Estimation of instrinsic dimension via clustering

The problem of estimating the intrinsic dimension of a set of points in high dimensional space is a critical issue for a wide range of disciplines, including genomics, finance, and networking. Current estimation techniques are dependent on either the ambient or intrinsic dimension in terms of computational complexity, which may cause these methods to become intractable for large data sets. In this paper, we present a clustering-based methodology that exploits the inherent self-similarity of data to efficiently estimate the intrinsic dimension of a set of points. When the data satisfies a specified general clustering condition, we prove that the estimated dimension approaches the true Hausdorff dimension. Experiments show that the clustering-based approach allows for more efficient and accurate intrinsic dimension estimation compared with all prior techniques, even when the data does not conform to obvious self-similarity structure. Finally, we present empirical results which show the clustering-based estimation allows for a natural partitioning of the data points that lie on separate manifolds of varying intrinsic dimension

Shape matching and clustering in design

Generalising knowledge and matching patterns is a basic human trait in re-using past experiences. We often cluster (group) knowledge of similar attributes as a process of learning and or aid to manage the complexity and re-use of experiential knowledge [1, 2]. In conceptual design, an ill-defined shape may be recognised as more than one type. Resulting in shapes possibly being classified differently when different criteria are applied. This paper outlines the work being carried out to develop a new technique for shape clustering. It highlights the current methods for analysing shapes found in computer aided sketching systems, before a method is proposed that addresses shape clustering and pattern matching. Clustering for vague geometric models and multiple viewpoint support are explored

The Data Big Bang and the Expanding Digital Universe: High-Dimensional, Complex and Massive Data Sets in an Inflationary Epoch

Recent and forthcoming advances in instrumentation, and giant new surveys, are creating astronomical data sets that are not amenable to the methods of analysis familiar to astronomers. Traditional methods are often inadequate not merely because of the size in bytes of the data sets, but also because of the complexity of modern data sets. Mathematical limitations of familiar algorithms and techniques in dealing with such data sets create a critical need for new paradigms for the representation, analysis and scientific visualization (as opposed to illustrative visualization) of heterogeneous, multiresolution data across application domains. Some of the problems presented by the new data sets have been addressed by other disciplines such as applied mathematics, statistics and machine learning and have been utilized by other sciences such as space-based geosciences. Unfortunately, valuable results pertaining to these problems are mostly to be found only in publications outside of astronomy. Here we offer brief overviews of a number of concepts, techniques and developments, some "old" and some new. These are generally unknown to most of the astronomical community, but are vital to the analysis and visualization of complex datasets and images. In order for astronomers to take advantage of the richness and complexity of the new era of data, and to be able to identify, adopt, and apply new solutions, the astronomical community needs a certain degree of awareness and understanding of the new concepts. One of the goals of this paper is to help bridge the gap between applied mathematics, artificial intelligence and computer science on the one side and astronomy on the other.Comment: 24 pages, 8 Figures, 1 Table. Accepted for publication: "Advances in Astronomy, special issue "Robotic Astronomy

Machine learning techniques applied to multiband spectrum sensing in cognitive radios

This research received funding of the Mexican National Council of Science and Technology (CONACYT), Grant (no. 490180). Also, this work was supported by the Program for Professional Development Teacher (PRODEP).In this work, three specific machine learning techniques (neural networks, expectation maximization and k-means) are applied to a multiband spectrum sensing technique for cognitive radios. All of them have been used as a classifier using the approximation coefficients from a Multiresolution Analysis in order to detect presence of one or multiple primary users in a wideband spectrum. Methods were tested on simulated and real signals showing a good performance. The results presented of these three methods are effective options for detecting primary user transmission on the multiband spectrum. These methodologies work for 99% of cases under simulated signals of SNR higher than 0 dB and are feasible in the case of real signalsPeer ReviewedPostprint (published version

A Fully Unsupervised Texture Segmentation Algorithm

This paper presents a fully unsupervised texture segmentation algorithm by using a modified discrete wavelet frames decomposition and a mean shift algorithm. By fully unsupervised, we mean the algorithm does not require any knowledge of the type of texture present nor the number of textures in the image to be segmented. The basic idea of the proposed method is to use the modified discrete wavelet frames to extract useful information from the image. Then, starting from the lowest level, the mean shift algorithm is used together with the fuzzy c-means clustering to divide the data into an appropriate number of clusters. The data clustering process is then refined at every level by taking into account the data at that particular level. The final crispy segmentation is obtained at the root level. This approach is applied to segment a variety of composite texture images into homogeneous texture areas and very good segmentation results are reported