in the IIEFA model to release the FA from the constraints of biological law, as the exploitation capability in the neighbourhood is elevated from a one-dimensional to multi-dimensional search mechanism with enhanced diversity in search scopes, scales, and directions. Besides that, we employ a dispersing mechanism in the second CIEFA model to dispatch fireflies with high similarities to new positions out of the close neighbourhood to perform global exploration. This dispersing mechanism ensures sufficient variance between fireflies in comparison to increase search efficiency. The ALL-IDB2 database, a skin lesion data set, and a total of 15 UCI data sets are employed to evaluate efficiency of the proposed FA models on clustering tasks. The minimum Redundancy Maximum Relevance (mRMR)-based feature selection method is also adopted to reduce feature dimensionality. The empirical results indicate that the proposed FA models demonstrate statistically significant superiority in both distance and performance measures for clustering tasks in comparison with conventional K-means clustering, five classical search methods, and five advanced FA variants

Study of Small-Scale Anisotropy of Ultrahigh Energy Cosmic Rays Observed in Stereo by HiRes

The High Resolution Fly's Eye (HiRes) experiment is an air fluorescence detector which, operating in stereo mode, has a typical angular resolution of 0.6 degrees and is sensitive to cosmic rays with energies above 10^18 eV. HiRes is thus an excellent instrument for the study of the arrival directions of ultrahigh energy cosmic rays. We present the results of a search for anisotropies in the distribution of arrival directions on small scales (<5 degrees) and at the highest energies (>10^19 eV). The search is based on data recorded between 1999 December and 2004 January, with a total of 271 events above 10^19 eV. No small-scale anisotropy is found, and the strongest clustering found in the HiRes stereo data is consistent at the 52% level with the null hypothesis of isotropically distributed arrival directions.Comment: 4 pages, 3 figures. Matches accepted ApJL versio

Subspace Clustering via Optimal Direction Search

This letter presents a new spectral-clustering-based approach to the subspace clustering problem. Underpinning the proposed method is a convex program for optimal direction search, which for each data point d finds an optimal direction in the span of the data that has minimum projection on the other data points and non-vanishing projection on d. The obtained directions are subsequently leveraged to identify a neighborhood set for each data point. An alternating direction method of multipliers framework is provided to efficiently solve for the optimal directions. The proposed method is shown to notably outperform the existing subspace clustering methods, particularly for unwieldy scenarios involving high levels of noise and close subspaces, and yields the state-of-the-art results for the problem of face clustering using subspace segmentation

Search for Small-Scale Anisotropy of Cosmic Rays above 10^19 eV with HiRes Stereo

We present the results of a search for small-scale anisotropy in the distribution of arrival directions of cosmic rays above 10^19 eV measured in stereo by the High Resolution Fly's Eye (HiRes) experiment. Performing an autocorrelation scan in energy and angular separation, we find that the strongest correlation signal in the HiRes stereo data set recorded between December 1999 and January 2004 is consistent with the null hypothesis of isotropically distributed arrival directions. These results are compared to previous claims of significant small-scale clustering in the AGASA data set.Comment: 6 pages, 4 figures; to appear in the proceedings of CRIS 2004, Catania, Italy, 31 May - 4 June 2004 (Nuclear Phys. B

Search for Point Sources of Ultra-High Energy Cosmic Rays Above 40 EeV Using a Maximum Likelihood Ratio Test

We present the results of a search for cosmic ray point sources at energies above 40 EeV in the combined data sets recorded by the AGASA and HiRes stereo experiments. The analysis is based on a maximum likelihood ratio test using the probability density function for each event rather than requiring an a priori choice of a fixed angular bin size. No statistically significant clustering of events consistent with a point source is found.Comment: 7 pages, 7 figures. Accepted for publication in The Astrophysical Journa

Innovation Pursuit: A New Approach to Subspace Clustering

In subspace clustering, a group of data points belonging to a union of subspaces are assigned membership to their respective subspaces. This paper presents a new approach dubbed Innovation Pursuit (iPursuit) to the problem of subspace clustering using a new geometrical idea whereby subspaces are identified based on their relative novelties. We present two frameworks in which the idea of innovation pursuit is used to distinguish the subspaces. Underlying the first framework is an iterative method that finds the subspaces consecutively by solving a series of simple linear optimization problems, each searching for a direction of innovation in the span of the data potentially orthogonal to all subspaces except for the one to be identified in one step of the algorithm. A detailed mathematical analysis is provided establishing sufficient conditions for iPursuit to correctly cluster the data. The proposed approach can provably yield exact clustering even when the subspaces have significant intersections. It is shown that the complexity of the iterative approach scales only linearly in the number of data points and subspaces, and quadratically in the dimension of the subspaces. The second framework integrates iPursuit with spectral clustering to yield a new variant of spectral-clustering-based algorithms. The numerical simulations with both real and synthetic data demonstrate that iPursuit can often outperform the state-of-the-art subspace clustering algorithms, more so for subspaces with significant intersections, and that it significantly improves the state-of-the-art result for subspace-segmentation-based face clustering