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.

UPLC-ESI-TOFMS-based metabolomics and gene expression dynamics inspector self-organizing metabolomic maps as tools for understanding the cellular response to ionizing radiation

Global transcriptomic and proteomic profiling platforms have yielded important insights into the complex response to ionizing radiation (IR). Nonetheless, little is known about the ways in which small cellular metabolite concentrations change in response to IR. Here, a metabolomics approach using ultraperformance liquid chromatography coupled with electrospray time-of-flight mass spectrometry was used to profile, over time, the hydrophilic metabolome of TK6 cells exposed to IR doses ranging from 0.5 to 8.0 Gy. Multivariate data analysis of the positive ions revealed dose- and time-dependent clustering of the irradiated cells and identified certain constituents of the water-soluble metabolome as being significantly depleted as early as 1 h after IR. Tandem mass spectrometry was used to confirm metabolite identity. Many of the depleted metabolites are associated with oxidative stress and DNA repair pathways. Included are reduced glutathione, adenosine monophosphate, nicotinamide adenine dinucleotide, and spermine. Similar measurements were performed with a transformed fibroblast cell line, BJ, and it was found that a subset of the identified TK6 metabolites were effective in IR dose discrimination. The GEDI (Gene Expression Dynamics Inspector) algorithm, which is based on self-organizing maps, was used to visualize dynamic global changes in the TK6 metabolome that resulted from IR. It revealed dose-dependent clustering of ions sharing the same trends in concentration change across radiation doses. "Radiation metabolomics," the application of metabolomic analysis to the field of radiobiology, promises to increase our understanding of cellular responses to stressors such as radiation.

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.

Feature selection by multi-objective optimisation: Application to network anomaly detection by hierarchical self-organising maps

Feature selection is an important and active issue in clustering and classification problems. By choosing an adequate feature subset, a dataset dimensionality reduction is allowed, thus contributing to decreasing the classification computational complexity, and to improving the classifier performance by avoiding redundant or irrelevant features. Although feature selection can be formally defined as an optimisation problem with only one objective, that is, the classification accuracy obtained by using the selected feature subset, in recent years, some multi-objective approaches to this problem have been proposed. These either select features that not only improve the classification accuracy, but also the generalisation capability in case of supervised classifiers, or counterbalance the bias toward lower or higher numbers of features that present some methods used to validate the clustering/classification in case of unsupervised classifiers. The main contribution of this paper is a multi-objective approach for feature selection and its application to an unsupervised clustering procedure based on Growing Hierarchical Self-Organising Maps (GHSOMs) that includes a new method for unit labelling and efficient determination of the winning unit. In the network anomaly detection problem here considered, this multi-objective approach makes it possible not only to differentiate between normal and anomalous traffic but also among different anomalies. The efficiency of our proposals has been evaluated by using the well-known DARPA/NSL-KDD datasets that contain extracted features and labelled attacks from around 2 million connections. The selected feature sets computed in our experiments provide detection rates up to 99.8% with normal traffic and up to 99.6% with anomalous traffic, as well as accuracy values up to 99.12%.

The complete works of Robert Burns (self-interpreting) Illustrated with sixty etchings and wood cuts, maps and facsimiles...

Mode of access: Internet.

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.

Model Probability in Self-organising Maps

Growing models have been widely used for clustering or topology learning. Traditionally these models work on stationary environments, grow incrementally and adapt their nodes to a given distribution based on global parameters. In this paper, we present an enhanced unsupervised self-organising network for the modelling of visual objects. We first develop a framework for building non-rigid shapes using the growth mechanism of the self-organising maps, and then we define an optimal number of nodes without overfitting or underfitting the network based on the knowledge obtained from information-theoretic considerations. We present experimental results for hands and we quantitatively evaluate the matching capabilities of the proposed method with the topographic product.