Using self organizing maps on compositional data

Self-organizing maps (Kohonen 1997) is a type of artificial neural network developed to explore patterns in high-dimensional multivariate data. The conventional version of the algorithm involves the use of Euclidean metric in the process of adaptation of the model vectors, thus rendering in theory a whole methodology incompatible with non-Euclidean geometries. In this contribution we explore the two main aspects of the problem: 1. Whether the conventional approach using Euclidean metric can shed valid results with compositional data. 2. If a modification of the conventional approach replacing vectorial sum and scalar multiplication by the canonical operators in the simplex (i.e. perturbation and powering) can converge to an adequate solution. Preliminary tests showed that both methodologies can be used on compositional data. However, the modified version of the algorithm performs poorer than the conventional version, in particular, when the data is pathological. Moreover, the conventional ap- proach converges faster to a solution, when data is \well-behaved". Key words: Self Organizing Map; Artificial Neural networks; Compositional data

Fast training of self organizing maps for the visual exploration of molecular compounds

Visual exploration of scientific data in life science area is a growing research field due to the large amount of available data. The Kohonen’s Self Organizing Map (SOM) is a widely used tool for visualization of multidimensional data. In this paper we present a fast learning algorithm for SOMs that uses a simulated annealing method to adapt the learning parameters. The algorithm has been adopted in a data analysis framework for the generation of similarity maps. Such maps provide an effective tool for the visual exploration of large and multi-dimensional input spaces. The approach has been applied to data generated during the High Throughput Screening of molecular compounds; the generated maps allow a visual exploration of molecules with similar topological properties. The experimental analysis on real world data from the National Cancer Institute shows the speed up of the proposed SOM training process in comparison to a traditional approach. The resulting visual landscape groups molecules with similar chemical properties in densely connected regions.

Use of self-organizing maps and molecular descriptors to predict the cytotoxic activity of sesquiterpene lactones

Some sesquiterpene lactones (SLs) are the active compounds of a great number of traditionally medicinal plants from the Asteraceae family and possess considerable cytotoxic activity. Several studies in vitro have shown the inhibitory activity against cells derived from human carcinoma of the nasopharynx (KB). Chemical studies showed that the cytotoxic activity is due to the reaction of alpha,beta-unsaturated carbonyl structures of the SLs with thiols, such as cysteine. These studies support the view that SLs inhibit tumour growth by selective alkylation of growth-regulatory biological macromolecules, such as key enzymes, which control cell division, thereby inhibiting a variety of cellular functions, which directs the cells into apoptosis. In this study we investigated a set of 55 different sesquiterpene lactones, represented by 5 skeletons (22 germacranolides, 6 elemanolides, 2 eudesmanolides, 16 guaianolides and nor-derivatives and 9 pseudoguaianolides), in respect to their cytotoxic properties. The experimental results and 3D molecular descriptors were submitted to Kohonen self-organizing map (SOM) to classify (training set) and predict (test set) the cytotoxic activity. From the obtained results, it was concluded that only the geometrical descriptors showed satisfactory values. The Kohonen map obtained after training set using 25 geometrical descriptors shows a very significant match, mainly among the inactive compounds (similar to 84%). Analyzing both groups, the percentage seen is high (83%). The test set shows the highest match, where 89% of the substances had their cytotoxic activity correctly predicted. From these results, important properties for the inhibition potency are discussed for the whole dataset and for subsets of the different structural skeletons. (C) 2008 Elsevier Masson SAS. All rights reserved.

New developmental stages for common marmosets (Callithrix jacchus) using mass and age variables obtained by K-means algorithm and self-organizing maps (SOM)

LEÃO, Adriano de Castro; DÓRIA NETO, Adrião Duarte; SOUSA, Maria Bernardete Cordeiro de. New developmental stages for common marmosets (Callithrix jacchus) using mass and age variables obtained by K-means algorithm and self-organizing maps (SOM). Computers in Biology and Medicine, v. 39, p. 853-859, 2009

Self-Organizing Maps as a New Tool for Classification of Plants at Lower Hierarchical Levels

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The Meaningful Fractal Fuzzy Dimension Applied to the Design of Self Organizing Maps

This paper presents the principal results of a detailed study about the use of the Meaningful Fractal Fuzzy Dimension measure in the problem in determining adequately the topological dimension of output space of a Self-Organizing Map. This fractal measure is conceived by combining the Fractals Theory and Fuzzy Approximate Reasoning. In this work this measure was applied on the dataset in order to obtain a priori knowledge, which is used to support the decision making about the SOM output space design. Several maps were designed with this approach and their evaluations are discussed here.

Self-Organizing Maps of Molecular Descriptors for Sesquiterpene Lactones and Their Application to the Chemotaxonomy of the Asteraceae Family

The Asteraceae, one of the largest families among angiosperms, is chemically characterised by the production of sesquiterpene lactones (SLs). A total of 1,111 SLs, which were extracted from 658 species, 161 genera, 63 subtribes and 15 tribes of Asteraceae, were represented and registered in two dimensions in the SISTEMATX, an in-house software system, and were associated with their botanical sources. The respective 11 block of descriptors: Constitutional, Functional groups, BCUT, Atom-centred, 2D autocorrelations, Topological, Geometrical, RDF, 3D-MoRSE, GETAWAY and WHIM were used as input data to separate the botanical occurrences through self-organising maps. Maps that were generated with each descriptor divided the Asteraceae tribes, with total index values between 66.7% and 83.6%. The analysis of the results shows evident similarities among the Heliantheae, Helenieae and Eupatorieae tribes as well as between the Anthemideae and Inuleae tribes. Those observations are in agreement with systematic classifications that were proposed by Bremer, which use mainly morphological and molecular data, therefore chemical markers partially corroborate with these classifications. The results demonstrate that the atom-centred and RDF descriptors can be used as a tool for taxonomic classification in low hierarchical levels, such as tribes. Descriptors obtained through fragments or by the two-dimensional representation of the SL structures were sufficient to obtain significant results, and better results were not achieved by using descriptors derived from three-dimensional representations of SLs. Such models based on physico-chemical properties can project new design SLs, similar structures from literature or even unreported structures in two-dimensional chemical space. Therefore, the generated SOMs can predict the most probable tribe where a biologically active molecule can be found according Bremer classification.

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

The Self-OrganizingMap (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 topologypreservation is the most common concept used to implement this measure. Several qualitative and quantitative methods have been proposed for measuring the degree of SOM topologypreservation, particularly using Kohonen's model. In this work, two methods for measuring the topologypreservation of the Growing Cell Structures (GCSs) model are proposed: the topographic function and the topology preserving map

Detecting false testimonies in reputation systems using self-organizing maps

It has been demonstrated that rating trust and reputation of individual nodes is an effective approach in distributed environments in order to improve security, support decision-making and promote node collaboration. Nevertheless, these systems are vulnerable to deliberate false or unfair testimonies. In one scenario, the attackers collude to give negative feedback on the victim in order to lower or destroy its reputation. This attack is known as bad mouthing attack. In another scenario, a number of entities agree to give positive feedback on an entity (often with adversarial intentions). This attack is known as ballot stuffing. Both attack types can significantly deteriorate the performances of the network. The existing solutions for coping with these attacks are mainly concentrated on prevention techniques. In this work, we propose a solution that detects and isolates the abovementioned attackers, impeding them in this way to further spread their malicious activity. The approach is based on detecting outliers using clustering, in this case self-organizing maps. An important advantage of this approach is that we have no restrictions on training data, and thus there is no need for any data pre-processing. Testing results demonstrate the capability of the approach in detecting both bad mouthing and ballot stuffing attack in various scenarios.

Dynamics and topographic organization of recursive self-organizing maps

Recently there has been an outburst of interest in extending topographic maps of vectorial data to more general data structures, such as sequences or trees. However, there is no general consensus as to how best to process sequences using topographicmaps, and this topic remains an active focus of neurocomputational research. The representational capabilities and internal representations of the models are not well understood. Here, we rigorously analyze a generalization of the self-organizingmap (SOM) for processing sequential data, recursive SOM (RecSOM) (Voegtlin, 2002), as a nonautonomous dynamical system consisting of a set of fixed input maps. We argue that contractive fixed-input maps are likely to produce Markovian organizations of receptive fields on the RecSOM map. We derive bounds on parameter β (weighting the importance of importing past information when processing sequences) under which contractiveness of the fixed-input maps is guaranteed. Some generalizations of SOM contain a dynamic module responsible for processing temporal contexts as an integral part of the model. We show that Markovian topographic maps of sequential data can be produced using a simple fixed (nonadaptable) dynamic module externally feeding a standard topographic model designed to process static vectorial data of fixed dimensionality (e.g., SOM). However, by allowing trainable feedback connections, one can obtain Markovian maps with superior memory depth and topography preservation. We elaborate on the importance of non-Markovian organizations in topographic maps of sequential data. © 2006 Massachusetts Institute of Technology.

String Measure Applied to String Self-Organizing Maps and Networks of Evolutionary Processors

* Supported by projects CCG08-UAM TIC-4425-2009 and TEC2007-68065-C03-02

New developmental stages for common marmosets (Callithrix jacchus) using mass and age variables obtained by K-means algorithm and self-organizing maps (SOM)

LEÃO, Adriano de Castro; DÓRIA NETO, Adrião Duarte; SOUSA, Maria Bernardete Cordeiro de. New developmental stages for common marmosets (Callithrix jacchus) using mass and age variables obtained by K-means algorithm and self-organizing maps (SOM). Computers in Biology and Medicine, v. 39, p. 853-859, 2009

New developmental stages for common marmosets (Callithrix jacchus) using mass and age variables obtained by K-means algorithm and self-organizing maps (SOM)

LEÃO, Adriano de Castro; DÓRIA NETO, Adrião Duarte; SOUSA, Maria Bernardete Cordeiro de. New developmental stages for common marmosets (Callithrix jacchus) using mass and age variables obtained by K-means algorithm and self-organizing maps (SOM). Computers in Biology and Medicine, v. 39, p. 853-859, 2009

A three-dimensional representation method for noisy point clouds based on growing self-organizing maps accelerated on GPUs

The research described in this thesis was motivated by the need of a robust model capable of representing 3D data obtained with 3D sensors, which are inherently noisy. In addition, time constraints have to be considered as these sensors are capable of providing a 3D data stream in real time. This thesis proposed the use of Self-Organizing Maps (SOMs) as a 3D representation model. In particular, we proposed the use of the Growing Neural Gas (GNG) network, which has been successfully used for clustering, pattern recognition and topology representation of multi-dimensional data. Until now, Self-Organizing Maps have been primarily computed offline and their application in 3D data has mainly focused on free noise models, without considering time constraints. It is proposed a hardware implementation leveraging the computing power of modern GPUs, which takes advantage of a new paradigm coined as General-Purpose Computing on Graphics Processing Units (GPGPU). The proposed methods were applied to different problem and applications in the area of computer vision such as the recognition and localization of objects, visual surveillance or 3D reconstruction.