Soledad Delgado

Visualizing high-dimensional input data with growing self-organizing maps

Currently, there exist many research areas that produce large multivariable datasets that are difficult to visualize in order to extract useful information. Kohonen self-organizing maps have been used successfully in the visualization and analysis of multidimensional data. In this work, a projection technique that compresses multidimensional datasets into two dimensional space using growing self-organizing maps is described. With this embedding scheme, traditional Kohonen visualization methods have been implemented using growing cell structures networks. New graphical map displays have been compared with Kohonen graphs using two groups of simulated data and one group of real multidimensional data selected from a satellite scene.

Realistic Three Dimensional Fitness Landscapes Generated by Self Organizing Maps for the Analysis of Experimental HIV-1 Evolution

Human Immunodeficiency Virus type 1 (HIV-1) because of high mutation rates, large population sizes, and rapid replication, exhibits complex evolutionary strategies. For the analysis of evolutionary processes, the graphical representation of fitness landscapes provides a significant advantage. The experimental determination of viral fitness remains, in general, difficult and consequently most published fitness landscapes have been artificial, theoretical or estimated. Self-Organizing Maps (SOM) are a class of Artificial Neural Network (ANN) for the generation of topological ordered maps. Here, three-dimensional (3D) data driven fitness landscapes, derived from a collection of sequences from HIV-1 viruses after “in vitro” passages and labelled with the corresponding experimental fitness values, were created by SOM. These maps were used for the visualization and study of the evolutionary process of HIV-1 “in vitro” fitness recovery, by directly relating fitness values with viral sequences. In addition to the representation of the sequence space search carried out by the viruses, these landscapes could also be applied for the analysis of related variants like members of viral quasiespecies. SOM maps permit the visualization of the complex evolutionary pathways in HIV-1 fitness recovery. SOM fitness landscapes have an enormous potential for the study of evolution in related viruses of “in vitro” works or from “in vivo” clinical studies with human, animal or plant viral infections.

A combined measure for quantifying and qualifying the topology preservation of growing self-organizing maps

Abstract The Self-Organizing Map (SOM) is a neural network model that performs an ordered projection of a high dimensional input space in a low-dimensional topological structure. The process in which such mapping is formed is defined by the SOM algorithm, which is a competitive, unsupervised and nonparametric method, since it does not make any assumption about the input data distribution. The feature maps provided by this algorithm have been successfully applied for vector quantization, clustering and high dimensional data visualization processes. However, the initialization of the network topology and the selection of the SOM training parameters are two difficult tasks caused by the unknown distribution of the input signals. A misconfiguration of these parameters can generate a feature map of low-quality, so it is necessary to have some measure of the degree of adaptation of the SOM network to the input data model. The topology preservation is the most common concept used to implement this measure. Several qualitative and quantitative methods have been proposed for measuring the degree of SOM topology preservation, particularly using Kohonens model. In this work, two methods for measuring the topology preservation of the Growing Cell Structures (GCSs) model are proposed: the topographic function and the topology preserving map.

Topology Preserving Visualization Methods for Growing Self-Organizing Maps

Self-organizing map (SOM) is a neural network model widely used in high dimensional data visualization processes. A trained SOM provides a simplified data model as well as a projection of the multidimensional input data into a bi-dimensional plane that reflects the relationships involving the training patters. Visualization methods based in SOM explore different characteristics related to the data learned by the network. It is necessary to find methods to determine the goodness of a trained network in order to evaluate the quality of the high dimensional data visualizations generated using the SOM simplified model. The degree of topology preservation is the most common concept used to implement this measure. Several qualitative and quantitative methods have been proposed for measuring the degree of SOM topology preservation, in particular using Kohonen model. In this work, two measuring topology preservation methods for Growing Cell Structures (GCS) model are proposed: the topographic function and the topology preserving map.

A SOM prototype-based cluster analysis methodology

An original computational approach for cluster analysis is proposed.The method consists of two phases, which are based on Self-Organizing Map.Topology-preserving and connectivity functions are used in the clustering process.The method is proved using three benchmark datasets and a real biological dataset.Automation in parameterization results in a user-friendly methodology. Data clustering is aimed at finding groups of data that share common hidden properties. These kinds of techniques are especially critical at early stages of data analysis where no information about the dataset is available. One of the mayor shortcomings of the clustering algorithms is the difficulty for non-experts users to configure them and, in some cases, interpret the results. In this work a computational approach with a two-layer structure based on Self-Organizing Map (SOM) is presented for cluster analysis. In the first level, a quantization of the data samples using topology-preserving metrics to automatically determine the number of units in the SOM is proposed. In the second level the obtained SOM prototypes are clustered by means of a connectivity analysis to explore the quality of the partitioning with different number of clusters. The most important benefit of this two-layer procedure is that computational load decreases considerably in comparison with data based clustering methods, making it possible to cluster large data sets and to consider several different clustering alternatives in a limited time. This methodology produces a two-dimensional map representation of the, usually, high dimensional input space, along with quantitative information on viable clustering alternatives, which facilitates the exploration of the possible partitions in a dataset. The efficiency and interpretation of the methodology is illustrated by its application to artificial, benchmark and real complex biological datasets. The experimental results demonstrate the ability of the method to identify possible segmentations in a dataset, compared to algorithms that only yield a single clustering solution. The proposed algorithm tackles the intrinsic limitations of SOM and the parameter settings associated with the clustering methodology, without requiring the number of clusters or the SOM architecture as a prerequisite, among others. This way, it makes possible its application even by researchers with a limited expertise in machine learning.

Suitability of Using Self-Organizing Neural Networks in Configuring P-System Communications Architectures

Nowadays, it is possible to find out different viable architectures that implements P Systems in a distributed cluster of processors. These proposed architectures have reached a certain compromise between the massively parallelism character of the system and the evolution step times. They are based in the distribution of several membranes in each processor, the use of proxies to control the communication between membranes and mainly, the suitable distribution of the architecture in a balanced tree of processors. For a given P-system and K processors, there exists a great volume of possible distributions of membranes over these. The main disadvantage related with these architectures is focused in the selection of the distribution of membranes that minimizes the external communications between them and maximizes the parallelism grade. In this paper, we suggest the use of Self-Organizing Neural Networks (SONN) with growing capability to help in this selection process for a given P-system.

P-system communications architecture configuration based on growing self-organizing maps

The different viable architectures that implement P-systems (membrane systems) over distributed clusters of processors have a major drawback: the distribution of these architectures in a balanced tree of processors can minimize external communications and maximize the parallelism grade. For a given P-system and K processors, there exists a great number of possible distributions of membranes. In a recent article, the feasibility of using self-organizing neural networks (SONN) with a growing capacity to help in the selection process of a distribution for a given P-system has been demonstrated, although the nature of the two-dimensional patterns used in the study limited the possibility of defining more flexible degrees of communication, making it more difficult to locate the best distribution. In this article, the capacity of a growing cell structure (GCS) model for projecting high-dimensional spaces in bi-dimensional graphs is explored.