Data-driven cluster reinforcement and visualization in sparsely-matched self-organizing maps

Self-Organizing Neuroevolution for Solving Carpool Service Problem With Dynamic Capacity to Alternate Matches

Traffic congestion often incurs environmental problems. One of the most effective ways to mitigate this is carpooling transportation, which substantially reduces automobile demands. Due to the popularization of smartphones and mobile applications, a carpool service can be conveniently accessed via the intelligent carpool system. In this system, the service optimization required to intelligently and adaptively distribute the carpool participant resources is called the carpool service problem (CSP). Several previous studies have examined viable and preliminary solutions to the CSP by using exact and metaheuristic optimization approaches. For CSP-solving, evolutionary computation (e.g., metaheuristics) is a more promising option in comparison to exact-type approaches. However, all the previous state-of-the-art approaches use pure optimization to solve the CSP. In this paper, we employ the framework of neuroevolution to propose the self-organizing map-based neuroevolution (SOMNE) solver by which the SOM-like network represents the abstract CSP solution and is well-trained by using neural learning and evolutionary mechanism. The experimental section of this paper investigates the comparisons and analyses of two objective functions of the CSP and demonstrates that the proposed SOMNE solver achieves superior results when compared against those the other approaches produce, especially in regard to the optimization of the primary objective functions of the CSP. Finally, the visual results of the SOM are illustrated to show the effectiveness and efficiency of the evolutionary neural learning process.

An Information-Theoretic-Cluster Visualization for Self-Organizing Maps

Improved data visualization will be a significant tool to enhance cluster analysis. In this paper, an information-theoretic-based method for cluster visualization using self-organizing maps (SOMs) is presented. The information-theoretic visualization (IT-vis) has the same structure as the unified distance matrix, but instead of depicting Euclidean distances between adjacent neurons, it displays the similarity between the distributions associated with adjacent neurons. Each SOM neuron has an associated subset of the data set whose cardinality controls the granularity of the IT-vis and with which the first- and second-order statistics are computed and used to estimate their probability density functions. These are used to calculate the similarity measure, based on Renyi's quadratic cross entropy and cross information potential (CIP). The introduced visualizations combine the low computational cost and kernel estimation properties of the representative CIP and the data structure representation of a single-linkage-based grouping algorithm to generate an enhanced SOM-based visualization. The visual quality of the IT-vis is assessed by comparing it with other visualization methods for several real-world and synthetic benchmark data sets. Thus, this paper also contains a significant literature survey. The experiments demonstrate the IT-vis cluster revealing capabilities, in which cluster boundaries are sharply captured. Additionally, the information-theoretic visualizations are used to perform clustering of the SOM. Compared with other methods, IT-vis of large SOMs yielded the best results in this paper, for which the quality of the final partitions was evaluated using external validity indices.

Topology-based clustering using polar self-organizing map

Cluster analysis of unlabeled data sets has been recognized as a key research topic in varieties of fields. In many practical cases, no a priori knowledge is specified, for example, the number of clusters is unknown. In this paper, grid clustering based on the polar self-organizing map (PolSOM) is developed to automatically identify the optimal number of partitions. The data topology consisting of both the distance and density is exploited in the grid clustering. The proposed clustering method also provides a visual representation as PolSOM allows the characteristics of clusters to be presented as a 2-D polar map in terms of the data feature and value. Experimental studies on synthetic and real data sets demonstrate that the proposed algorithm provides higher clustering accuracy and lower computational cost compared with six conventional methods.

A spiking self-organizing map combining STDP, oscillations, and continuous learning

The self-organizing map (SOM) is a neural network algorithm to create topographically ordered spatial representations of an input data set using unsupervised learning. The SOM algorithm is inspired by the feature maps found in mammalian cortices but lacks some important functional properties of its biological equivalents. Neurons have no direct access to global information, transmit information through spikes and may be using phasic coding of spike times within synchronized oscillations, receive continuous input from the environment, do not necessarily alter network properties such as learning rate and lateral connectivity throughout training, and learn through relative timing of action potentials across a synaptic connection. In this paper, a network of integrate-and-fire neurons is presented that incorporates solutions to each of these issues through the neuron model and network structure. Results of the simulated experiments assessing map formation using artificial data as well as the Iris and Wisconsin Breast Cancer datasets show that this novel implementation maintains fundamental properties of the conventional SOM, thereby representing a significant step toward further understanding of the self-organizational properties of the brain while providing an additional method for implementing SOMs that can be utilized for future modeling in software or special purpose spiking neuron hardware.

Function approximation using combined unsupervised and supervised learning

Function approximation is one of the core tasks that are solved using neural networks in the context of many engineering problems. However, good approximation results need good sampling of the data space, which usually requires exponentially increasing volume of data as the dimensionality of the data increases. At the same time, often the high-dimensional data is arranged around a much lower dimensional manifold. Here we propose the breaking of the function approximation task for high-dimensional data into two steps: (1) the mapping of the high-dimensional data onto a lower dimensional space corresponding to the manifold on which the data resides and (2) the approximation of the function using the mapped lower dimensional data. We use over-complete self-organizing maps (SOMs) for the mapping through unsupervised learning, and single hidden layer neural networks for the function approximation through supervised learning. We also extend the two-step procedure by considering support vector machines and Bayesian SOMs for the determination of the best parameters for the nonlinear neurons in the hidden layer of the neural networks used for the function approximation. We compare the approximation performance of the proposed neural networks using a set of functions and show that indeed the neural networks using combined unsupervised and supervised learning outperform in most cases the neural networks that learn the function approximation using the original high-dimensional data.

Dictionary learning-based subspace structure identification in spectral clustering

In this paper, we study dictionary learning (DL) approach to identify the representation of low-dimensional subspaces from high-dimensional and nonnegative data. Such representation can be used to provide an affinity matrix among different subspaces for data clustering. The main contribution of this paper is to consider both nonnegativity and sparsity constraints together in DL such that data can be represented effectively by nonnegative and sparse coding coefficients and nonnegative dictionary bases. In the algorithm, we employ the proximal point technique for the resulting DL and sparsity optimization problem. We make use of coding coefficients to perform spectral clustering (SC) for data partitioning. Extensive experiments on real-world high-dimensional and nonnegative data sets, including text, microarray, and image data demonstrate that the proposed method can discover their subspace structures. Experimental results also show that our algorithm is computationally efficient and effective for obtaining high SC performance and interpreting the clustering results compared with the other testing methods.

Qualitative adaptive reward learning with success failure maps: applied to humanoid robot walking

In the human brain, rewards are encoded in a flexible and adaptive way after each novel stimulus. Neurons of the orbitofrontal cortex are the key reward structure of the brain. Neurobiological studies show that the anterior cingulate cortex of the brain is primarily responsible for avoiding repeated mistakes. According to vigilance threshold, which denotes the tolerance to risks, we can differentiate between a learning mechanism that takes risks and one that averts risks. The tolerance to risk plays an important role in such a learning mechanism. Results have shown the differences in learning capacity between risk-taking and risk-avert behaviors. These neurological properties provide promising inspirations for robot learning based on rewards. In this paper, we propose a learning mechanism that is able to learn from negative and positive feedback with reward coding adaptively. It is composed of two phases: evaluation and decision making. In the evaluation phase, we use a Kohonen self-organizing map technique to represent success and failure. Decision making is based on an early warning mechanism that enables avoiding repeating past mistakes. The behavior to risk is modulated in order to gain experiences for success and for failure. Success map is learned with adaptive reward that qualifies the learned task in order to optimize the efficiency. Our approach is presented with an implementation on the NAO humanoid robot, controlled by a bioinspired neural controller based on a central pattern generator. The learning system adapts the oscillation frequency and the motor neuron gain in pitch and roll in order to walk on flat and sloped terrain, and to switch between them.

Unsupervised learning by minimal entropy encoding

Following basic principles of information-theoretic learning, in this paper, we propose a novel approach to data clustering, referred to as minimal entropy encoding (MEE), which is based on a set of functions (features) projecting each input onto a minimum entropy configuration (code). Inspired by traditional parsimony principles, we seek solutions in reproducing kernel Hilbert spaces and then we prove that the encoding functions are expressed in terms of kernel expansion. In order to avoid trivial solutions, the developed features must be as different as possible by means of a soft constraint on the empirical estimation of the entropy associated with the encoding functions. This leads to an unconstrained optimization problem that can be efficiently solved by conjugate gradient. We also investigate an optimization strategy based on concave-convex algorithms. The relationships with maximum margin clustering are studied, showing that MEE overcomes some of its critical issues, such as the lack of a multiclass extension and the need to face problems with a large number of constraints. A massive evaluation on several benchmarks of the proposed approach shows improvements over state-of-the-art techniques, both in terms of accuracy and computational complexity.