Applications of fuzzy counterpropagation neural networks to non-linear function approximation and background noise elimination

An adaptive filter which can operate in an unknown environment by performing a learning mechanism that is suitable for the speech enhancement process. This research develops a novel ANN model which incorporates the fuzzy set approach and which can perform a non-linear function approximation. The model is used as the basic structure of an adaptive filter. The learning capability of ANN is expected to be able to reduce the development time and cost of the designing adaptive filters based on fuzzy set approach. A combination of both techniques may result in a learnable system that can tackle the vagueness problem of a changing environment where the adaptive filter operates. This proposed model is called Fuzzy Counterpropagation Network (Fuzzy CPN). It has fast learning capability and self-growing structure. This model is applied to non-linear function approximation, chaotic time series prediction and background noise elimination

Learning as a Nonlinear Line of Attraction for Pattern Association, Classification and Recognition

Development of a mathematical model for learning a nonlinear line of attraction is presented in this dissertation, in contrast to the conventional recurrent neural network model in which the memory is stored in an attractive fixed point at discrete location in state space. A nonlinear line of attraction is the encapsulation of attractive fixed points scattered in state space as an attractive nonlinear line, describing patterns with similar characteristics as a family of patterns. It is usually of prime imperative to guarantee the convergence of the dynamics of the recurrent network for associative learning and recall. We propose to alter this picture. That is, if the brain remembers by converging to the state representing familiar patterns, it should also diverge from such states when presented by an unknown encoded representation of a visual image. The conception of the dynamics of the nonlinear line attractor network to operate between stable and unstable states is the second contribution in this dissertation research. These criteria can be used to circumvent the plasticity-stability dilemma by using the unstable state as an indicator to create a new line for an unfamiliar pattern. This novel learning strategy utilizes stability (convergence) and instability (divergence) criteria of the designed dynamics to induce self-organizing behavior. The self-organizing behavior of the nonlinear line attractor model can manifest complex dynamics in an unsupervised manner. The third contribution of this dissertation is the introduction of the concept of manifold of color perception. The fourth contribution of this dissertation is the development of a nonlinear dimensionality reduction technique by embedding a set of related observations into a low-dimensional space utilizing the result attained by the learned memory matrices of the nonlinear line attractor network. Development of a system for affective states computation is also presented in this dissertation. This system is capable of extracting the user\u27s mental state in real time using a low cost computer. It is successfully interfaced with an advanced learning environment for human-computer interaction

Models for time series prediction based on neural networks. Case study : GLP sales prediction from ANCAP.

A time series is a sequence of real values that can be considered as observations of a certain system. In this work, we are interested in time series coming from dynamical systems. Such systems can be sometimes described by a set of equations that model the underlying mechanism from where the samples come. However, in several real systems, those equations are unknown, and the only information available is a set of temporal measures, that constitute a time series. On the other hand, by practical reasons it is usually required to have a prediction, v.g. to know the (approximated) value of the series in a future instant t. The goal of this thesis is to solve one of such real-world prediction problem: given historical data related with the lique ed bottled propane gas sales, predict the future gas sales, as accurately as possible. This time series prediction problem is addressed by means of neural networks, using both (dynamic) reconstruction and prediction. The problem of to dynamically reconstruct the original system consists in building a model that captures certain characteristics of it in order to have a correspondence between the long-term behavior of the model and of the system. The networks design process is basically guided by three ingredients. The dimensionality of the problem is explored by our rst ingredient, the Takens-Mañé's theorem. By means of this theorem, the optimal dimension of the (neural) network input can be investigated. Our second ingredient is a strong theorem: neural networks with a single hidden layer are universal approximators. As the third ingredient, we faced the search of the optimal size of the hidden layer by means of genetic algorithms, used to suggest the number of hidden neurons that maximizes a target tness function (related with prediction errors). These algorithms are also used to nd the most in uential networks inputs in some cases. The determination of the hidden layer size is a central (and hard) problem in the determination of the network topology. This thesis includes a state of the art of neural networks design for time series prediction, including related topics such as dynamical systems, universal approximators, gradient-descent searches and variations, as well as meta-heuristics. The survey of the related literature is intended to be extensive, for both printed material and electronic format, in order to have a landscape of the main aspects for the state of the art in time series prediction using neural networks. The material found was sometimes extremely redundant (as in the case of the back-propagation algorithm and its improvements) and scarce in others (memory structures or estimation of the signal subspace dimension in the stochastic case). The surveyed literature includes classical research works ([27], [50], [52]) as well as more recent ones ([79] , [16] or [82]), which pretends to be another contribution of this thesis. Special attention is given to the available software tools for neural networks design and time series processing. After a review of the available software packages, the most promising computational tools for both approaches are discussed. As a result, a whole framework based on mature software tools was set and used. In order to work with such dynamical systems, software intended speci cally for the analysis and processing of time series was employed, and then chaotic series were part of our focus. Since not all randomness is attributable to chaos, in order to characterize the dynamical system generating the time series, an exploration of chaotic-stochastic systems is required, as well as network models to predict a time series associated to one of them. Here we pretend to show how the knowledge of the domain, something extensively treated in the bibliography, can be someway sophisticated (such as the Lyapunov's spectrum for a series or the embedding dimension). In order to model the dynamical system generated by the time series we used the state-space model, so the time series prediction was translated in the prediction of the next system state. This state-space model, together with the delays method (delayed coordinates) have practical importance for the development of this work, speci cally, the design of the input layer in some networks (multi-layer perceptrons - MLPs) and other parameters (taps in the TFLNs). Additionally, the rest of the network components where determined in many cases through procedures traditionally used in neural networks : genetic algorithms. The criteria of model (network) selection are discussed and a trade-o between performance and network complexity is further explored, inspired in the Rissanen's minimum description length and its estimation given by the chosen software. Regarding the employed network models, the network topologies suggested from the literature as adequate for the prediction are used (TLFNs and recurrent networks) together with MLPs (a classic of arti cial neural networks) and networks committees. The e ectiveness of each method is con rmed for the proposed prediction problem. Network committees, where the predictions are a naive convex combination of predictions from individual networks, are also extensively used. The need of criteria to compare the behaviors of the model and of the real system, in the long run, for a dynamic stochastic systems, is presented and two alternatives are commented. The obtained results proof the existence of a solution to the problem of learning of the dependence Input ! Output . We also conjecture that the system is dynamic-stochastic but not chaotic, because we only have a realization of the random process corresponding to the sales. As a non-chaotic system, the mean of the predictions of the sales would improve as the available data increase, although the probability of a prediction with a big error is always non-null due to the randomness present. This solution is found in a constructive and exhaustive way. The exhaustiveness can be deduced from the next ve statements: the design of a neural network requires knowing the input and output dimension,the number of the hidden layers and of the neurons in each of them. the use of the Takens-Mañé's theorem allows to derive the dimension of the input data by theorems such as the Kolmogorov's and Cybenko's ones the use of multi-layer perceptrons with only one hidden layer is justi ed so several of such models were tested the number of neurons in the hidden layer is determined many times heuristically using genetic algorithms a neuron in the output gives the desired prediction As we said, two tasks are carried out: the development of a time series prediction model and the analysis of a feasible model for the dynamic reconstruction of the system. With the best predictive model, obtained by an ensemble of two networks, an acceptable average error was obtained when the week to be predicted is not adjacent to the training set (7.04% for the week 46/2011). We believe that these results are acceptable provided the quantity of information available, and represent an additional validation that neural networks are useful for time series prediction coming from dynamical systems, no matter whether they are stochastic or not. Finally, the results con rmed several already known facts (such as that adding noise to the inputs and outputs of the training values can improve the results; that recurrent networks trained with the back-propagation algorithm don't have the problem of vanishing gradients in short periods and that the use of committees - which can be seen as a very basic of distributed arti cial intelligence - allows to improve signi cantly the predictions).Una serie temporal es una secuencia de valores reales que pueden ser considerados como observaciones de un cierto sistema. En este trabajo, estamos interesados en series temporales provenientes de sistemas dinámicos. Tales sistemas pueden ser algunas veces descriptos por un conjunto de ecuaciones que modelan el mecanismo subyacente que genera las muestras. sin embargo, en muchos sistemas reales, esas ecuaciones son desconocidas, y la única información disponible es un conjunto de medidas en el tiempo, que constituyen la serie temporal. Por otra parte, por razones prácticas es generalmente requerida una predicción, es decir, conocer el valor (aproximado) de la serie en un instante futuro t. La meta de esta tesis es resolver un problema de predicción del mundo real: dados los datos históricos relacionados con las ventas de gas propano licuado, predecir las ventas futuras, tan aproximadamente como sea posible. Este problema de predicción de series temporales es abordado por medio de redes neuronales, tanto para la reconstrucción como para la predicción. El problema de reconstruir dinámicamente el sistema original consiste en construir un modelo que capture ciertas características de él de forma de tener una correspondencia entre el comportamiento a largo plazo del modelo y del sistema. El proceso de diseño de las redes es guiado básicamente por tres ingredientes. La dimensionalidad del problema es explorada por nuestro primer ingrediente, el teorema de Takens-Mañé. Por medio de este teorema, la dimensión óptima de la entrada de la red neuronal puede ser investigada. Nuestro segundo ingrediente es un teorema muy fuerte: las redes neuronales con una sola capa oculta son un aproximador universal. Como tercer ingrediente, encaramos la búsqueda del tamaño oculta de la capa oculta por medio de algoritmos genéticos, usados para sugerir el número de neuronas ocultas que maximizan una función objetivo (relacionada con los errores de predicción). Estos algoritmos se usan además para encontrar las entradas a la red que influyen más en la salida en algunos casos. La determinación del tamaño de la capa oculta es un problema central (y duro) en la determinación de la topología de la red. Esta tesis incluye un estado del arte del diseño de redes neuronales para la predicción de series temporales, incluyendo tópicos relacionados tales como sistemas dinámicos, aproximadores universales, búsquedas basadas en el gradiente y sus variaciones, así como meta-heurísticas. El relevamiento de la literatura relacionada busca ser extenso, para tanto el material impreso como para el que esta en formato electrónico, de forma de tener un panorama de los principales aspectos del estado del arte en la predicción de series temporales usando redes neuronales. El material hallado fue algunas veces extremadamente redundante (como en el caso del algoritmo de retropropagación y sus mejoras) y escaso en otros (estructuras de memoria o estimación de la dimensión del sub-espacio de señal en el caso estocástico). La literatura consultada incluye trabajos de investigación clásicos ( ([27], [50], [52])' así como de los más reciente ([79] , [16] or [82]). Se presta especial atención a las herramientas de software disponibles para el diseño de redes neuronales y el procesamiento de series temporales. Luego de una revisión de los paquetes de software disponibles, las herramientas más promisiorias para ambas tareas son discutidas. Como resultado, un entorno de trabajo completo basado en herramientas de software maduras fue definido y usado. Para trabajar con los mencionados sistemas dinámicos, software especializado en el análisis y proceso de las series temporales fue empleado, y entonces las series caóticas fueron estudiadas. Ya que no toda la aleatoriedad es atribuible al caos, para caracterizar al sistema dinámico que genera la serie temporal se requiere una exploración de los sistemas caóticos-estocásticos, así como de los modelos de red para predecir una serie temporal asociada a uno de ellos. Aquí se pretende mostrar cómo el conocimiento del dominio, algo extensamente tratado en la literatura, puede ser de alguna manera sofisticado (tal como el espectro de Lyapunov de la serie o la dimensión del sub-espacio de señal). Para modelar el sistema dinámico generado por la serie temporal se usa el modelo de espacio de estados, por lo que la predicción de la serie temporal es traducida en la predicción del siguiente estado del sistema. Este modelo de espacio de estados, junto con el método de los delays (coordenadas demoradas) tiene importancia práctica en el desarrollo de este trabajo, específicamente, en el diseño de la capa de entrada en algunas redes (los perceptrones multicapa) y otros parámetros (los taps de las redes TLFN). Adicionalmente, el resto de los componentes de la red con determinados en varios casos a través de procedimientos tradicionalmente usados en las redes neuronales: los algoritmos genéticos. Los criterios para la selección de modelo (red) son discutidos y un balance entre performance y complejidad de la red es explorado luego, inspirado en el minimum description length de Rissanen y su estimación dada por el software elegido. Con respecto a los modelos de red empleados, las topologóas de sugeridas en la literatura como adecuadas para la predicción son usadas (TLFNs y redes recurrentes) junto con perceptrones multicapa (un clásico de las redes neuronales) y comités de redes. La efectividad de cada método es confirmada por el problema de predicción propuesto. Los comités de redes, donde las predicciones son una combinación convexa de las predicciones dadas por las redes individuales, son también usados extensamente. La necesidad de criterios para comparar el comportamiento del modelo con el del sistema real, a largo plazo, para un sistema dinámico estocástico, es presentada y dos alternativas son comentadas. Los resultados obtenidos prueban la existencia de una solución al problema del aprendizaje de la dependencia Entrada - Salida . Conjeturamos además que el sistema generador de serie de las ventas es dinámico-estocástico pero no caótico, ya que sólo tenemos una realización del proceso aleatorio correspondiente a las ventas. Al ser un sistema no caótico, la media de las predicciones de las ventas debería mejorar a medida que los datos disponibles aumentan, aunque la probabilidad de una predicción con un gran error es siempre no nula debido a la aleatoriedad presente. Esta solución es encontrada en una forma constructiva y exhaustiva. La exhaustividad puede deducirse de las siguiente cinco afirmaciones : el diseño de una red neuronal requiere conocer la dimensión de la entrada y de la salida, el número de capas ocultas y las neuronas en cada una de ellas el uso del teorema de takens-Mañé permite derivar la dimensión de la entrada por teoremas tales como los de Kolmogorov y Cybenko el uso de perceptrones con solo una capa oculta es justificado, por lo que varios de tales modelos son probados el número de neuronas en la capa oculta es determinada varias veces heurísticamente a través de algoritmos genéticos una sola neurona de salida da la predicción deseada. Como se dijo, dos tareas son llevadas a cabo: el desarrollo de un modelo para la predicción de la serie temporal y el análisis de un modelo factible para la reconstrucción dinámica del sistema. Con el mejor modelo predictivo, obtenido por el comité de dos redes se logró obtener un error aceptable en la predicción de una semana no contigua al conjunto de entrenamiento (7.04% para la semana 46/2011). Creemos que este es un resultado aceptable dada la cantidad de información disponible y representa una validación adicional de que las redes neuronales son útiles para la predicción de series temporales provenientes de sistemas dinámicos, sin importar si son estocásticos o no. Finalmente, los resultados experimentales confirmaron algunos hechos ya conocidos (tales como que agregar ruido a los datos de entrada y de salida de los valores de entrenamiento puede mejorar los resultados: que las redes recurrentes entrenadas con el algoritmo de retropropagación no presentan el problema del gradiente evanescente en periodos cortos y que el uso de de comités - que puede ser visto como una forma muy básica de inteligencia artificial distribuida - permite mejorar significativamente las predicciones)

Trajectory prediction of moving objects by means of neural networks

Thesis (Master)--Izmir Institute of Technology, Computer Engineering, Izmir, 1997Includes bibliographical references (leaves: 103-105)Text in English; Abstract: Turkish and Englishviii, 105 leavesEstimating the three-dimensional motion of an object from a sequence of object positions and orientation is of significant importance in variety of applications in control and robotics. For instance, autonomous navigation, manipulation, servo, tracking, planning and surveillance needs prediction of motion parameters. Although "motion estimation" is an old problem (the formulations date back to the beginning of the century), only recently scientists have provided with the tools from nonlinear system estimation theory to solve this problem eural Networks are the ones which have recently been used in many nonlinear dynamic system parameter estimation context. The approximating ability of the neural network is used to identifY the relation between system variables and parameters of a dynamic system. The position, velocity and acceleration of the object are estimated by several neural networks using the II most recent measurements of the object coordinates as input to the system Several neural network topologies with different configurations are introduced and utilized in the solution of the problem. Training schemes for each configuration are given in detail. Simulation results for prediction of motion having different characteristics via different architectures with alternative configurations are presented comparatively

A neural network-based trajectory planner for redundant systems using direct inverse modeling

Redundant (i.e., under-determined) systems can not be trained effectively using direct inverse modeling with supervised learning, for reasons well out-lined by Michael Jordan at MIT. There is a loop-hole , however, in Jordan\u27s preconditions, which seems to allow just such an architecture. A robot path planner implementing a cerebellar inspired habituation paradigm with such an architecture will be introduced. The system, called ARTFORMS, for Adaptive Redundant Trajectory Formation System uses on-line training of multiple CMACS. CMACs are locally generalizing networks, and have an a priori deterministic geometric input space mapping. These properties together with on-line learning and rapid convergence satisfy the loop-hole conditions. Issues of stability/plasticity, presentation order and generalization, computational complexity, and subsumptive fusion of multiple networks are discussed. Two implementations are described. The first is shown not to be goal directed enough for ultimate success. The second, which is highly successful, is made more goal directed by the addition of secondary training, which reduces the dimensionality of the problem by using a set of constraint equations. Running open loop with respect to posture (the system metric which reduces dimensionality) is seen to be the root cause of the first system\u27s failure, not the use of the direct inverse method. In fact, several nice properties of direct inverse modeling contribute to the system\u27s convergence speed, robustness and compliance. The central problem used to demonstrate this method is the control of trajectory formation for a planar kinematic chain with a variable number of joints. Finally, this method is extended to implement adaptive obstacle avoidance

Design, implementation and evaluation of automated surveillance systems

El reconocimiento de patrones ha conseguido un nivel de complejidad que nos permite reconocer diferente tipo de eventos, incluso peligros, y actuar en concordancia para minimizar el impacto de una situación complicada y abordarla de la mejor manera posible. Sin embargo, creemos que todavía se puede llegar a alcanzar aplicaciones más eficientes con algoritmos más precisos. Nuestra aplicación quiere probar a incluir el nuevo paradigma de la programación, las redes neuronales. Nuestra idea en principio fue explorar la alternativa que las nuevas redes neuronales convolucionales aportaban, en donde se podía ver en vídeos de ejemplos la alta tasa de detección e identificación que, por ejemplo, YOLOv2 podría mostrar. Después de comparar las características, vimos que YOLOv3 ofrecía un buen balance entre precisión y rapidez como comentaremos más adelante. Debido a la tasa de baja detecciones, haremos uso de los filtros de Kalman para ayudarnos a la hora de hacer reidentificación de personas y objetos. En este proyecto, haremos un estudio además de las alternativas de videovigilancia con las que cuentan empresas del sector y veremos que clase de productos ofrecen y, por otro lado, observaremos cuales son los trabajos de los grupos de investigadores de otras universidades que más similitudes tienen con nuestro objetivo. Dedicaremos, por lo tanto, el uso de esta red neuronal para detectar eventos como el abandono de mochilas y para mostrar la densidad de tránsito en localizaciones concretas, así como utilizaremos una metodología más tradicional, el flujo óptico, para detectar actuaciones anormales en una multitud.Automatic surveillance system is getting more and more sophisticated with the increasing calculation power that computers are reaching. The aim of this project is to take advantage of these tools and with the new classification and detection technology brought by neural networks, develop a surveillance application that can recognize certain behaviours (which are the detection of lost backpacks and suitcases, detection of abnormal crowd activity and heatmap of density occupation). To develop this program, python has been the selected programming language used, where YOLO and OpenCV form the spine of this project. After testing the code, it has been proved that due to the constrains of the detection for small objects, the project does not perform as it should for real development, but still it shows potential for the detection of lost backpacks in certain videos from the GBA dataset [1] and PETS2006 dataset [2]. The abnormal activity detection for crowds is made with a simple algorithm that seems to perform well, detecting the anomalies in all the testing dataset used, generated by the University of Minnesota [3]. Finally, the heatmap can display correctly the projection of people on the ground for five second, just as intended. The objective of this software is to be part of the core of what could be a future application with more modules that will be able to perform full automated surveillance tasks and gather useful information data, and these advances and future proposal will be explained in this memory.Máster Universitario en Ingeniería Industrial (M141