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Most of the work done on self-organizing maps relies on the minimization of the mean squared error. This nonrobust approach leads to poor performance in the presence of outliers. Here we consider robust M-estimators as an alternative for least squares in the context of self-organization. New learning rules are derived, so that the original Kohonen׳s SOFM learning rule is a particular case. Experimental results are presented which demonstrate the robustness of our method against outliers, when compared to other robust self-organizing maps. [ABSTRACT FROM AUTHOR]

Interval-valued data is most utilized to represent either the uncertainty related to a single measurement, or the variability of the information inherent to a group rather than an individual. In this paper, we focus on Kohonen self-organizing maps (SOMs) for interval-valued data, and design a new Batch SOM algorithm that optimizes an explicit objective function. This algorithm can handle, respectively, suitable City-Block, Euclidean and Hausdorff distances with the purpose to compare interval-valued data during the training of the SOM. Moreover, most often conventional batch SOM algorithms consider that all variables are equally important in the training of the SOM. However, in real situations, some variables may be more or less important or even irrelevant for this task. Thanks to a parameterized definition of the above-mentioned distances, we propose also an adaptive version of the new algorithm that tackles this problem with an additional step where a relevance weight is automatically learned for each interval-valued variable. Several examples with synthetic and real interval-valued data sets illustrate the usefulness of the two novel batch SOM algorithms. [ABSTRACT FROM AUTHOR]

Interval Type-2 fuzzy-neural-network (IT2FNN) has been widely used to model nonlinear systems. In current IT2FNN-based schemes, however, one of the main drawbacks is that the structure of IT2FNN is hard to be determined. In this paper, a self-organizing interval Type-2 fuzzy-neural-network (SOIT2FNN) is introduced via considering the structure adjustment and the parameters learning process simultaneously. Two main contributions of SOIT2FNN are summarized: Firstly, an intensity of information transmission algorithm, which can evaluate the independent component contributions of fuzzy rules, is introduced to optimize the structure of SOIT2FNN. Secondly, an adaptive second-order algorithm, which can obtain fast convergence, is developed to adjust the parameters of SOIT2FNN. To demonstrate the merits of SOIT2FNN, several benchmark nonlinear systems and a real world application are examined with comparisons against other existing methods. Moreover, a statistical analysis of the performance results indicates that the proposed SOIT2FNN performs better and is more suitable for modeling nonlinear systems than some existing methods. [ABSTRACT FROM AUTHOR]

Artificial raindrop algorithm (ARA) has been shown to be an effective methodology for solving optimization problems over continuous space. To further enhance the search performance of ARA, self-organizing map (SOM) and binomial crossover operator (BCO) are integrated into ARA. The purpose of the former is to enhance the diversity of population by dynamically dividing the current population into several sub-populations. The latter is to make the function landscape be pseudo-separable by covariance matrix learning, which efficiently directs the evolution of the population toward a global optimum. By incorporating the SOM and BCO into ARA, an enhanced ARA variant, which is called ARA e -SOM+BCO for short, is presented in this paper. For the comparison purposes, the forehand fourteen CEC2005 contest benchmark functions are selected as the test suite to evaluate the performance of the proposed ARA e -SOM+BCO. The experiment results show that the performance of ARA e -SOM+BCO significantly outperforms ARA and its extension variant, and is also competitive with other state-of-the-art evolutionary algorithms in most test functions. [ABSTRACT FROM AUTHOR]

Abstract: In this work, the problem of real-time monitoring of products’ properties from spectrophotoscopic measurements is presented. Light absorbance spectra are used as inputs to software sensors that estimate outputs otherwise difficult to measure on-line. We approached the problems associated to calibrating the estimation models from very high-dimensional inputs and a reduced number of observations by selecting only a subset of relevant inputs emerging from the topological structure of the data. The topologically preserving representation is performed using the self-organizing map (SOM) where the input significance to the output is computed with the measure of topological relevance (MTR on SOM). As a result, we found that spectral inputs with a topology that is close to the output''s are also associated to the wavelengths that chemically explain the influence of the spectra to the property of interest. Being based on a selection of original spectral variables, the resulting models retain the chemical interpretability of the underlying system. Moreover, the selection approach is independent on the regression model to be embedded in the soft sensors. To support the presentation, the utility of the MTR on SOM is discussed on full-scale problems from pharmaceutical and refining industry. Based on our results, the approach leads to accurate and parsimonious models that can be efficiently implemented in industrial settings. [Copyright &y& Elsevier]

Data streams are found in many large-scale systems such as security, finance, and internet. In many of the data streams, the class distribution is imbalanced, and hence most of the traditional classification modeler fails to produce high accuracy for the samples from minority class. In addition, data streams are changing and the model should be updated to maintain the classification performance. However, obtaining the true class labels of the data samples is not an easy task since labeling process is extremely time-consuming and very often class labels are not available immediately after classification. The goal of this research is to reduce the labeling for an imbalanced data stream, and to produce high classification performance when compared to fully labeling setting. In an imbalanced data stream, the challenging part is to find and label minority class samples. In this paper, we propose RLS-SOM (Reduced labeled Samples-Self Organizing Map) framework for classification of the imbalanced data stream in a non-stationary environment. RLS-SOM locates the minority class samples in the feature space using SOM. It maintains an ensemble of the classifiers and builds a new model when the changes occur, using only partial labeled samples. In RLS-SOM, the classification results are obtained from the ensemble, as well as each individual model in the ensemble. An individual model classification results are selected over ensemble results, if its performance is higher than the ensemble's performance. This comparison is performed to improve the performance as there may be one model in the ensemble that produces higher performance than the ensemble. Our experimental results demonstrate that RLS-SOM obtains higher performance when it is compared with several partially labeling techniques over benchmark data sets. In addition, the experimental results with other state of the art fully labeling methods such as UCB, SERA, SEA, and Learn++.CDS shows RLS-SOM maintains equivalent classification performance by using 10–30% labeling, on average. [ABSTRACT FROM AUTHOR]

In this paper, a self-organizing map (SOM) neural network is used to visualize corrective actions of failure modes and effects analysis (FMEA). SOM is a popular unsupervised neural network model that aims to produce a low-dimensional map (typically a two-dimensional map) for visualizing high-dimensional data. With regards to FMEA, it is a popular methodology to identify potential failure modes for a product or a process, to assess the risk associated with those failure modes, also, to identify and carry out corrective actions to address the most serious concerns. Despite the popularity of FMEA in a wide range of industries, two well-known shortcomings are the complexity of the FMEA worksheet and its intricacy of use. To the best of our knowledge, the use of computation techniques for solving the aforementioned shortcomings is limited. The use of SOM in FMEA is new. In this paper, corrective actions in FMEA are described in their severity, occurrence and detect scores. SOM is then used as a visualization aid for FMEA users to see the relationship among corrective actions via a map. Color information from the SOM map is then included to the FMEA worksheet for better visualization. In addition, a Risk Priority Number Interval is used to allow corrective actions to be evaluated and ordered in groups. Such approach provides a quick and easily understandable framework to elucidate important information from a complex FMEA worksheet; therefore facilitating the decision-making tasks by FMEA users. The significance of this study is two-fold, viz., the use of SOM as an effective neural network learning paradigm to facilitate FMEA implementations, and the use of a computational visualization approach to tackle the two well-known shortcomings of FMEA. [ABSTRACT FROM AUTHOR]

Hashing based approximate nearest neighbor (ANN) search techniques have attracted considerable attention in media search community because of its good potential for low storage cost and fast query speed. Many hashing based ANN search methods have been proposed; but, most of them just consider to keep the similarity relationship of data points during mapping instead of topology of data. It is well known that Self-Organizing Map can keep topology structure while conducting mapping task. Motivated by this, in this paper, we propose a Self-Organizing Map based hashing framework–SOMH, which cannot only keep similarity relationship, but also preserve topology of data. Specifically, in SOMH, Self-Organizing Map is introduced to map data points into hamming space. In addition, in order to make it work well on short and long binary codes, we propose a relaxed version of SOMH and a product space SOMH, respectively. For the optimization problem of the relaxed SOMH, we also present an iterative solution. Moreover, we further propose an extended version of SOMH, which can work well on multimodal data search task, i.e., cross-modal search. To test the performance of these proposed algorithms, we conduct experiments on three data sets–SIFT1M, GIST1M and Wiki (a multimodal dataset). Experimental results show that SOMH can outperform or is comparable to several state-of-the-arts. [ABSTRACT FROM AUTHOR]

Active Contour Models ( ACM s) constitute a powerful energy-based minimization framework for image segmentation, based on the evolution of an active contour. Among ACM s, supervised ACM s are able to exploit the information extracted from supervised examples to guide the contour evolution. However, their applicability is limited by the accuracy of the probability models they use. As a consequence, effectiveness and efficiency of supervised ACM s are among their main real challenges, especially when handling images containing regions characterized by intensity inhomogeneity. In this paper, to deal with such kinds of images, we propose a new supervised ACM , named Self-Organizing Active Contour ( SOAC ) model, which combines a variational level set method (a specific kind of ACM ) with the weights of the neurons of two Self-Organizing Maps ( SOM s). Its main contribution is the development of a new ACM energy functional optimized in such a way that the topological structure of the underlying image intensity distribution is preserved – using the two SOM s – in a parallel-processing and local way. The model has a supervised component since training pixels associated with different regions are assigned to different SOM s. Experimental results show the superior efficiency and effectiveness of SOAC versus several existing ACM s. [ABSTRACT FROM AUTHOR]

• This paper presents a memory augmented convolutional neural network. • This paper utilizes the augmenting SOM as memory for better network generalization. • This paper instantiates the distributed knowledge representation with SOM and CNN. The long short-term memory (LSTM) network underpins many achievements and breakthroughs especially in natural language processing fields. Essentially, it is endowed with certain memory capabilities to boost its performance. Currently, the volume and speed of big data generation are increasing exponentially, and such data require efficient models to acquire memory augmented knowledge. In this paper, we propose a memory augmented convolutional neural network (MACNN) with utilizing self-organizing maps (SOM) as the memory module. First, we depict the potential challenge about just applying solely a convolutional neural network (CNN) so as to highlight the advantage of augmenting SOM memory for better network generalization. Then, we dissert a corresponding network architecture incorporating memory to instantiate the distributed knowledge representation machanism, which tactically combines both SOM and CNN. Each component of the input vector is connected with a neuron in a two-dimensional lattice. Finally, we test the proposed network on various datasets and the experimental results reveal that MACNN can achieve competitive performance, especially for bioimages datasets. Meanwhile, we further illustrate the learned representations to interpret the SOM behavior and to comprehend the achieved results, which indicates that the proposed memory-incorporating model can exhibit the better performance. [ABSTRACT FROM AUTHOR]

Abstract: We present an expectation-maximization (EM) algorithm that yields topology preserving maps of data based on probabilistic mixture models. Our approach is applicable to any mixture model for which we have a normal EM algorithm. Compared to other mixture model approaches to self-organizing maps (SOMs), the function our algorithm maximizes has a clear interpretation: it sums data log-likelihood and a penalty term that enforces self-organization. Our approach allows principled handling of missing data and learning of mixtures of SOMs. We present example applications illustrating our approach for continuous, discrete, and mixed discrete and continuous data. [Copyright &y& Elsevier]

Global modelling consists in fitting a single regression model to the available data, using the whole set of input and output observations. On the other side of the spectrum stands the local modelling approach, in which the input space is segmented into several small partitions and a specialized regression model is fit to each partition. In this paper, we propose a novel approach, called Regional Models (RM), that stands in between the global and local modelling ones. The proposal extends the two-level clustering approach by Vesanto and Alhoniemi (2000 [1] ) to regression problems, more specifically, to system identification. In this regard, we first partition the input space using the Self-Organizing Map (SOM), and then perform clustering over the prototypes of the trained SOM. Finally, regional regression models are built over the clusters (i.e. over the regions) of SOM prototypes, not over each SOM prototype as in local modelling. Under the proposed framework, we build regional linear and nonlinear regression models. For the linear case, we use autoregressive models with eXogenous (ARX) whose parameters are estimated using the ordinary least-squares (OLS) method. Regional nonlinear ARX (NARX) models are built using the Extreme Learning Machine network. Additionally, we develop robust variants of the proposed regional models through the use of M -estimation, a statistical framework for handling outliers, since the OLS is highly sensitive to them. Comprehensive performance evaluation of the proposed models on synthetic and real-world datasets is carried out and the results compared to those achieved by standard global and local models. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes an organized generalization of Newman and Girvan''s modularity measure for graph clustering. Optimized via a deterministic annealing scheme, this measure produces topologically ordered graph clusterings that lead to faithful and readable graph representations based on clustering induced graphs. Topographic graph clustering provides an alternative to more classical solutions in which a standard graph clustering method is applied to build a simpler graph that is then represented with a graph layout algorithm. A comparative study on four real world graphs ranging from 34 to 1133 vertices shows the interest of the proposed approach with respect to classical solutions and to self-organizing maps for graphs. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a new information-theoretic approach to competitive learning and self-organizing maps. We use several information-theoretic measures, such as conditional information and information losses, to extract main features in input patterns. For each competitive unit, conditional information content is used to show how much information on input patterns is contained. In addition, for detecting the importance of each variable, information losses are introduced. The information loss is defined as the difference between information with all input units and information without an input unit. We applied the information loss to conventional competitive learning to show that distinctive features could be extracted by the information loss. Then, we analyzed the self-organizing maps by the conditional information and the information loss. Experimental results showed that main features in input patterns were more clearly detected. [Copyright &y& Elsevier]

Abstract: We propose a method for inferring semantic information from textual data in content-based multimedia retrieval. Training examples of images and videos belonging to a specific semantic class are associated with their low-level visual and aural descriptors augmented with textual features such as frequencies of significant words. A fuzzy mapping of a semantic class in the training set to a class of similar objects in the test set is created by using Self-Organizing Maps (SOMs) trained from the low-level descriptors. Experiments with two databases and different textual features show promising results, indicating the usefulness of the approach in bridging the gap from low-level visual features to semantic concepts. [Copyright &y& Elsevier]

In this contribution we give a short overview about actual developments in hybrid systems combining self-organizing maps and evolutionary algorithms. Thereby, we pay attention to both directions of influence: neural network improvement by incorporating evolutionary elements and evolutionary design using ideas of learning in neural maps. In more detail, we highlight neighborhood cooperation in evolutionary systems for multiple population systems as well as genetic operators. We show the possibilities and properties of these approaches for exemplary real world applications. [Copyright &y& Elsevier]

Mobile robot navigation needs to be fast, reliable, and accurate. However, research has shown that there is always a performance tradeoff between these requirements. Gerecke et al. (Proceedings of the Second International Symposium on Robotics and Automation (ISRA-2000), Monterrey, Mexico, 2000, pp. 515–520) introduced an ensemble approach to a localization system with self-organizing maps at its core. Although all of the ensembles showed improved reliability, this came at a cost of localization speed. This paper presents and evaluates a new approach to fuse the individual classifications of the neural nets, to improve the speed of ensemble localization while retaining the reliability advantages. The new method employs a common evidence vector for disambiguation of multiple candidate locations. The results demonstrate that this approach significantly reduces the number of required localization steps and that the performance tradeoff can be improved in all respects. [Copyright &y& Elsevier]

This paper, proposes a novel artificial neural network, called self-adjusting feature map (SAM), and develop its unsupervised learning ability with self-adjusting mechanism. The trained network structure of representative connected neurons not only displays the spatial relation of the input data distribution but also quantizes the data well. The SAM can automatically isolate a set of connected neurons, in which, the used number of the sets may indicate the number of clusters. The idea of self-adjusting mechanism is based on combining of mathematical statistics and neurological advantages and retreat of waste. In the training process, for each representative neuron has are three phases, growth, adaptation and decline. The network of representative neurons, first create the necessary neurons according to the local density of the input data in the growth phase. In the adaption phase, it adjusts neighborhood neuron pair׳s connected/disconnected topology constantly according to the statistics of input feature data. Finally, the unnecessary neurons of the network are merged or remove in the decline phase. In this paper, we exploit the SAM to handle some peculiar cases that cannot be handled easily by classical unsupervised learning networks such as self-organizing map (SOM) network. The remarkable characteristics of the SAM can be seen on various real world cases in the experimental results. [ABSTRACT FROM AUTHOR]

In this paper we develop a set of parallel algorithms for image segmentation basing on the authors׳ former work, the self-organizing map (SOM) based vector quantization (VQ) approach, by extending the method from serial computation to parallel processing, in order to accelerate the computation process. The parallel segmentation scheme is composed of a group of parallel algorithms for implementing the whole segmentation process, including parallel classification of the image into edge and non-edge pattern vectors, parallel training of an SOM network, parallel segmentation of the image by using the trained SOM model with VQ method, and adaptive parallel estimation of the segment number of the image being processed. In the paper, all the parallel algorithms have been implemented on graphic processing units (GPU) and applied to segmenting the human brain MRI images. The experimental results obtained in the work show that, compared with the original serial method implemented on CPU, the proposed parallel approach can achieve a significant improvement on the computation efficiency with overall speedup ratios increasing from 28.81 to 89.12 as image sizes increasing from 128×128 to 1024×1024, while keeping the segmentation performance unchanged. [ABSTRACT FROM AUTHOR]

Human activity prediction is defined as inferring the high-level activity category with the observation of only a few action units. It is very meaningful for time-critical applications such as emergency surveillance. For efficient prediction, we represent the ongoing human activity by using body part movements and taking full advantage of inherent sequentiality, then find the best matching activity template by a proper aligning measurement. In streaming videos, dense spatio-temporal interest points (STIPs) are first extracted as low-level descriptors for their high detection efficiency. Then, sparse grouplets, i.e., clustered point groups, are located to represent body part movements, for which we propose a scale-adaptive mean shift method that can determine grouplet number and scale for each frame adaptively. To learn the sequentiality, located grouplets are successively mapped to Recurrent Self-Organizing Map (RSOM), which has been pre-trained to preserve the temporal topology of grouplet sequences. During this mapping, a growing RSOM trajectory, which represents the ongoing activity, is obtained. For the special structure of RSOM trajectory, a combination of dynamic time warping (DTW) distance and edit distance, called DTW-E distance, is designed for similarity measurement. Four activity datasets with different characteristics such as complex scenes and inter-class ambiguities serve for performance evaluation. Experimental results confirm that our method is very efficient for predicting human activity and yields better performance than state-of-the-art works. [ABSTRACT FROM AUTHOR]

Currently, most of the multiobjective evolutionary algorithms (MOEAs) directly adopt the reproduction operators designed for the single-objective optimization. Since these operators do not consider the characteristics of multiobjective optimization problems (MOPs), they cannot always perform well in the MOEAs. Inspired by this case, this paper presents a self-organizing reproduction mechanism based on the regularity property of MOPs, and proposes a self-organizing multiobjective evolutionary algorithm based on decomposition with neighborhood ensemble. In the new reproduction, a self-organizing map approach is firstly employed to discover the population distribution structure, and to build a mating pool for each solution. Thereafter, reproductions are only allowed among the solutions within the same mating pools. In order to establish the mating pools, an ensemble of multiple neuron neighborhood sizes is also introduced. The probability of choosing different neighborhood sizes is updated based on their performance on producing new solutions over the last certain generations. Comprehensive experiments denote that the proposed algorithm is efficient and competitive. The contributions of the new reproduction mechanism and neighborhood ensemble are also experimentally validated. [ABSTRACT FROM AUTHOR]

In this paper we will propose a modular structure to control the human-like movements of a robot in a way similar to which human brain does to perform the motor control. Modeling of human motor control and motor learning has attracted researchers׳ attention in robotics and artificial intelligence for decades. It is obvious that discovering the motor control functionality of brain as the most complex, sophisticated and powerful information-processing device leads to significant advancements in robots movement. Hence, our proposed modular controller is based on human brain behavior in using neural mechanisms named internal models and primitive motion identification which leads to extract and learn the latent simple motions in order to imitate observed complex movements. The study is accomplished based on formerly proposed structure, MOSAIC, which provides remarkable efficiency in motor control modeling. Examination of the proposed structure with real recorded data, confirms the performance of the controller in learning and executing motion tasks. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we propose a new information-theoretic method to simplify the computation of information and to unify several methods in one framework. The new method is called “supposed maximum information,” used to produce humanly comprehensible representations in competitive learning by taking into account the importance of input units. In the new learning method, by supposing the maximum information of input units, the actual information of input units is estimated. Then, the competitive network is trained with the estimated information in input units. The method is applied not to pure competitive learning, but to self-organizing maps, because it is easy to demonstrate visually how well the new method can produce more interpretable representations. We applied the method to three well-known sets of data, namely, the Kohonen animal data, the SPECT heart data and the voting data from the machine learning database. With these data, we succeeded in producing more explicit class boundaries on the U-matrices than did the conventional SOM. In addition, for all the data, quantization and topographic errors produced by our method were lower than those by the conventional SOM. [Copyright &y& Elsevier]

This article is an extended version of a paper presented in the WSOM׳2012 conference (Bourgeois et al., 2012 [1] ). We display a combination of factorial projections, SOM algorithm and graph techniques applied to a text mining problem. The corpus contains eight medieval manuscripts which were used to teach arithmetic techniques to merchants. Among the techniques for Data Analysis, those used for Lexicometry (such as Factorial Analysis) highlight the discrepancies between manuscripts. The reason for this is that they focus on the deviation from the independence between words and manuscripts. Still, we also want to discover and characterize the common vocabulary among the whole corpus. Using the properties of stochastic Kohonen maps, which define neighborhood between inputs in a non-deterministic way, we highlight the words which seem to play a special role in the vocabulary. We call them fickle and use them to improve both Kohonen map robustness and significance of FCA visualization. Finally we use graph algorithmic to exploit this fickleness for classification of words. [ABSTRACT FROM AUTHOR]

Finding an appropriate transfer function (TF) for mapping color and opacity values in direct volume rendering (DVR) can be a daunting task. This paper presents a novel approach towards TF generation for DVR, where the traditional low-level color and opacity parameter manipulations are not necessary. The TF generation process is hidden behind a simple and intuitive spherical self-organizing map (SSOM) visualization. The SSOM represents a visual form of the topological relations among the clusters. The user interacts with the SSOM lattice to find interesting regions in the volume. The color and opacity values are generated automatically from the voxel features based on the user׳s perception. We also use harmonic colors to present a visually pleasing result. Due to the independence of SSOM from feature type, our proposed method is flexible in nature and can be integrated with any set of features. The GPU implementation provides real-time volume rendering and fast interaction. Experimental results on several benchmark volume datasets show the effectiveness of our proposed method. [ABSTRACT FROM AUTHOR]

In some applications and in order to address real-world situations better, data may be more complex than simple numerical vectors. In some examples, data can be known only through their pairwise dissimilarities or through multiple dissimilarities, each of them describing a particular feature of the data set. Several variants of the Self-Organizing Map (SOM) algorithm were introduced to generalize the original algorithm to the framework of dissimilarity data. Whereas median SOM is based on a rough representation of the prototypes, relational SOM allows representing these prototypes by a virtual linear combination of all elements in the data set, referring to a pseudo-Euclidean framework. In the present article, an on-line version of relational SOM is introduced and studied. Similar to the situation in the Euclidean framework, this on-line algorithm provides a better organization and is much less sensible to prototype initialization than standard (batch) relational SOM. In a more general case, this stochastic version allows us to integrate an additional stochastic gradient descent step in the algorithm which can tune the respective weights of several dissimilarities in an optimal way: the resulting multiple relational SOM thus has the ability to integrate several sources of data of different types, or to make a consensus between several dissimilarities describing the same data. The algorithms introduced in this paper are tested on several data sets, including categorical data and graphs. On-line relational SOM is currently available in the R package SOMbrero that can be downloaded at http://sombrero.r-forge.r-project.org/ or directly tested on its Web User Interface at http://shiny.nathalievilla.org/sombrero . [ABSTRACT FROM AUTHOR]

In this paper, we study fundamental properties of the Self-Organizing Map (SOM) and the Generative Topographic Mapping (GTM), ramifications of the initialization of the algorithms and properties of the algorithms in the presence of missing data. We show that the commonly used principal component analysis (PCA) initialization of the GTM does not guarantee good learning results with high-dimensional data. Initializing the GTM with the SOM is shown to yield improvements in self-organization with three high-dimensional data sets: commonly used MNIST and ISOLET data sets and epigenomic ENCODE data set. We also propose a revision of handling missing data to the batch SOM algorithm called the Imputation SOM and show that the new algorithm is more robust in the presence of missing data. We benchmark the performance of the topographic mappings in the missing value imputation task and conclude that there are better methods for this particular task. Finally, we announce a revised version of the SOM Toolbox for Matlab with added GTM functionality. [ABSTRACT FROM AUTHOR]

Profitability and other economic aspects of farming in Finland are analyzed using clustering of the self-organizing map. The analysis of profitability bookkeeping data reveals several interesting relationships between the monitored financial variables. Economic profiles of farms are presented based on the clustering, and the findings are confirmed with statistical tests. A weight optimization system is proposed for upscaling financial figures of the sample of profitability bookkeeping farms to the whole country level. The system output is analyzed, and it is confirmed that the most important large and medium-sized enterprises are represented well by the sample. Furthermore, it seems that the utilized arable area is the key factor in guiding the weight optimization process. These findings may turn out to be useful in developing the sampling of bookkeeping farms in the future. [ABSTRACT FROM AUTHOR]

In help of the Kohonen''s self-organizing maps we present a topological local principal component analysis model which is capable of exploiting both the global topological structure and each local cluster structure. A newly proposed self-organizing strategy that can enhance the learning speed is introduced to train the model. [Copyright &y& Elsevier]

In the present contribution, the application of neural networks and, especially, maps in medical applications is considered. Thereby, we shortly highlight some problems in medical applications and refer to recently developed example solutions. We review extensions and modifications of the basic self-organizing map for faithful data representation. We demonstrate these approaches in two typical medical applications: high-dimensional time series analysis and data visualization. [Copyright &y& Elsevier]

A novel, unsupervised, artificial intelligence system is presented, whose input signals and trainable weights consist of complex or hypercomplex values. The system uses the effect given by the complex multiplication that the multiplicand is not only scaled but also rotated. The more similar an input signal and the reference signal are, the more likely the input signal belongs to the corresponding class. The data assigned to a class during training is stored on a generic layer as well as on a layer extracting special features of the signal. As a result, the same cluster can hold a general description and the details of the signal. This property is vital for assigning a signal to an existing or a new class. To ensure that only valid new classes are opened, the system determines the variances by comparing each input signal component with the weights and adaptively adjusts its activation and threshold functions for an optimal classification decision. The presented system knows at any time all boundaries of its clusters. Experimentally, it is demonstrated that the system is able to cluster the data of multiple classes autonomously, fast, and with high accuracy. • Unsupervised learning without prior knowledge is an unsolved challenge. • Unsupervised trained model achieves high classification accuracy. • System parameters are adapted automatically to data scattering. • Activation as well as threshold functions are adapted online. • Using hypercomplex-valued weights improves possibilities for classification. [ABSTRACT FROM AUTHOR]

Abstract: We propose a millimeter-wave imaging system for moving targets, and show the dependence of its dynamics on the self-organization parameters in the complex-valued self-organizing map (CSOM) by presenting systematic experimental results. The system consists of one-dimensional array antenna, parallel front-end and a CSOM to deal with complex texture. Experiments demonstrate that the CSOM visualizes successfully a liquid-filled small plastic bottle. The system construction is presented with the adaptive processing dynamics as well as the complex-valued inner product used for determining the winner in the CSOM. It is found that the dynamics shows a higher tolerance on the self-organization coefficient for neighbors β, showing almost stable self-organization for changes over one order of magnitude, than on that for winners α. [Copyright &y& Elsevier]

Abstract: Mixed numeric and categorical data are commonly seen nowadays in corporate databases in which precious patterns may be hidden. Analyzing mixed-type data to extract the hidden patterns valuable to decision-making is therefore beneficial and critical for corporations to remain competitive. In addition, visualization facilitates exploration in the early stage of data analysis. In the paper, we present a visualized approach to analyzing multivariate mixed-type data. The proposed framework based on an extended self-organizing map allows visualized data cluster analysis as well as classification. We demonstrate the feasibility of the approach by analyzing two real-world datasets and compare with other existing models to show its advantages. [Copyright &y& Elsevier]

Whether or not periodicity is a property of the environment, for a cognitive system a period is always a dynamical mental construct. This study suggests a dynamical implementation of this hypothesis using recurrent oscillatory self-organizing map of the feature space of such streams. The mapping allows the system to assign identity and class-membership to each stream point, represented by a locus on a two-dimensional map. The model is shown to detect periodicities of various regular and behavior-originated, single- and multi-channel wave patterns, and to reproduce such signals, relying solely on the oscillating activation of the units. [Copyright &y& Elsevier]

Abstract: This paper extends the use of recently introduced Self-Organizing Time Map (SOTM) by pairing it with classical cluster analysis. The SOTM is an adaptation of the Self-Organizing Map for visualizing dynamics in cluster structures. While enabling visual dynamic clustering of temporal and cross-sectional patterns, the stand-alone SOTM lacks means for objectively representing temporal changes in cluster structures. This paper combines the SOTM with clustering and illustrates the usefulness of second-level clustering for representing changes in cluster structures in an easily interpretable format. This provides means for identification of changing, emerging and disappearing clusters over time. Experiments are performed on two toy datasets and two real-world datasets. The first real-world application explores evolution dynamics of European banks before and during the global financial crisis. Not surprisingly, the results indicate a build-up of risks and vulnerabilities throughout the European banking sector prior to the start of the crisis. The second application identifies the cyclicality of currency crises through changes in the most vulnerable clusters. [Copyright &y& Elsevier]

Abstract: In this paper we compare a scalable FPGA-based hardware accelerator for the emulation of Self-Organizing Feature Maps (SOMs) with a multi-threaded software implementation on a state-of-the-art multi-core microprocessor. After discussing the mapping of SOMs to the reconfigurable digital hardware implementation, we present how the modular system architecture can be flexibly adapted to various application datasets as well as to variants of SOMs like Conscience SOM. Hyperspectral image processing is used as a benchmark scenario for the comparison of our FPGA-based hardware accelerator and state-of-the-art multi-core microprocessors. The hardware costs, power consumption, and scalability of the FPGA-based accelerator using Xilinx Virtex-4 FPGAs are discussed. For the real-world datasets used here, which require large SOMs, a speedup and energy reduction of one order of magnitude are achieved. [Copyright &y& Elsevier]

Abstract: Self-Organizing Feature Maps (SOFMs) are extensively used for dimensionality reduction and rendering of inherent data structures. A novel model of a SOFM based on the notion of aggregate/reduced ordering (R-ordering) of vector sets is proposed and applied to the segmentation of color images. The so-called Cross-Order Distance Matrix is defined in order to measure the similarity between local histograms corresponding to ordered sets of color vectors. Color images are regarded as two-dimensional (2-D) vector fields. Basic image processing algorithms are modified since color is represented as a vector instead of a scalar gray level variable. Operators utilizing several distance and similarity measures are adopted in order to quantify the color distribution within a sliding window. The proposed window-based SOFM uses sets of one, two and more color vectors in order to approximate local color distributions within sliding windows. Each set represents a separate node of the SOFM that is trained according to a sequence of ordered input sets of color vectors. A 3×3 window is used to capture color components in uniform color space (L ⁎ u ⁎ v ⁎). The color vectors within the sliding window are R-ordered. The neuron featuring the smallest aggregated distance (similarity) is activated during training. Segmentation results suggest that clustered nodes represent populations of pixels in rather compact segments of the images featuring similar texture. [Copyright &y& Elsevier]

Abstract: This paper adopts and adapts Kohonen’s standard self-organizing map (SOM) for exploratory temporal structure analysis. The self-organizing time map (SOTM) implements SOM-type learning to one-dimensional arrays for individual time units, preserves the orientation with short-term memory and arranges the arrays in an ascending order of time. The two-dimensional representation of the SOTM attempts thus twofold topology preservation, where the horizontal direction preserves time topology and the vertical direction data topology. This enables discovering the occurrence and exploring the properties of temporal structural changes in data. For representing qualities and properties of SOTMs, we adapt measures and visualizations from the standard SOM paradigm, as well as introduce a measure of temporal structural changes. The functioning of the SOTM, and its visualizations and quality and property measures, are illustrated on artificial toy data. The usefulness of the SOTM in a real-world setting is shown on poverty, welfare and development indicators. [Copyright &y& Elsevier]