A self-organising mixture network for density modelling

A completely unsupervised mixture distribution network, namely the self-organising mixture network, is proposed for learning arbitrary density functions. The algorithm minimises the Kullback-Leibler information by means of stochastic approximation methods. The density functions are modelled as mixtures of parametric distributions such as Gaussian and Cauchy. The first layer of the network is similar to the Kohonen's self-organising map (SOM), but with the parameters of the class conditional densities as the learning weights. The winning mechanism is based on maximum posterior probability, and the updating of weights can be limited to a small neighbourhood around the winner. The second layer accumulates the responses of these local nodes, weighted by the learning mixing parameters. The network possesses simple structure and computation, yet yields fast and robust convergence. Experimental results are also presente

Winner-Relaxing Self-Organizing Maps

A new family of self-organizing maps, the Winner-Relaxing Kohonen Algorithm, is introduced as a generalization of a variant given by Kohonen in 1991. The magnification behaviour is calculated analytically. For the original variant a magnification exponent of 4/7 is derived; the generalized version allows to steer the magnification in the wide range from exponent 1/2 to 1 in the one-dimensional case, thus provides optimal mapping in the sense of information theory. The Winner Relaxing Algorithm requires minimal extra computations per learning step and is conveniently easy to implement.Comment: 14 pages (6 figs included). To appear in Neural Computatio

Structure in the 3D Galaxy Distribution: I. Methods and Example Results

Three methods for detecting and characterizing structure in point data, such as that generated by redshift surveys, are described: classification using self-organizing maps, segmentation using Bayesian blocks, and density estimation using adaptive kernels. The first two methods are new, and allow detection and characterization of structures of arbitrary shape and at a wide range of spatial scales. These methods should elucidate not only clusters, but also the more distributed, wide-ranging filaments and sheets, and further allow the possibility of detecting and characterizing an even broader class of shapes. The methods are demonstrated and compared in application to three data sets: a carefully selected volume-limited sample from the Sloan Digital Sky Survey redshift data, a similarly selected sample from the Millennium Simulation, and a set of points independently drawn from a uniform probability distribution -- a so-called Poisson distribution. We demonstrate a few of the many ways in which these methods elucidate large scale structure in the distribution of galaxies in the nearby Universe.Comment: Re-posted after referee corrections along with partially re-written introduction. 80 pages, 31 figures, ApJ in Press. For full sized figures please download from: http://astrophysics.arc.nasa.gov/~mway/lss1.pd

A Hybrid Artificial Neural Network Model For Data Visualisation, Classification, And Clustering [QP363.3. T253 2006 f rb].

Tesis ini mempersembahkan penyelidikan tentang satu model hibrid rangkaian neural buatan yang boleh menghasilkan satu peta pengekalan-topologi, serupa dengan penerangan teori bagi peta otak, untuk visualisasi, klasifikasi dan pengklusteran data. In this thesis, the research of a hybrid Artificial Neural Network (ANN) model that is able to produce a topology-preserving map, which is akin to the theoretical explanation of the brain map, for data visualisation, classification, and clustering is presented

Statistical and Dynamical Modeling of Riemannian Trajectories with Application to Human Movement Analysis

abstract: The data explosion in the past decade is in part due to the widespread use of rich sensors that measure various physical phenomenon -- gyroscopes that measure orientation in phones and fitness devices, the Microsoft Kinect which measures depth information, etc. A typical application requires inferring the underlying physical phenomenon from data, which is done using machine learning. A fundamental assumption in training models is that the data is Euclidean, i.e. the metric is the standard Euclidean distance governed by the L-2 norm. However in many cases this assumption is violated, when the data lies on non Euclidean spaces such as Riemannian manifolds. While the underlying geometry accounts for the non-linearity, accurate analysis of human activity also requires temporal information to be taken into account. Human movement has a natural interpretation as a trajectory on the underlying feature manifold, as it evolves smoothly in time. A commonly occurring theme in many emerging problems is the need to \emph{represent, compare, and manipulate} such trajectories in a manner that respects the geometric constraints. This dissertation is a comprehensive treatise on modeling Riemannian trajectories to understand and exploit their statistical and dynamical properties. Such properties allow us to formulate novel representations for Riemannian trajectories. For example, the physical constraints on human movement are rarely considered, which results in an unnecessarily large space of features, making search, classification and other applications more complicated. Exploiting statistical properties can help us understand the \emph{true} space of such trajectories. In applications such as stroke rehabilitation where there is a need to differentiate between very similar kinds of movement, dynamical properties can be much more effective. In this regard, we propose a generalization to the Lyapunov exponent to Riemannian manifolds and show its effectiveness for human activity analysis. The theory developed in this thesis naturally leads to several benefits in areas such as data mining, compression, dimensionality reduction, classification, and regression.Dissertation/ThesisDoctoral Dissertation Electrical Engineering 201

A Clustering Method for Data in Cylindrical Coordinates

We propose a new clustering method for data in cylindrical coordinates based on the k-means. The goal of the k-means family is to maximize an optimization function, which requires a similarity. Thus, we need a new similarity to obtain the new clustering method for data in cylindrical coordinates. In this study, we first derive a new similarity for the new clustering method by assuming a particular probabilistic model. A data point in cylindrical coordinates has radius, azimuth, and height. We assume that the azimuth is sampled from a von Mises distribution and the radius and the height are independently generated from isotropic Gaussian distributions. We derive the new similarity from the log likelihood of the assumed probability distribution. Our experiments demonstrate that the proposed method using the new similarity can appropriately partition synthetic data defined in cylindrical coordinates. Furthermore, we apply the proposed method to color image quantization and show that the methods successfully quantize a color image with respect to the hue element

Image Compression Using Cascaded Neural Networks

Images are forming an increasingly large part of modern communications, bringing the need for efficient and effective compression. Many techniques developed for this purpose include transform coding, vector quantization and neural networks. In this thesis, a new neural network method is used to achieve image compression. This work extends the use of 2-layer neural networks to a combination of cascaded networks with one node in the hidden layer. A redistribution of the gray levels in the training phase is implemented in a random fashion to make the minimization of the mean square error applicable to a broad range of images. The computational complexity of this approach is analyzed in terms of overall number of weights and overall convergence. Image quality is measured objectively, using peak signal-to-noise ratio and subjectively, using perception. The effects of different image contents and compression ratios are assessed. Results show the performance superiority of cascaded neural networks compared to that of fixedarchitecture training paradigms especially at high compression ratios. The proposed new method is implemented in MATLAB. The results obtained, such as compression ratio and computing time of the compressed images, are presented

Image Compression Using Cascaded Neural Networks

Images are forming an increasingly large part of modern communications, bringing the need for efficient and effective compression. Many techniques developed for this purpose include transform coding, vector quantization and neural networks. In this thesis, a new neural network method is used to achieve image compression. This work extends the use of 2-layer neural networks to a combination of cascaded networks with one node in the hidden layer. A redistribution of the gray levels in the training phase is implemented in a random fashion to make the minimization of the mean square error applicable to a broad range of images. The computational complexity of this approach is analyzed in terms of overall number of weights and overall convergence. Image quality is measured objectively, using peak signal-to-noise ratio and subjectively, using perception. The effects of different image contents and compression ratios are assessed. Results show the performance superiority of cascaded neural networks compared to that of fixedarchitecture training paradigms especially at high compression ratios. The proposed new method is implemented in MATLAB. The results obtained, such as compression ratio and computing time of the compressed images, are presented