Batch Self-organizing Maps Research Articles

Batch Self-Organizing Maps for Distributional Data with an Automatic Weighting of Variables and Components

Batch Self-Organizing Maps for Distributional Data with an Automatic Weighting of Variables and Components

Flexible Self-Organizing Maps in kohonen 3.0

Self-organizing maps (SOMs) are popular tools for grouping and visualizing data in many areas of science. This paper describes recent changes in package kohonen, implementing several different forms of SOMs. These changes are primarily focused on making the package more useable for large data sets. Memory consumption has decreased dramatically, amongst others, by replacing the old interface to the underlying compiled code by a new one relying on Rcpp. The batch SOM algorithm for training has been added in both sequential and parallel forms. A final important extension of the package's repertoire is the possibility to define and use data-dependent distance functions, extremely useful in cases where standard distances like the Euclidean distance are not appropriate. Several examples of possible applications are presented.

An Online Synchronous Brain Wave Signal Pattern Classifier with Parallel Processing Optimization for Embedded System Implementation

Commercial Brain Computer Interface applications are currently expanding due to the success of widespread dis-semination of low cost devices. Reducing the cost of a traditional system requires appropriate resources, such as proper software tools for signal processing and characterization. In this paper, a methodology for classifying a set of attention and meditation brain wave signal patterns is presented by means of unsupervised signal feature clustering with batch Self-Organizing Maps (b-SOM) and supervised classification by Support Vector Machine (SVM). Previous research on this matter did not combine both methods and also required an important amount of computation time. With the use of a small square neuron grid by b-SOM and an RBF kernel SVM, a well delimited classifier was obtained. The recognition rate was 70% after parameter tuning. In terms of optimization, the parallel b-SOM algorithm reduced drastically the computation time, allowing online clustering and classification for full length input data.

Batch SOM algorithms for interval-valued data with automatic weighting of the variables

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.

Extending parallelization of the self-organizing map by combining data and network partitioned methods

High-dimensional data is pervasive in many fields such as engineering, geospatial, and medical. It is a constant challenge to build tools that help people in these fields understand the underlying complexities of their data. Many techniques perform dimensionality reduction or other “compression” to show views of data in either two or three dimensions, leaving the data analyst to infer relationships with remaining independent and dependent variables. Contextual self-organizing maps offer a way to represent and interact with all dimensions of a data set simultaneously. However, computational times needed to generate these representations limit their feasibility to realistic industry settings. Batch self-organizing maps provide a data-independent method that allows the training process to be parallelized and therefore sped up, saving time and money involved in processing data prior to analysis. This research parallelizes the batch self-organizing map by combining network partitioning and data partitioning methods with CUDA on the graphical processing unit to achieve significant training time reductions. Reductions in training times of up to twenty-five times were found while using map sizes where other implementations have shown weakness. The reduced training times open up the contextual self-organizing map as viable option for engineering data visualization.

Insights into the implementation of synoptic weather-type classification using self-organizing maps: an Australian case study

The two-fold utility (data projection and cluster analysis) of a two-phase batch self-organizing map (SOM) procedure (CP2) has been previously explored using the NCEP/NCAR geopotential height data for east Australia. That study focused on examining the performance of CP2 in comparison with a traditional cluster analysis procedure, CP1, for the purpose of synoptic typing. The present paper provides additional documentation on the implementation of CP2 for the same region, with broader considerations on the effect of SOM map size, seasonality, data standardization and the choice of neighbourhood functions. A total of 215 SOMs (classifications) were trained through CP2 with various data processing and parameter settings. The examination of these SOMs shows that the two-fold utility of CP2 leads to supplementary visualization of the dominant synoptic patterns over the study region. For SOMs of the same map size (i.e. number of synoptic types), cluster analysis via CP2 provides data groupings with relatively high accuracy and large separation but reduced level of pattern self-organization, while data projection via CP2 tends to create data groupings with a high level of pattern self-organization but reduced accuracy and separation. The choice of map size affects the accuracy, separation and self-organization of data groupings. As a compromise, a map size of 10–20 for cluster analysis and 20–30 for data projection is recommended for the study region. To account for the seasonality and latitudinal heterogeneity in the activity of synoptic systems, a relatively larger SOM size is needed to capture typical synoptic features prevailing in different seasons. Data standardization helps to provide a relatively balanced representation between larger-scale synoptic systems (e.g. anticyclones) and smaller-scale synoptic features (e.g. thermal lows), and also improves the level of pattern self-organization on the SOM across seasons. The additional documentation in this paper encourages a wider application of CP2 in environmental research.

Self-organization and missing values in SOM and GTM

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.

Batch kernel SOM and related Laplacian methods for social network analysis

Large graphs are natural mathematical models for describing the structure of the data in a wide variety of fields, such as web mining, social networks, information retrieval, biological networks, etc. For all these applications, automatic tools are required to get a synthetic view of the graph and to reach a good understanding of the underlying problem. In particular, discovering groups of tightly connected vertices and understanding the relations between those groups is very important in practice. This paper shows how a kernel version of the batch self-organizing map can be used to achieve these goals via kernels derived from the Laplacian matrix of the graph, especially when it is used in conjunction with more classical methods based on the spectral analysis of the graph. The proposed method is used to explore the structure of a medieval social network modelled through a weighted graph that has been directly built from a large corpus of agrarian contracts.

A Scalable Parallel Algorithm for Self-Organizing Maps with Applicationsto 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.