A Kohonen Self-Organizing Map Approach to Modeling Growth Pole Dynamics

Economic growth poles remain an important concept in regional development policy analysis. Recent attention has focused for example on the emergence and promotion of technopoles, or agglomerations of high technology activities within a region. This paper presents a neural network approach for analyzing these evolutionary processes. Kohonen self-organizing maps are used to simulate the spread and backwash effects associated with the emergence of regional growth poles. Unlike other models of growth pole development, which rely heavily on conventional economic theory, the approach outlined in this paper allows for increasing returns, multiple equilibria, `satisficing' behavior, imperfect information and stochasticity. The model could be used to explore spatio-temporal dynamics under different assumptions relating to industrial composition, interindustry linkages, and the spatial juxtaposition of firms (industries). The model is applied to the Washington, D.C. metropolitan area, and the patterns of development that have arisen from the location behavior of high technology firms in this region.     

Redundant Hash Addressing of Feature Sequences Using the Self-Organizing Map

Kohonen's Self-Organizing Map (SOM) is combined with the Redundant Hash Addressing (RHA) principle. The SOM encodes the input feature vector sequence into the sequence of best-matching unit (BMU) indices and the RHA principle is then used to associate the BMU index sequence with the dictionary items. This provides a fast alternative for dynamic programming (DP) based methods for comparing and matching temporal sequences. Experiments include music retrieval and speech recognition. The separation of the classes can be improved by error-corrective learning. Comparisons to DP-based methods are presented.     

Bringing Knowing-When and Knowing-What Together: Periodically Tuned Categorization and Category-Based Timing Modeled with the Recurrent Oscillatory Self-Organizing Map (ROSOM)

The study addresses the cyclically temporal aspect of sequence recognition, storage and recall using the Recurrent Oscillatory Self-Organizing Map (ROSOM), first introduced by Kaipainen, Papadopoulos and Karhu (1997). The unique solution of the network is that oscillatory States are assigned to network units, corresponding to their `readiness-to-fire'. The ROSOM is a categorizer, a temporal sequence storage system and a periodicity detector designed for use in an ambiguous cyclically repetitive environment. As its external input, the model accepts a multidimensional stream of environment-describing feature configurations with implicit periodicities. The output of the model is one or a few closed cycles abstracted from such a stream, mapped as trajectories on a two-dimensional sheet with an organization reminiscent of multi-dimensional scaling. The model's capabilities are explored with a variety of workbench data.     

Self-Organizing Maps and Learning Vector Quantization for Feature Sequences

The Self-Organizing Map (SOM) and Learning Vector Quantization (LVQ) algorithms are constructed in this work for variable-length and warped feature sequences. The novelty is to associate an entire feature vector sequence, instead of a single feature vector, as a model with each SOM node. Dynamic time warping is used to obtain time-normalized distances between sequences with different lengths. Starting with random initialization, ordered feature sequence maps then ensue, and Learning Vector Quantization can be used to fine tune the prototype sequences for optimal class separation. The resulting SOM models, the prototype sequences, can then be used for the recognition as well as synthesis of patterns. Good results have been obtained in speaker-independent speech recognition.     

TCSOM: Clustering Transactions Using Self-Organizing Map

Self-Organizing Map (SOM) networks have been successfully applied as a clustering method to numeric datasets. However, it is not feasible to directly apply SOM for clustering transactional data. This paper proposes the Transactions Clustering using SOM (TCSOM) algorithm for clustering binary transactional data. In the TCSOM algorithm, a normalized Dot Product norm based dissimilarity measure is utilized for measuring the distance between input vector and output neuron. And a modified weight adaptation function is employed for adjusting weights of the winner and its neighbors. More importantly, TCSOM is a one-pass algorithm, which is extremely suitable for data mining applications. Experimental results on real datasets show that TCSOM algorithm is superior to those state-of-the-art transactional data clustering algorithms with respect to clustering accuracy.     

Self-Organization by Temporal Inhibition (SOTI)

A model is presented for a neural network with competitive learning that demonstrates the self-organizing capabilities arising from the inclusion of a simple temporal inhibition mechanism within the neural units. This mechanism consists of the inhibition, for a certain time, of the neuron that generates an action potential; such a process is termed Post_Fire inhibition. The neural inhibition period, or degree of inhibition, and the way it is varied during the learning process, represents a decisive factor in the behaviour of the network, in addition to constituting the main basis for the exploitation of the model. Specifically, we show how Post_Fire inhibition is a simple mechanism that promotes the participation of and cooperation between the units comprising the network; it produces self-organized neural responses that reveal spatio–temporal characteristics of input data. Analysis of the inherent properties of the Post_Fire inhibition and the examples presented show its potential for applications such as vector quantization, clustering, pattern recognition, feature extraction and object segmentation. Finally, it should be noted that the Post_Fire inhibition mechanism is treated here as an efficient abstraction of biologically plausible mechanisms, which simplifies its implementation.     

Decomposing the global financial crisis: A Self-Organizing Time Map

A key starting point for financial stability surveillance is understanding past, current and possible future risks and vulnerabilities. Through temporal data and dimensionality reduction, or visual dynamic clustering, this paper aims to present a holistic view of cross-sectional macro-financial patterns over time. The Self-Organizing Time Map (SOTM) is a recent adaptation of the Self-Organizing Map for exploratory temporal structure analysis, which disentangles cross-sectional data structures over time. We apply the SOTM, as well as its combination with classical cluster analysis, in financial stability surveillance. Thus, this paper uses the SOTM for decomposing and identifying temporal structural changes in macro-financial data before, during and after the global financial crisis of 2007–2009.     

The Supervised Network Self-Organizing Map for Classification of Large Data Sets

Complex application domains involve difficult pattern classification problems. The state space of these problems consists of regions that lie near class separation boundaries and require the construction of complex discriminants while for the rest regions the classification task is significantly simpler. The motivation for developing the Supervised Network Self-Organizing Map (SNet-SOM) model is to exploit this fact for designing computationally effective solutions. Specifically, the SNet-SOM utilizes unsupervised learning for classifying at the simple regions and supervised learning for the difficult ones in a two stage learning process. The unsupervised learning approach is based on the Self-Organizing Map (SOM) of Kohonen. The basic SOM is modified with a dynamic node insertion/deletion process controlled with an entropy based criterion that allows an adaptive extension of the SOM. This extension proceeds until the total number of training patterns that are mapped to neurons with high entropy (and therefore with ambiguous classification) reduces to a size manageable numerically with a capable supervised model. The second learning phase (the supervised training) has the objective of constructing better decision boundaries at the ambiguous regions. At this phase, a special supervised network is trained for the computationally reduced task of performing the classification at the ambiguous regions only. The performance of the SNet-SOM has been evaluated on both synthetic data and on an ischemia detection application with data extracted from the European ST-T database. In all cases, the utilization of SNet-SOM with supervised learning based on both Radial Basis Functions and Support Vector Machines has improved the results significantly related to those obtained with the unsupervised SOM and has enhanced the scalability of the supervised learning schemes. The highly disciplined design of the generalization performance of the Support Vector Machine allows to design the proper model for the particular training set.     

Self-organization of the batch Kohonen network under quantization effects

In this work, we investigate the effect of quantized weights and inputs on the self-organizing properties of the batch variant of Kohonen's self-organizing map algorithm. In particular, we examine necessary and sufficient conditions that ensure self-organization of the batch SOM algorithm for one-dimensional (1D) networks mapping a quantized 1D input space. Using Markov chain formalism, it is shown that the existing analysis for the original algorithm can be extended to also include the more general batch variant. Finally, simulations verify the theoretical results, relate the speed of weight ordering to the distribution of the inputs, extend the results to the 2D case, and show the existence of metastable states of the Markov chain.     

Parallel Implementation of Self-Organizing Map on the Partial Tree Shape Neurocomputer

A parallel mapping of self-organizing map (SOM) algorithm is presented for a partial tree shape neurocomputer (PARNEU). PARNEU is a general purpose parallel neurocomputer that is designed for soft computing applications. Practical scalability and a reconfigurable partial tree network are the main architectural features. The presented neuron parallel mapping of SOM with on-line learning illustrates a parallel winner neuron search and a coordinate transfer that are performed in the partial tree network. Phase times are measured to analyse speedup and scalability of the mapping. The performance of the learning phase in SOM with a four processor PARNEU configuration is about 26 MCUPS and the recall phase performs 30 MCPS. Compared to other mappings done for general purpose neurocomputers, PARNEU's performance is very good.     

Visualizing Demographic Trajectories with Self-Organizing Maps

In recent years, the proliferation of multi-temporal census data products and the increased capabilities of geospatial analysis and visualization techniques have encouraged longitudinal analyses of socioeconomic census data. Traditional cartographic methods for illustrating socioeconomic change tend to rely either on comparison of multiple temporal snapshots or on explicit representation of the magnitude of change occurring between different time periods. This paper proposes to add another perspective to the visualization of temporal change, by linking multi-temporal observations to a geometric configuration that is not based on geographic space, but on a spatialized representation of n-dimensional attribute space. The presented methodology aims at providing a cognitively plausible representation of changes occurring inside census areas by representing their attribute space trajectories as line features traversing a two-dimensional display space. First, the self-organizing map (SOM) method is used to transform n-dimensional data such that the resulting two-dimensional configuration can be represented with standard GIS data structures. Then, individual census observations are mapped onto the neural network and linked as temporal vertices to represent attribute space trajectories as directed graphs. This method is demonstrated for a data set containing 254 counties and 32 demographic variables. Various transformations and visual results are presented and discussed in the paper, from the visualization of individual component planes and trajectory clusters to the mapping of different attributes onto temporal trajectories.     

A Scalable Parallel Algorithm for Self-Organizing Maps with Applications to Sparse Data Mining Problems

We describe a scalable parallel implementation of the self organizing map (SOM) suitable for data-mining applications involving clustering or segmentation against large data sets such as those encountered in the analysis of customer spending patterns. The parallel algorithm is based on the batch SOM formulation in which the neural weights are updated at the end of each pass over the training data. The underlying serial algorithm is enhanced to take advantage of the sparseness often encountered in these data sets. Analysis of a realistic test problem shows that the batch SOM algorithm captures key features observed using the conventional on-line algorithm, with comparable convergence rates.Performance measurements on an SP2 parallel computer are given for two retail data sets and a publicly available set of census data.These results demonstrate essentially linear speedup for the parallel batch SOM algorithm, using both a memory-contained sparse formulation as well as a separate implementation in which the mining data is accessed directly from a parallel file system. We also present visualizations of the census data to illustrate the value of the clustering information obtained via the parallel SOM method.     

Feature Competitive Algorithm for Dimension Reduction of the Self-Organizing Map Input Space

The self-organizing map (SOM) can classify documents by learning about their interrelationships from its input data. The dimensionality of the SOM input data space based on a document collection is generally high. As the computational complexity of the SOM increases in proportion to the dimension of its input space, high dimensionality not only lowers the efficiency of the initial learning process but also lowers the efficiencies of the subsequent retrieval and the relearning process whenever the input data is updated. A new method called feature competitive algorithm (FCA) is proposed to overcome this problem. The FCA can capture the most significant features that characterize the underlying interrelationships of the entities in the input space to form a dimensionally reduced input space without excessively losing of essential information about the interrelationships. The proposed method was applied to a document collection, consisting of 97 UNIX command manual pages, to test its feasibility and effectiveness. The test results are encouraging. Further discussions on several crucial issues about the FCA are also presented.     

Speech Dimensionality Analysis on Hypercubical Self-Organizing Maps

The problem of finding the intrinsic dimension of speech is addressed in this paper. Astructured vector quantization lattice, Self-Organizing Map (SOM), is used as a projection space for the data. The goal is to find a hypercubical SOM lattice where the sequences of projected speech feature vectors form continuous trajectories. The effect of varying the dimension of the lattice is investigated using feature vector sequences computed from the TIMIT database.     

Knowledge Discovery Through Self-Organizing Maps: Data Visualization and Query Processing

In data mining, the usefulness of a data pattern depends on the user of the database and does not solely depend on the statistical strength of the pattern. Based on the premise that heuristic search in combinatorial spaces built on computer and human cognitive theories is useful for effective knowledge discovery, this study investigates how the use of self-organizing maps as a tool of data visualization in data mining plays a significant role in human–computer interactive knowledge discovery. This article presents the conceptual foundations of the integration of data visualization and query processing for knowledge discovery, and proposes a set of query functions for the validation of self-organizing maps in data mining. Received 1 November 1999 / Revised 2 March 2000 / Accepted in revised form 20 October 2000     

Temporal Constraints: A Survey

Temporal Constraint Satisfaction is an information technology useful for representing and answering queries about temporal occurrences and temporal relations between them. Information is represented as a Constraint Satisfaction Problem (CSP) where variables denote event times and constraints represent the possible temporal relations between them. The main tasks are two: (i) deciding consistency, and (ii) answering queries about scenarios that satisfy all constraints. This paper overviews results on several classes of Temporal CSPs: qualitative interval, qualitative point, metric point, and some of their combinations. Research has progressed along three lines: (i) identifying tractable subclasses, (ii) developing exact search algorithms, and (iii) developing polynomial-time approximation algorithms. Most available techniques are based on two principles: (i) enforcing local consistency (e.g. path-consistency) and (ii) enhancing naive backtracking search.     

基于自组织映射和模糊隶属度的混合像元分解

遥感图像中普遍存在着混合像元,将混合像元分解为端元和它们之间混合的丰度,对于高精度的地物识别和定量遥感具有重要意义.结合自组织映射神经网络和模糊理论中的模糊隶属度,提出一种新的多光谱和高光谱遥感图像混合像元分解的方法.首先对自组织映射神经网络进行有监督的训练,然后基于模糊模型对混合像元进行分解.其分解结果自动满足混合像元分解问题所要求的2个约束:丰度值非负约束及丰度值和为1约束.实验结果表明,该方法不仅适用于线性光谱混合的情况,也适用于非线性光谱混合的情况,能够获得较好的混合像元分解结果,同时具有较强的抗噪声能力.     

Spatio-Temporal Analysis with the Self-Organizing Feature Map

Spatio-temporal pattern recognition problems are particularly challenging. They typically involve detecting change that occurs over time in two-dimensional patterns. Analytic techniques devised for temporal data must take into account the spatial relationships among data points. An artificial neural network known as the self-organizing feature map (SOM) has been used to analyze spatial data. This paper further investigates the use of the SOM with spatio-temporal pattern recognition. The principles of the two-dimensional SOM are developed into a novel three-dimensional network and experiments demonstrate that (i) the three-dimensional network makes a better topological ordering and (ii) there is a difference in terms of the spatio-temporal analysis that can be made with the three-dimensional network. Received 21 October 1999 / Revised 11 February 2000 / Accepted 2 May 2000     

基于贝叶斯自组织映射和高斯混合模型的混合像元分解

提出一种新的对多通道遥感图像进行混合像元分解的方法.该方法将贝叶斯自组织映射算法引入混合像元分解问题中,通过最小化Kullback-Leibler信息度实现高斯参数的估计,并结合高斯混合模型完成解混.为了获得较高的解混精度,要求适当地扩展正态分布的范围,提出了3σ的方差调整方法来解决这一问题.所采用的解混模型自动满足混合像元分解问题所要求的2个约束条件:丰度值非负约束,丰度值和为1约束.实验结果表明,该方法有较好的混合像元分解结果,同时具有较强的抗噪声能力.     

The Kohonen self-organizing map: an application to the study of strategic groups in the UK hotel industry

This paper examines a neural network method known as the self-organizing map (SOM). The motivation behind the SOM is to transform the data to a two-dimensional grid of nodes while preserving its 'topological' structure. In neural network terminology this involves unsupervised learning. The nearest related statistical technique is cluster analysis. We employ the SOM in the task of identifying strategic groups of companies, using data which relate to the generic strategies suggested by Porter. Following identification of different groups of hotels with certain strategic emphases, the study investigates correlations between strategies followed and hotel performance. We compare and contrast the 'feature map' generated by the SOM with the results of a standard cluster analysis using the k-means method. The data also cover performance indicators and the results indicate that performance varies between strategic groups.