Šiame magistro darbe apžvelgiami daugiamačių duomenų dimensijos mažinimo (vizualizavimo) metodai, tarp kurių nagrinėjami dirbtiniai neuroniniai tinklai. Pateikiamos pagrindinės dirbtinių neuroninių tinklų sąvokos (biologinis neuronas ir dirbtinio neurono modelis, mokymo strategijos, daugiasluoksnis neuronas ir pan.). Nagrinėjami autoasociatyviniai neuroniniai tinklai. Darbo tikslas – išnagrinėti autoasociatyviųjų neuroninių tinklų taikymo daugiamačių duomenų dimensijos mažinimui ir vizualizavimui galimybes bei ištirti gaunamų rezultatų priklausomybę nuo skirtingų parametrų. Siekiant šio tikslo atlikti eksperimentai naudojant kelias daugiamačių duomenų aibes. Tyrimų metu nustatyti parametrai, įtakojantys autoasociatyvinio neuroninio tinklo veikimą. Be to, gauti rezultatai lyginti pagal dvi skirtingas tinklo daromas paklaidas – MDS ir autoasociatyvinę. MDS paklaida parodo, kaip gerai išlaikomi atstumai tarp analizuojamų taškų (vektorių) pereinant iš daugiamatės erdvės į mažesnės dimensijos erdvę. Autoasociatyvinio tinklo išėjimuose gautos reikšmės turi sutapti su įėjimo reikšmėmis, taigi autoasociatyvinė paklaida parodo, kaip gerai tai gaunama (vertinamas skirtumas tarp įėjimų ir išėjimų). Tirta, kaip paklaidas įtakoja šie autoasociatyvinio neuroninio tinklo parametrai: aktyvacijos funkcija, minimizuojama funkcija, mokymo funkcija, epochų skaičius, paslėptų neuronų skaičius ir dimensijos mažinimo skaičiaus pasirinkimas. / This thesis gives an overview of dimensionality reduction of multivariate data (visualization) techniques, including the issue of artificial neural networks. Presents the main concepts of artificial neural networks (biological and artificial neuron to neuron model, teaching strategies, multi-neuron and so on.). Autoassociative neural networks are analyzed. The aim of this work - to consider the application of autoassociative neural networks for multidimensional data visualization and dimension reduction and to explore the possibilities of the results obtained from the dependence of different parameters. To achieve this, several multidimensional data sets were used. In analysis determinate parameters influencing autoassociative neural network effect. In addition, the results obtained by comparing two different network made errors - MDS and autoassociative. MDS error shows how well maintained the distance between the analyzed points (vectors), in transition from the multidimensional space into a lower dimension space. Autoassociative network output values obtained should coincide with the input values, so autoassociative error shows how well it is received (evaluated the difference between inputs and outputs). Researched how autoassociative neural network errors are influenced by this parameters: the activation function, minimizing function, training function, the number of epochs, hidden neurons number and choices of the number of dimension reduction.

This thesis presents an abstract model of the mammalian neocortex. The model was constructed by taking a top-down view on the cortex, where it is assumed that cortex to a first approximation works as a system with attractor dynamics. The model deals with the processing of static inputs from the perspectives of biological mapping, algorithmic, and physical implementation, but it does not consider the temporal aspects of these inputs. The purpose of the model is twofold: Firstly, it is an abstract model of the cortex and as such it can be used to evaluate hypotheses about cortical function and structure. Secondly, it forms the basis of a general information processing system that may be implemented in computers. The characteristics of this model are studied both analytically and by simulation experiments, and we also discuss its parallel implementation on cluster computers as well as in digital hardware. The basic design of the model is based on a thorough literature study of the mammalian cortex’s anatomy and physiology. We review both the layered and columnar structure of cortex and also the long- and short-range connectivity between neurons. Characteristics of cortex that defines its computational complexity such as the time-scales of cellular processes that transport ions in and out of neurons and give rise to electric signals are also investigated. In particular we study the size of cortex in terms of neuron and synapse numbers in five mammals; mouse, rat, cat, macaque, and human. The cortical model is implemented with a connectionist type of network where the functional units correspond to cortical minicolumns and these are in turn grouped into hypercolumn modules. The learning-rules used in the model are local in space and time, which make them biologically plausible and also allows for efficient parallel implementation. We study the implemented model both as a single- and multi-layered network. Instances of the model with sizes up to that of a rat-cortex equivalent are implemented and run on cluster computers in 23% of real time. We demonstrate on tasks involving image-data that the cortical model can be used for meaningful computations such as noise reduction, pattern completion, prototype extraction, hierarchical clustering, classification, and content addressable memory, and we show that also the largest cortex equivalent instances of the model can perform these types of computations. Important characteristics of the model are that it is insensitive to limited errors in the computational hardware and noise in the input data. Furthermore, it can learn from examples and is self-organizing to some extent. The proposed model contributes to the quest of understanding the cortex and it is also a first step towards a brain-inspired computing system that can be implemented in the molecular scale computers of tomorrow. The main contributions of this thesis are: (i) A review of the size, modularization, and computational structure of the mammalian neocortex. (ii) An abstract generic connectionist network model of the mammalian cortex. (iii) A framework for a brain-inspired self-organizing information processing system. (iv) Theoretical work on the properties of the model when used as an autoassociative memory. (v) Theoretical insights on the anatomy and physiology of the cortex. (vi) Efficient implementation techniques and simulations of cortical sized instances. (vii) A fixed-point arithmetic implementation of the model that can be used in digital hardware. / QC 20100903

abstract: Feature learning and the discovery of nonlinear variation patterns in high-dimensional data is an important task in many problem domains, such as imaging, streaming data from sensors, and manufacturing. This dissertation presents several methods for learning and visualizing nonlinear variation in high-dimensional data. First, an automated method for discovering nonlinear variation patterns using deep learning autoencoders is proposed. The approach provides a functional mapping from a low-dimensional representation to the original spatially-dense data that is both interpretable and efficient with respect to preserving information. Experimental results indicate that deep learning autoencoders outperform manifold learning and principal component analysis in reproducing the original data from the learned variation sources. A key issue in using autoencoders for nonlinear variation pattern discovery is to encourage the learning of solutions where each feature represents a unique variation source, which we define as distinct features. This problem of learning distinct features is also referred to as disentangling factors of variation in the representation learning literature. The remainder of this dissertation highlights and provides solutions for this important problem. An alternating autoencoder training method is presented and a new measure motivated by orthogonal loadings in linear models is proposed to quantify feature distinctness in the nonlinear models. Simulated point cloud data and handwritten digit images illustrate that standard training methods for autoencoders consistently mix the true variation sources in the learned low-dimensional representation, whereas the alternating method produces solutions with more distinct patterns. Finally, a new regularization method for learning distinct nonlinear features using autoencoders is proposed. Motivated in-part by the properties of linear solutions, a series of learning constraints are implemented via regularization penalties during stochastic gradient descent training. These include the orthogonality of tangent vectors to the manifold, the correlation between learned features, and the distributions of the learned features. This regularized learning approach yields low-dimensional representations which can be better interpreted and used to identify the true sources of variation impacting a high-dimensional feature space. Experimental results demonstrate the effectiveness of this method for nonlinear variation pattern discovery on both simulated and real data sets. / Dissertation/Thesis / Doctoral Dissertation Industrial Engineering 2016