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

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.

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.

Artificial Immune Tissue using Self-Organizing Networks

As introduced by Bentley et al. (2005), artificial immune systems (AIS) are lacking tissue, which is present in one form or another in all living multi-cellular organisms. Some have argued that this concept in the context of AIS brings little novelty to the already saturated field of the immune inspired computational research. This article aims to show that such a component of an AIS has the potential to bring an advantage to a data processing algorithm in terms of data pre-processing, clustering and extraction of features desired by the immune inspired system. The proposed tissue algorithm is based on self-organizing networks, such as self-organizing maps (SOM) developed by Kohonen (1996) and an analogy of the so called Toll-Like Receptors (TLR) affecting the activation function of the clusters developed by the SOM.

Artificial Immune Tissue using Self-Organizing Networks

As introduced by Bentley et al. (2005), artificial immune systems (AIS) are lacking tissue, which is present in one form or another in all living multi-cellular organisms. Some have argued that this concept in the context of AIS brings little novelty to the already saturated field of the immune inspired computational research. This article aims to show that such a component of an AIS has the potential to bring an advantage to a data processing algorithm in terms of data pre-processing, clustering and extraction of features desired by the immune inspired system. The proposed tissue algorithm is based on self-organizing networks, such as self-organizing maps (SOM) developed by Kohonen (1996) and an analogy of the so called Toll-Like Receptors (TLR) affecting the activation function of the clusters developed by the SOM.

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.

Estimating the monthly pCO2 distribution in the North Atlantic using a self-organizing neural network

[EN] Here we present monthly, basin-wide maps of the partial pressure of carbon dioxide (pCO2) for the North Atlantic on a latitude by longitude grid for years 2004 through 2006 inclusive. The maps have been computed using a neural network technique which reconstructs the non-linear relationships between three biogeochemical parameters and marine pCO2. A self organizing map (SOM) neural network has been trained using 389 000 triplets of the SeaWiFSMODIS chlorophyll-a concentration, the NCEP/NCAR reanalysis sea surface temperature, and the FOAM mixed layer depth. The trained SOM was labelled with 137 000 underway pCO2 measurements collected in situ during 2004, 2005 and 2006 in the North Atlantic, spanning the range of 208 to 437atm. The root mean square error (RMSE) of the neural network fit to the data is 11.6?atm, which equals to just above 3 per cent of an average pCO2 value in the in situ dataset. The seasonal pCO2 cycle as well as estimates of the interannual variability in the major biogeochemical provinces are presented and discussed. High resolution combined with basin-wide coverage makes the maps a useful tool for several applications such as the monitoring of basin-wide air-sea CO2 fluxes or improvement of seasonal and interannual marine CO2 cycles in future model predictions. The method itself is a valuable alternative to traditional statistical modelling techniques used in geosciences.

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.

The parameterless self-organizing map algorithm

The parameterless self-organizing map (PLSOM) is a new neural network algorithm based on the self-organizing map (SOM). It eliminates the need for a learning rate and annealing schemes for learning rate and neighborhood size. We discuss the relative performance of the PLSOM and the SOM and demonstrate some tasks in which the SOM fails but the PLSOM performs satisfactory. Finally we discuss some example applications of the PLSOM and present a proof of ordering under certain limited conditions.

Recursive self-organizing map as a contractive iterative function system

Recently, there has been a considerable research activity in extending topographic maps of vectorial data to more general data structures, such as sequences or trees. However, the representational capabilities and internal representations of the models are not well understood. We rigorously analyze a generalization of the Self-Organizing Map (SOM) for processing sequential data, Recursive SOM (RecSOM [1]), as a non-autonomous dynamical system consisting off a set of fixed input maps. We show that contractive fixed input maps are likely to produce Markovian organizations of receptive fields o the RecSOM map. We derive bounds on parameter $\beta$ (weighting the importance of importing past information when processing sequences) under which contractiveness of the fixed input maps is guaranteed.

Self-Organizing Map Neural Architectures Based on Limit Cycle Attractors

Recent efforts to develop large-scale neural architectures have paid relatively little attention to the use of self-organizing maps (SOMs). Part of the reason is that most conventional SOMs use a static encoding representation: Each input is typically represented by the fixed activation of a single node in the map layer. This not only carries information in an inefficient and unreliable way that impedes building robust multi-SOM neural architectures, but it is also inconsistent with rhythmic oscillations in biological neural networks. Here I develop and study an alternative encoding scheme that instead uses limit cycle attractors of multi-focal activity patterns to represent input patterns/sequences. Such a fundamental change in representation raises several questions: Can this be done effectively and reliably? If so, will map formation still occur? What properties would limit cycle SOMs exhibit? Could multiple such SOMs interact effectively? Could robust architectures based on such SOMs be built for practical applications? The principal results of examining these questions are as follows. First, conditions are established for limit cycle attractors to emerge in a SOM through self-organization when encoding both static and temporal sequence inputs. It is found that under appropriate conditions a set of learned limit cycles are stable, unique, and preserve input relationships. In spite of the continually changing activity in a limit cycle SOM, map formation continues to occur reliably. Next, associations between limit cycles in different SOMs are learned. It is shown that limit cycles in one SOM can be successfully retrieved by another SOM’s limit cycle activity. Control timings can be set quite arbitrarily during both training and activation. Importantly, the learned associations generalize to new inputs that have never been seen during training. Finally, a complete neural architecture based on multiple limit cycle SOMs is presented for robotic arm control. This architecture combines open-loop and closed-loop methods to achieve high accuracy and fast movements through smooth trajectories. The architecture is robust in that disrupting or damaging the system in a variety of ways does not completely destroy the system. I conclude that limit cycle SOMs have great potentials for use in constructing robust neural architectures.

Is a Majority Enough? Psychological Well-being and Its Relation to Academic and Prosocial Motivation, Self-regulation and Achievement at school

This cross-sectional study analyzed psychological well-being at school using the Self-Determination theory as a theoretical frame-work. The study explored basic psychological needs fulfillment (BPNS), academic (SRQ-A), prosocial self-regulation (SRQ-P) and motivation, and their relationship with achievement in general, special and selective education (N=786, 444 boys, 345 girls, mean age 12 yrs 8 mths). Motivation starts behavior which becomes guided by self-regulation. The perceived locus of control (PLOC) affects how self-determined this behavior will be; in other words, to what extent it is autonomously regulated. In order learn and thus to be able to accept external goals, a student has to feel emotionally safe and have sufficient ego-flexibility—all of which builds on satisfied psychological needs. In this study those conditions were explored. In addition to traditional methods Self-organizing maps (SOM), was used in order to cluster the students according to their well-being, self-regulation, motivation and achievement scores. The main impacts of this research were: a presentation of the theory based alternative of studying psychological well-being at school and usage of both the variable and person-oriented approach. In this Finnish sample the results showed that the majority of students felt well, but the well-being varied by group. Overall about for 11–15% the basic needs were deprived depending on the educational group. Age and educational group were the most effective factors; gender was important in relation to prosocial identified behavior. Although the person-oriented SOM-approach, was in a large extent confirming what was no-ticed by using comparison of the variables: the SEN groups had lower levels of basic needs fulfillment and less autonomous self-regulation, interesting deviations of that rule appeared. Some of the SEL- and GEN-group members ended up in the more unfavorable SOM-clusters, and not all SEN-group members belonged to the poorest clusters (although not to the best either). This evidence refines the well-being and self-regulation picture, and may re-direct intervention plans, and turn our focus also on students who might otherwise remain unnoticed. On the other hand, these results imply simultaneously that in special education groups the average is not the whole truth. On the basis of theoretical and empirical considerations an intervention model was sug-gested. The aim of the model was to shift amotivation or external motivation in a more intrinsic direction. According to the theoretical and empirical evidence this can be achieved first by studying the self-concept a student has, and then trying to affect both inner and environmental factors—including a consideration of the basic psychological needs. Keywords: academic self-regulation, prosocial self-regulation, basic psychological needs, moti-vation, achievement

Relação entre as variáveis sociais, económicas e ambientais com o padrão da distribuição espaço-temporal dos casos de Dengue por munícipio no Brasil : de 2008 até 2012, utilizando o SOM

Atualmente, um dos principais desafios que afeta a saúde pública no Brasil é a crescente evolução no número de casos e epidemias provocados pelo vírus da dengue. Não existem estudos suficientes que consigam elucidar quais fatores contribuem para a evolução das epidemias de Dengue. Fatores como condições sanitárias, localização geográfica, investimentos financeiros em infraestrutura e qualidade de vida podem estar relacionados com a incidência de Dengue. Além disso, outra questão que merece um maior destaque é o estudo para se identificar o grau de impacto das variáveis determinantes da dengue e se existe um padrão que está correlacionado com a taxa de incidência. Desta forma, este trabalho tem como objetivo principal a correlação da taxa de incidência da dengue na população de cada município brasileiro, utilizando dados relativos aos aspectos sociais, econômicos, demográficos e ambientais. Outra contribuição relevante do trabalho, foi a análise dos padrões de distribuição espacial da taxa de incidência de Dengue e sua relação com os padrões encontrados utilizando as variáveis socioeconômicas e ambientais, sobretudo analisando a evolução temporal no período de 2008 até 2012. Para essa análises, utilizou-se o Sistema de Informação Geográfica (SIG) aliado com a mineração de dados, através da metodologia de rede neural mais especificamente o mapa auto organizável de Kohonen ou self-organizing maps (SOM). Tal metodologia foi empregada para a identificação de padrão de agrupamentos dessas variáveis e sua relação com as classes de incidência de dengue no Brasil (Alta, Média e Baixa). Assim, este projeto contribui de forma significativa para uma melhor compreensão dos fatores que estão associados à ocorrência de Dengue, e como essa doença está correlacionada com fatores como: meio ambiente, infraestrutura e localização no espaço geográfico.