Self Organizing Maps - Research Paper Example

? Table of Contents Table of Contents 2 0 Introduction 3 2.0 Basic principles of SOM 4 3.0 Architecture for Self Organizing Maps 4 3.1 Algorithm 5 3.2 Feature-map properties 5 4.0 Applications of SOMs 8 4.1 Product design 9 4.2 Mapping Performance Space to Design Space (ESMPD) 10 4.3 Use of SOM in cluster analysis during multi-disease diagnosis 10 4.4 SOMs in clustering and visualization of the bankruptcy trajectory through self-organizing maps 11 4.5 SOMs in gene clustering 13 4.6 SOMs in Benchmarking of the world cities 13 References List 14 Self Organizing Maps (SOMs) 1.0 Introduction SOMs refer to artificial neural networks that use unsupervised learning in production of low-dimensional and discretized output space referred to as maps (Arribas-Bel et al 2013, p. 248). The artificial neural networks (ANNs) have been used for many years in modeling information processing systems inspired by the biological neural structures. The performance of ANNs is better than that of traditional methods of problem solving. This enhances a comprehensive understanding of the human cognitive abilities. From the available learning algorithms and neural network architectures, the SOM forms the most popular SOM. They use data visualization techniques by Teuvo Kohonen to reduce data dimension using self-organizing neural networks. The data visualization problems attempt to handle problems that are beyond human visualization for high dimensional data. SOMs act as a non-parametric network containing combination of data spatialization and abstraction, hence used in visual clustering. SOM is among the most popular methods of neural networks for use in cluster analysis. This occurs due to topology preserving and self organizing nature for SOM. The SOMs act as abstract model for topographic mapping. Modeling and analysis of mapping enhance understanding of perception, encoding, recognition and processes received and beneficial to the machine-based recognition of the patterns SOM possess prominent visualization properties. Developed from the associative memory model, SOM uses unsupervised learning algorithm characterized by simple computational form and structure enhanced by the retina-cortex mapping. The self-organization nature act as a fundamental process of pattern recognition, and allows learning the intra- and inter-pattern relationships for the stimuli without potential bias. SOM may provide the topologically preserved mapping to all the output spaces from input. Though the computational form proves to be simple, most aspects related to the algorithm must be investigated (Zhang et al 2010, p. 6359). 2.0 Basic principles of SOM The Kohonen self-organizing map encompasses a neural network, and various characteristics similar to the working of the human brain. Basically, SOM avails some classificatory resources that are organized based on patterns available for classification. The single layer of the neural network consists of neurons within n-dimensional grid. The grids allow the definition for the neighborhoods in the output space rather than the input space. The input and output spaces constitute the main SOM. This can also be performed through the use of tools that map vectors within the input space to output the space that preserves topological relations in the output space (Yang et al 2012, p.1371). SOM use unsupervised competitive learning and attempts to conform to the available input data. The SOM nodes act as inputs and contain some principle SOM features. Topological relationship between inputs is preserved after mapping into the SOM network. This pragmatically represents the complex data. SOMs use vector quantization in data compression processes. The SOMs offer an appropriate means of representing the multi-dimensional data in the lower dimensional space using one or two dimensions. This enhances visualization and understanding of data in low dimensions. Therefore, SOMs facilitates manipulation of complex data, especially in visualization of large quantities of data in an easy to understand way (Chen et al 2013, p. 385). 3.0 Architecture for Self Organizing Maps The Kohonen Network comprises of feed-forward structure containing a single computation layer with many neurons arranged in columns and rows. Every neuron connects to other source units within the input layer. Figure 1: One dimensional map contains a single column or row within the computational layer. 3.1 Algorithm The SOM algorithm necessitates learning of the feature maps from the spatial continuous input space used to accommodate the input vectors within the grid. SOM algorithm involves five major stages. These include initialization, sampling, matching, updating and continuation. Initialization allows choice of random variables used for initial weight vectors. Sampling enhances drawing of training sample for the input vector. Matching enhances identification of winning neuron whose weight vector lies closest to the input vector. Updating helps in applying the weight update equation while continuation necessitates return to sampling stage until feature map stops changing. 3.2 Feature-map properties After converging the SOM algorithm, feature map represents critical statistical characteristics of the input space. For an input x, the feature map equates to the winning neuron within the output space. Figure 2: diagrammatic representation of Feature Map The weight vector provides coordinates of the neuron’s image within the input space (Chang et al 2010, p.6689). The feature map allows for estimation of the input space, density matching and feature selection. In an estimation of the input space, the feature map can be represented using weight vectors and this provides an approximation for the input space. SOM aims at storing large sets of input vectors through the use of prototypes in order to provide for a good estimation of original input space. Theoretically, this idea depends on vector quantization theory of motivation that is dimensionally data compression and reduction. Approximation occurs through the use of total squared distance and work through gradient descent style mathematics that lead to weight update algorithm for SOM. This confirms the generation of good approximation for the input space (Chang et al 2010, p.6690). The topological offering results in topological ordering of the feature map by SOM algorithm. This allows special location of neuron within the output grid and allows movement towards the input vector. The weight updates may also move weight vector of closest neurons alongside winning neuron. The weight changes may cause the output space become appropriately ordered. This may make feature map appear as a virtual net or elastic with a grid topology. Every output space may be presented within the input space at their weight coordinates. The density matching property reflects the variations within distribution statistics where the regions within the input space containing the sample training vectors are gotten. The high probability occurrence results in larger domains within the output space, hence the need for better resolution than in the input space regions where training vectors may low at low probability. This relates the input vector probability to magnification factor in the feature map. Feature selection property within the input space having linear distribution makes the self-organizing map select best features in approximating underlying distribution. The SOM allows for principal surfaces that can be considered as non-generalization PCA (Yang et al, p.1371). SOM acts as a model used to cluster and visualize the high performance data. Visualization projects data on a graphical representation in order to provide properties of qualitative data. SOM containing multidimensional data becomes mapped onto the two-dimensional space containing hexagonal grids. This results to the complexity in visualization of multidimensional design variables. Figure 3.0: Diagrammatic sketch of the Self Organizing Maps From the diagrammatic sketch above, the SOM is depicted using n-dimensional design variables and the m-objective function vectors for the input-input layer, with m and n representing positive integers. This is assigned an (n + m) neuron. For the output layer, the weight vectors within the n + m dimensional weight vectors are represented by v and they randomly assign to neurons. The neurons connect the input vectors within the SOM algorithm. The unsupervised learning within the SOM enhances clustering of similar patterns and preserves topology for the input space. The learning process involves two main objectives, first the output layer looks for winning units represented by the neuron that contains closer weight vector for every input vector within the input layer. Secondly, the closeness to the input design variables as well as the objective function vectors must be updated. This results in the n + m dimensional input vectors being projected onto the neighboring neurons within the two dimensional grid. Based on the changing colors, judgment can be made in order to compare the changing trends for the design variables as well as establish the correlation between objective functions and design variables. 4.0 Applications of SOMs SOMs are applied in color classification that helps in demonstrating the SOM concept. This may not be practical, but it can be presented and used on a number of pragmatic applications. Classification requires a person change the calculation of the weight vector since the algorithm used is the same. Other application of SOMs includes use in expert systems using the rough test theories as well as the self organizing maps in designing the space explorations for complex products. The self organizing feature helps in mapping during cluster analysis in diagnosis of multiple diseases. Also, SOMs enhances benchmarking of the world cities as well as clustering and visualization of the bankruptcy trajectory (Yang et al 2012, p.1372). 4.1 Product design The mapping from product space during design guides engineers towards quick response and identification of interesting regions in order to provide the relative transparent optimization process. In design, the horizontal spaces form the design variables that denote multi-dimensional design variables. The vertical ordinate forms the disciplines and denotes multi discipline during development of the product. Horizontal and vertical ordinates divide the design space into grids, with each grid representing interval of the design variable in a given discipline. The grid containing the shadow represents regions within the design space located by mapping from particular performance of the complex product (Yang et al 2012, p.1373). The SOM results in high performance since they must be confirmed during the initial design. The black grids within the design space indicate incompleteness of information that may occur due to fixing new equipment in new product without the necessary performance information. Some of the product running the environment may not be forecasted making the intervals of design variables and expected values become hard to estimate during the initial stages. Some of the inherent mapping characters from performance to design space comprises of coupled design variables, uncertainties and the need for expertise. The design variables may be shared in multiple disciplines with different changing trends. Also, some uncertainties like fluctuations in the evaluation of product behavior may be missing. Also, making the decisions like selection of equipment depends on the knowledge of the designer. 4.2 Mapping Performance Space to Design Space (ESMPD) Based on mapping characters from design space, ESMPD facilitates the achievement of intelligent optimization and design. This entails data warehouse and three functional modules among others. Mapping from performance space to the designer’s space helps in optimizing for the regions interested in and built an ESMPD that allows the designer reuse the previous successful product data. Some of the product design data include the data used in the evaluation of product during simulations and experiments and the performance data for practical running among others. In product design, expert system manages the complex information about the product and disciplines and designs the variables across the management of complex product (Chen et al 2013, p. 386). 4.3 Use of SOM in cluster analysis during multi-disease diagnosis The diagnosis process forms a critical application within artificial intelligence. Multi-diseases may occur simultaneously in case of mechanical failure. A single disease may be caused by many factors and one factor may result in multiple diseases. Currently, diagnosis depends on expert systems and Neural Networks (NN). This may cope up easily with description in diagnosis of single disease as well as methods involved in intelligent diagnosis. Due to the binary tree character within the information searching tree in intelligent expert system and cognizant standard sample training in neural networks, a single disease can be diagnosed. This may not cope up with symptoms of complex diseases causing the difference between diagnostic results and real ones (Chen et al. 2013, p. 387). The SOM holds the input vectors for the topographic structure as well as maps data containing high-dimension network in order to decrease one, then form topological map. Relationship between the features for the input data and mapping may be discovered in order to offer recognizable method for inherent relationship between input and output. This facilitates formation of inherent expression, which may be mapped onto the output layer. The algorithm can be used during cluster analysis to strengthen objects and restrain unsuitable ones, after which the clustering groups are composed. This generates goods results during diagnosis of single diseases. Clustering the NNs and SOMs enhance discovery of trends in individual cardiovascular diseases on the patient condition. Other conditions use Learning Vector Quantization Network in classifying the thyroid diseases during the diagnosis. SOM algorithm by simple geometrical calculation uses complex character and co-effects for the Hebb rules. The character mapping enhances topological order and choosing of characters. This means that the space position within the neuron may be mapped from the character of the input sample (Chen et al 2013, p. 389). Choosing characters means that for a given data within the input space, SOM identifies the best character for the approach. This ensures that SOM network remains relevant in required construction and mapping the feature of the disease. The network denotes a combination of elements within the topological areas used in aggregation. Diseases in SOM divide into classes, and the clustered samples for the diseases may be developed. The process contains L features in networks to give L number of the input nodes. The input feature for the real disease may then be inputted in order to give a diagnosis in the network and classifies the clustered disease samples repeatedly and get the classification result (Yang et al 2012, p.1373). 4.4 SOMs in clustering and visualization of the bankruptcy trajectory through self-organizing maps The bankruptcy trajectory indicates dynamic changes within the financial institutions that help in keeping track of the evolution of the company in recognizing the trajectory patterns. Due to the increased financial failures and economic deterioration, the potential bankruptcy behaviors must be explored to enhance understanding of explicit patterns and give early warning of any impending failure. The SOM facilitates visual clustering in bankruptcy trajectory. SOM helps in the analysis of high-dimensional financial data in order to understand the phenomenon of unwanted bankruptcy. The bankruptcy prediction problem separates companies in predefined credit rates and health category. The SOM capability and related variants compare with other intelligent and statistical methods. This helps in the determination of credit class using visual exploration (Yang et al 2012, p.1372). The process involves the collection of multiple object movements of trajectory data as time-dependent sequences like visual surveillance and stock prediction. This attempts to explore implicit patterns within the trajectory data by introducing the SOM tool. The clustering model within SOM enhances visualization of dynamic behaviors for the industrial processes related with human supervision and detection of faults. The SOM-framework enables the users monitor and control clustering process for the trajectory data. In bankruptcy analysis, financial situation may be mapped onto the two-dimensional space to help observe the evolution of financial situation in the form of a trajectory within the space. The trajectories reflect dynamic changes instead of static snapshot for the financial situation making the detection of time evolution for the companies become possible and enhance recognition of trajectory patterns. Therefore, SOM acts as an information visualization technique during the analysis of bankruptcy trajectory because of its superiority when transforming the information to graphical representation to enhance recognition of patterns and allow visual reasoning by decision makers. A hierarchical SOM model enhances exploration of yearly trajectory for enterprises and monitoring of time evolution for the situation (Arribas-Bel et al 2013, p. 249). 4.5 SOMs in gene clustering The process of clustering genes enhances extraction of underlying biological information about gene expression data. The microarray technology enables biologists monitor and measure expression levels for genes. This creates need for data mining technologies in order to extract meaningful and fundamental patterns from gene expression data. The data clustering algorithm facilitates partitioning of genes into groups based similarity between expression profiles. Co-regulation takes place for genes with similar patterns of expression and share common function. Use of SOM in gene clustering results due to its availability and superiority of its free software (Arribas-Bel et al 2013, p. 250). 4.6 SOMs in Benchmarking of the world cities Most cities within the world form powerhouses allowing for creative thinkers and innovators. The powerhouses may act as for vitality and economic growth in the world. The cultural heritage and history in these cities remains diverse. Implementation of effective actions and strategies ensures cities understand their strengths and weaknesses, and that they can adapt with the changes in a global setting. Cities operate like business firms within the globalizing world and enhance the international image within their cultural or socio-economic profiles. Most cities have attempted to establish a ranking system to enhance a systematic performance assessment for the cities. Such a ranking system provides comparative insights to the local shareholders, as well as offering evidence based information for the policies within the city (Zhang et al 2010, p. 6361). SOM offers strong visualization capabilities where it enhances assimilation of knowledge and allow closing of the gap between the decision making process and available data. The algorithm allows evolution of the network and captures information within the dataset. This translates statistical dissimilarity into spatial distance, and the close up regions within the SOM represents similar original database and statistical properties. This occurs due to learning nature of the algorithm that allows the network evolve through the training stage as well as capture information in input dataset, then compressed into output map to enhance its presentation. SOM maps allow comprehensive perspective for multidimensional (dis)similarity for the various items (Zhang et al. 2010, p. 6363). References List Arribas-Bel, D., Kourtit, K., & Nijkamp, P. (2013). Benchmarking of world cities through Self-Organizing Maps, Cities 31(2), pp. 248-257. Zhang, K., Chai, Y., & Xang, S. (2010). Self-organizing feature map for cluster analysis in multi-disease diagnosis, Expert Systems with Applications 37 (9), pp. 6359-6357. Yang, L., Ouyanga, Z. & Shi, Y. (2012). A Modified Clustering Method Based on Self-Organizing Mapsand Its Applications, Procedia Computer Science 9 (2), pp.1371-1379. Chen, N., Ribeiro, B., Vieira, A. & Chen, A. (2013). Clustering and visualization of bankruptcy trajectory using self-organizing maps, Expert Systems with Applications 40 (1), pp. 385-393. Chang, R., Chu, C., Wu, Y. & Chen, Y. (2010). Gene clustering by using query-based self-organizing maps, Expert Systems with Applications 37 (9), pp. 6689-6694. Read More