Fast Algorithm and Implementation of Dissimilarity Self-Organizing Maps

In many real world applications, data cannot be accurately represented by vectors. In those situations, one possible solution is to rely on dissimilarity measures that enable sensible comparison between observations. Kohonen's Self-Organizing Map (SOM) has been adapted to data described only through their dissimilarity matrix. This algorithm provides both non linear projection and clustering of non vector data. Unfortunately, the algorithm suffers from a high cost that makes it quite difficult to use with voluminous data sets. In this paper, we propose a new algorithm that provides an important reduction of the theoretical cost of the dissimilarity SOM without changing its outcome (the results are exactly the same as the ones obtained with the original algorithm). Moreover, we introduce implementation methods that result in very short running times. Improvements deduced from the theoretical cost model are validated on simulated and real world data (a word list clustering problem). We also demonstrate that the proposed implementation methods reduce by a factor up to 3 the running time of the fast algorithm over a standard implementation

Computing Exact Clustering Posteriors with Subset Convolution

An exponential-time exact algorithm is provided for the task of clustering n items of data into k clusters. Instead of seeking one partition, posterior probabilities are computed for summary statistics: the number of clusters, and pairwise co-occurrence. The method is based on subset convolution, and yields the posterior distribution for the number of clusters in O(n * 3^n) operations, or O(n^3 * 2^n) using fast subset convolution. Pairwise co-occurrence probabilities are then obtained in O(n^3 * 2^n) operations. This is considerably faster than exhaustive enumeration of all partitions.Comment: 6 figure

Analysis of Data Clusters Obtained by Self-Organizing Methods

The self-organizing methods were used for the investigation of financial market. As an example we consider data time-series of Dow Jones index for the years 2002-2003 (R. Mantegna, cond-mat/9802256). In order to reveal new structures in stock market behavior of the companies drawing up Dow Jones index we apply SOM (Self-Organizing Maps) and GMDH (Group Method of Data Handling) algorithms. Using SOM techniques we obtain SOM-maps that establish a new relationship in market structure. Analysis of the obtained clusters was made by GMDH.Comment: 10 pages, 4 figure

How to use the Kohonen algorithm to simultaneously analyse individuals in a survey

The Kohonen algorithm (SOM, Kohonen,1984, 1995) is a very powerful tool for data analysis. It was originally designed to model organized connections between some biological neural networks. It was also immediately considered as a very good algorithm to realize vectorial quantization, and at the same time pertinent classification, with nice properties for visualization. If the individuals are described by quantitative variables (ratios, frequencies, measurements, amounts, etc.), the straightforward application of the original algorithm leads to build code vectors and to associate to each of them the class of all the individuals which are more similar to this code-vector than to the others. But, in case of individuals described by categorical (qualitative) variables having a finite number of modalities (like in a survey), it is necessary to define a specific algorithm. In this paper, we present a new algorithm inspired by the SOM algorithm, which provides a simultaneous classification of the individuals and of their modalities.Comment: Special issue ESANN 0

Self-Organizing Time Map: An Abstraction of Temporal Multivariate Patterns

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