Cartes auto-organisées pour l'analyse exploratoire de données et la visualisation

Article de synthèse sur les applications de l'algorithme de Kohonen pour la visualisation et l'analyse de donnéesThis paper shows how to use the Kohonen algorithm to represent multidimensional data, by exploiting the self-organizing property. It is possible to get such maps as well for quantitative variables as for qualitative ones, or for a mixing of both. The contents of the paper come from various works by SAMOS-MATISSE members, in particular by E. de Bodt, B. Girard, P. Letrémy, S. Ibbou, P. Rousset. Most of the examples have been studied with the computation routines written by Patrick Letrémy, with the language IML-SAS, which are available on the WEB page http://samos.univ-paris1.fr

Self-organising maps : statistical analysis, treatment and applications.

This thesis presents some substantial theoretical analyses and optimal treatments of Kohonen's self-organising map (SOM) algorithm, and explores the practical application potential of the algorithm for vector quantisation, pattern classification, and image processing. It consists of two major parts. In the first part, the SOM algorithm is investigated and analysed from a statistical viewpoint. The proof of its universal convergence for any dimensionality is obtained using a novel and extended form of the Central Limit Theorem. Its feature space is shown to be an approximate multivariate Gaussian process, which will eventually converge and form a mapping, which minimises the mean-square distortion between the feature and input spaces. The diminishing effect of the initial states and implicit effects of the learning rate and neighbourhood function on its convergence and ordering are analysed and discussed. Distinct and meaningful definitions, and associated measures, of its ordering are presented in relation to map's fault-tolerance. The SOM algorithm is further enhanced by incorporating a proposed constraint, or Bayesian modification, in order to achieve optimal vector quantisation or pattern classification. The second part of this thesis addresses the task of unsupervised texture-image segmentation by means of SOM networks and model-based descriptions. A brief review of texture analysis in terms of definitions, perceptions, and approaches is given. Markov random field model-based approaches are discussed in detail. Arising from this a hierarchical self-organised segmentation structure, which consists of a local MRF parameter estimator, a SOM network, and a simple voting layer, is proposed and is shown, by theoretical analysis and practical experiment, to achieve a maximum likelihood or maximum a posteriori segmentation. A fast, simple, but efficient boundary relaxation algorithm is proposed as a post-processor to further refine the resulting segmentation. The class number validation problem in a fully unsupervised segmentation is approached by a classical, simple, and on-line minimum mean-square-error method. Experimental results indicate that this method is very efficient for texture segmentation problems. The thesis concludes with some suggestions for further work on SOM neural networks

Soft self-organizing map.

by John Pui-fai Sum.Thesis (M.Phil.)--Chinese University of Hong Kong, 1995.Includes bibliographical references (leaves 99-104).Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Motivation --- p.1Chapter 1.2 --- Idea of SSOM --- p.3Chapter 1.3 --- Other Approaches --- p.3Chapter 1.4 --- Contribution of the Thesis --- p.4Chapter 1.5 --- Outline of Thesis --- p.5Chapter 2 --- Self-Organizing Map --- p.7Chapter 2.1 --- Introduction --- p.7Chapter 2.2 --- Algorithm of SOM --- p.8Chapter 2.3 --- Illustrative Example --- p.10Chapter 2.4 --- Property of SOM --- p.14Chapter 2.4.1 --- Convergence property --- p.14Chapter 2.4.2 --- Topological Order --- p.15Chapter 2.4.3 --- Objective Function of SOM --- p.15Chapter 2.5 --- Conclusion --- p.17Chapter 3 --- Algorithms for Soft Self-Organizing Map --- p.18Chapter 3.1 --- Competitive Learning and Soft Competitive Learning --- p.19Chapter 3.2 --- How does SOM generate ordered map? --- p.21Chapter 3.3 --- Algorithms of Soft SOM --- p.23Chapter 3.4 --- Simulation Results --- p.25Chapter 3.4.1 --- One dimensional map under uniform distribution --- p.25Chapter 3.4.2 --- One dimensional map under Gaussian distribution --- p.27Chapter 3.4.3 --- Two dimensional map in a unit square --- p.28Chapter 3.5 --- Conclusion --- p.30Chapter 4 --- Application to Uncover Vowel Relationship --- p.31Chapter 4.1 --- Experiment Set Up --- p.32Chapter 4.1.1 --- Network structure --- p.32Chapter 4.1.2 --- Training procedure --- p.32Chapter 4.1.3 --- Relationship Construction Scheme --- p.34Chapter 4.2 --- Results --- p.34Chapter 4.2.1 --- Hidden-unit labeling for SSOM2 --- p.34Chapter 4.2.2 --- Hidden-unit labeling for SOM --- p.35Chapter 4.3 --- Conclusion --- p.37Chapter 5 --- Application to vowel data transmission --- p.42Chapter 5.1 --- Introduction --- p.42Chapter 5.2 --- Simulation --- p.45Chapter 5.2.1 --- Setup --- p.45Chapter 5.2.2 --- Noise model and demodulation scheme --- p.46Chapter 5.2.3 --- Performance index --- p.46Chapter 5.2.4 --- Control experiment: random coding scheme --- p.46Chapter 5.3 --- Results --- p.47Chapter 5.3.1 --- Null channel noise (σ = 0) --- p.47Chapter 5.3.2 --- Small channel noise (0 ≤ σ ≤1) --- p.49Chapter 5.3.3 --- Large channel noise (1 ≤σ ≤7) --- p.49Chapter 5.3.4 --- Very large channel noise (σ > 7) --- p.49Chapter 5.4 --- Conclusion --- p.50Chapter 6 --- Convergence Analysis --- p.53Chapter 6.1 --- Kushner and Clark Lemma --- p.53Chapter 6.2 --- Condition for the Convergence of Jou's Algorithm --- p.54Chapter 6.3 --- Alternative Proof on the Convergence of Competitive Learning --- p.56Chapter 6.4 --- Convergence of Soft SOM --- p.58Chapter 6.5 --- Convergence of SOM --- p.60Chapter 7 --- Conclusion --- p.61Chapter 7.1 --- Limitations of SSOM --- p.62Chapter 7.2 --- Further Research --- p.63Chapter A --- Proof of Corollary1 --- p.65Chapter A.l --- Mean Average Update --- p.66Chapter A.2 --- Case 1: Uniform Distribution --- p.68Chapter A.3 --- Case 2: Logconcave Distribution --- p.70Chapter A.4 --- Case 3: Loglinear Distribution --- p.72Chapter B --- Different Senses of neighborhood --- p.79Chapter B.l --- Static neighborhood: Kohonen's sense --- p.79Chapter B.2 --- Dynamic neighborhood --- p.80Chapter B.2.1 --- Mou-Yeung Definition --- p.80Chapter B.2.2 --- Martinetz et al. Definition --- p.81Chapter B.2.3 --- Tsao-Bezdek-Pal Definition --- p.81Chapter B.3 --- Example --- p.82Chapter B.4 --- Discussion --- p.84Chapter C --- Supplementary to Chapter4 --- p.86Chapter D --- Quadrature Amplitude Modulation --- p.92Chapter D.l --- Amplitude Modulation --- p.92Chapter D.2 --- QAM --- p.93Bibliography --- p.9

Simulating sensorimotor systems with cortical topology

Due to the character of the original source materials and the nature of batch digitization, quality control issues may be present in this document. Please report any quality issues you encounter to [email protected], referencing the URI of the item.Includes bibliographical references.Not availabl

A Physiologically Based System Theory of Consciousness

A system which uses large numbers of devices to perform a complex functionality is forced to adopt a simple functional architecture by the needs to construct copies of, repair, and modify the system. A simple functional architecture means that functionality is partitioned into relatively equal sized components on many levels of detail down to device level, a mapping exists between the different levels, and exchange of information between components is minimized. In the instruction architecture functionality is partitioned on every level into instructions, which exchange unambiguous system information and therefore output system commands. The von Neumann architecture is a special case of the instruction architecture in which instructions are coded as unambiguous system information. In the recommendation (or pattern extraction) architecture functionality is partitioned on every level into repetition elements, which can freely exchange ambiguous information and therefore output only system action recommendations which must compete for control of system behavior. Partitioning is optimized to the best tradeoff between even partitioning and minimum cost of distributing data. Natural pressures deriving from the need to construct copies under DNA control, recover from errors, failures and damage, and add new functionality derived from random mutations has resulted in biological brains being constrained to adopt the recommendation architecture. The resultant hierarchy of functional separations can be the basis for understanding psychological phenomena in terms of physiology. A theory of consciousness is described based on the recommendation architecture model for biological brains. Consciousness is defined at a high level in terms of sensory independent image sequences including self images with the role of extending the search of records of individual experience for behavioral guidance in complex social situations. Functional components of this definition of consciousness are developed, and it is demonstrated that these components can be translated through subcomponents to descriptions in terms of known and postulated physiological mechanisms

Mapping large-scale FEM-graphs to highly parallel computers with grid-like topology by self-organization

We consider the problem of mapping large scale FEM graphs for the solution of partial differential equations to highly parallel distributed memory computers. Typically, these programs show a low-dimensional grid-like communication structure. We argue that conventional domain decomposition methods that are usually employed today are not well suited for future highly parallel computers as they do not take into account the interconnection structure of the parallel computer resulting in a large communication overhead. Therefore we propose a new mapping heuristic which performs both, partitioning of the solution domain and processor allocation in one integrated step. Our procedure is based on the ability of Kohonen neural networks to exploit topological similarities of an input space and a grid-like structured network to compute a neighborhood preserving mapping between the set of discretization points and the parallel computer. We report about results of mapping up to 44,000-node FEM graphs to a 4096-processor parallel computer and demonstrate the capability of the proposed scheme for dynamic remapping considering adaptive refinement of the discretization graph

Improved Methods for Cluster Identification and Visualization

Self-organizing maps (SOMs) are self-organized projections of high dimensional data onto a low, typically two dimensional (2D), map wherein vector similarity is implicitly translated into topological closeness in the 2D projection. They are thus used for clustering and visualization of high dimensional data. However it is often challenging to interpret the results due to drawbacks of currently used methods for identifying and visualizing cluster boundaries in the resulting feature maps. In this thesis we introduce a new phase to the SOM that we refer to as the Cluster Reinforcement (CR) phase. The CR phase amplifies within-cluster similarity with the consequence that cluster boundaries become much more evident. We also define a new Boundary (B) matrix that makes cluster boundaries easy to visualize, can be thresholded at various levels to make cluster hierarchies apparent, and can be overlain directly onto maps of component planes (something that was not possible with previous methods). The combination of the SOM, CR phase and B-matrix comprise an automated method for improved identification and informative visualization of clusters in high dimensional data. We demonstrate these methods on three data sets: the classic 13- dimensional binary-valued “animal” benchmark test, actual 60-dimensional binaryvalued phonetic word clustering problem, and 3-dimensional real-valued geographic data clustering related to fuel efficiency of vehicle choice

Contributions towards smart cities : exploring block level census data for the characterization of change in Lisbon

Dissertation presented as the partial requirement for obtaining a Master's degree in Information Management, specialization in Information Systems and Technologies ManagementThe interest in using information to improve the quality of living in large urban areas and its governance efficiency has been around for decades. Nevertheless, the improvements in Information and Communications Technology has sparked a new dynamic in academic research, usually under the umbrella term of Smart Cities. This concept of Smart City can probably be translated, in a simplified version, into cities that are lived, managed and developed in an information-saturated environment. While it makes perfect sense and we can easily foresee the benefits of such a concept, presently there are still several significant challenges that need to be tackled before we can materialize this vision. In this work we aim at providing a small contribution in this direction, which maximizes the relevancy of the available information resources. One of the most detailed and geographically relevant information resource available, for the study of cities, is the census, more specifically the data available at block level (Subsecção Estatística). In this work, we use Self-Organizing Maps (SOM) and the variant Geo-SOM to explore the block level data from the Portuguese census of Lisbon city, for the years of 2001 and 2011. We focus on gauging change, proposing ways that allow the comparison of the two time periods, which have two different underlying geographical bases. We proceed with the analysis of the data using different SOM variants, aiming at producing a two-fold portrait: one, of the evolution of Lisbon during the first decade of the XXI century, another, of how the census dataset and SOM’s can be used to produce an informational framework for the study of cities

NASA JSC neural network survey results

A survey of Artificial Neural Systems in support of NASA's (Johnson Space Center) Automatic Perception for Mission Planning and Flight Control Research Program was conducted. Several of the world's leading researchers contributed papers containing their most recent results on artificial neural systems. These papers were broken into categories and descriptive accounts of the results make up a large part of this report. Also included is material on sources of information on artificial neural systems such as books, technical reports, software tools, etc