Quantitative self-organizing maps for clustering electron tomograms

Tomography emerges as a powerful methodology for determining the complex architectures of biological specimens that are better regarded from the structural point of view as singular entities. However, once the structure of a sufficiently large number of singular specimens is solved, quite possibly structural patterns start to emerge. This latter situation is addressed here, where the clustering of a set of 3D reconstructions using a novel quantitative approach is presented. In general terms, we propose a new variant of a self-organizing neural network for the unsupervised classification of 3D reconstructions. The novelty of the algorithm lies in its rigorous mathematical formulation that, starting from a large set of noisy input data, finds a set of "representative" items, organized onto an ordered output map, such that the probability density of this set of representative items resembles at its possible best the probability density of the input data. In this study, we evaluate the feasibility of application of the proposed neural approach to the problem of identifying similar 3D motifs within tomograms of insect flight muscle. Our experimental results prove that this technique is suitable for this type of problem, providing the electron microscopy community with a new tool for exploring large sets of tomogram data to find complex patterns.     

Foreground detection in video sequences with probabilistic self-organizing maps

Background modeling and foreground detection are key parts of any computer vision system. These problems have been addressed in literature with several probabilistic approaches based on mixture models. Here we propose a new kind of probabilistic background models which is based on probabilistic self-organising maps. This way, the background pixels are modeled with more flexibility. On the other hand, a statistical correlation measure is used to test the similarity among nearby pixels, so as to enhance the detection performance by providing a feedback to the process. Several well known benchmark videos have been used to assess the relative performance of our proposal with respect to traditional neural and non neural based methods, with favourable results, both qualitatively and quantitatively. A statistical analysis of the differences among methods demonstrates that our method is significantly better than its competitors. This way, a strong alternative to classical methods is presented.     

Analysis of metabolite profile data using batch-learning self-organizing maps

Novel tools are needed for efficient analysis and visualization of the massive data sets associated with metabolomics. Here, we describe a batch-learning self-organizing map (BL-SOM) for metabolome informatics that makes the learning process and resulting map independent of the order of data input. This approach was successfully used in analyzing and organizing the metabolome data forArabidopsis thaliana cells cultured under salt stress. Our 6 × 4 matrix presented patterns of metabolite levels at different time periods. A negative correlation was found between the levels of amino acids and metabolites related to glycolysis metabolism in response to this stress. Therefore, BL-SOM could be an excellent tool for clustering and visualizing high dimensional, complex metabolome data in a single map.     

Analysis of gene expression data using self-organizing maps.

DNA microarray technologies together with rapidly increasing genomic sequence information is leading to an explosion in available gene expression data. Currently there is a great need for efficient methods to analyze and visualize these massive data sets. A self-organizing map (SOM) is an unsupervised neural network learning algorithm which has been successfully used for the analysis and organization of large data files. We have here applied the SOM algorithm to analyze published data of yeast gene expression and show that SOM is an excellent tool for the analysis and visualization of gene expression profiles.     

The combined use of self-organizing maps and Andrews' Curves

The use of self-organizing maps to analyze data often depends on finding effective methods to visualize the SOM's structure. In this paper we propose a new way to perform that visualization using a variant of Andrews' Curves. Also we show that the interaction between these two methods allows us to find sub-clusters within identified clusters. Perhaps more importantly, using the SOM to pre-process data by identifying gross features enables us to use Andrews' Curves on data sets which would have previously been too large for the methodology. Finally we show how a three way interaction between the human user and these two methods can be a valuable exploratory data analysis tool.     

Reducing topological defects in self-organizing maps using multiple scale neighborhood functions

In this paper, we propose a method of reducing topological defects in self-organizing maps (SOMs) using multiple scale neighborhood functions. The multiple scale neighborhood functions are inspired by multiple scale channels in the human visual system. To evaluate the proposed method, we applied it to the traveling salesman problem (TSP), and examined two indexes: the tour length of the solution and the number of kinks in the solution. Consequently, the two indexes are lower for the proposed method. These results indicate that our proposed method has the ability to reduce topological defects.     

Ordering process of self-organizing maps improved by asymmetric neighborhood function

The Self-organizing map (SOM) is an unsupervised learning method based on the neural computation, which has found wide applications. However, the learning process sometime takes multi-stable states, within which the map is trapped to an undesirable disordered state including topological defects on the map. These topological defects critically aggravate the performance of the SOM. In order to overcome this problem, we propose to introduce an asymmetric neighborhood function for the SOM algorithm. Compared with the conventional symmetric one, the asymmetric neighborhood function accelerates the ordering process even in the presence of the defect. However, this asymmetry tends to generate a distorted map. This can be suppressed by an improved method of the asymmetric neighborhood function. In the case of one-dimensional SOM, it is found that the required steps for perfect ordering is numerically shown to be reduced from O(N ³) to O(N ²). We also discuss the ordering process of a twisted state in two-dimensional SOM, which can not be rectified by the ordinary symmetric neighborhood function.     

Flexible structure multiple modeling using irregular self-organizing maps neural network

The MMSOM identification method, which had been presented by the authors, is improved to the multiple modeling by the irregular self-organizing map (MMISOM) using the irregular SOM (ISOM). Inputs to the neural networks are parameters of the instantaneous model computed adaptively at every instant. The neural network learns these models. The reference vectors of its output nodes are estimation of the parameters of the local models. At every instant, the model with closest output to the plant output is selected as the model of the plant. ISOM used in this paper is a graph of all the nodes and some of the weighted links between them to make a minimum spanning tree graph. It is shown in this paper that it is possible to add new models if the number of models is initially less than the appropriate one. The MMISOM shows more flexibility to cover the linear model space of the plant when the space is concave.     

Flexible structure multiple modeling using irregular self-organizing maps neural network

The MMSOM identification method, which had been presented by the authors, is improved to the multiple modeling by the irregular self-organizing map (MMISOM) using the irregular SOM (ISOM). Inputs to the neural networks are parameters of the instantaneous model computed adaptively at every instant. The neural network learns these models. The reference vectors of its output nodes are estimation of the parameters of the local models. At every instant, the model with closest output to the plant output is selected as the model of the plant. ISOM used in this paper is a graph of all the nodes and some of the weighted links between them to make a minimum spanning tree graph. It is shown in this paper that it is possible to add new models if the number of models is initially less than the appropriate one. The MMISOM shows more flexibility to cover the linear model space of the plant when the space is concave.     

Assessment of self-organizing maps to analyze sole-carbon source utilization profiles

The use of community-level physiological profiles obtained with Biolog microplates is widely employed to consider the functional diversity of bacterial communities. Biolog produces a great amount of data which analysis has been the subject of many studies. In most cases, after some transformations, these data were investigated with classical multivariate analyses. Here we provided an alternative to this method, that is the use of an artificial intelligence technique, the Self-Organizing Maps (SOM, unsupervised neural network). We used data from a microcosm study of algae-associated bacterial communities placed in various nutritive conditions. Analyses were carried out on the net absorbances at two incubation times for each substrates and on the chemical guild categorization of the total bacterial activity. Compared to Principal Components Analysis and cluster analysis, SOM appeared as a valuable tool for community classification, and to establish clear relationships between clusters of bacterial communities and sole-carbon sources utilization. Specifically, SOM offered a clear bidimensional projection of a relatively large volume of data and were easier to interpret than plots commonly obtained with multivariate analyses. They would be recommended to pattern the temporal evolution of communities' functional diversity.     

Self-enhancement learning: target-creating learning and its application to self-organizing maps

In this article, we propose a new learning method called "self-enhancement learning." In this method, targets for learning are not given from the outside, but they can be spontaneously created within a neural network. To realize the method, we consider a neural network with two different states, namely, an enhanced and a relaxed state. The enhanced state is one in which the network responds very selectively to input patterns, while in the relaxed state, the network responds almost equally to input patterns. The gap between the two states can be reduced by minimizing the Kullback-Leibler divergence between the two states with free energy. To demonstrate the effectiveness of this method, we applied self-enhancement learning to the self-organizing maps, or SOM, in which lateral interactions were added to an enhanced state. We applied the method to the well-known Iris, wine, housing and cancer machine learning database problems. In addition, we applied the method to real-life data, a student survey. Experimental results showed that the U-matrices obtained were similar to those produced by the conventional SOM. Class boundaries were made clearer in the housing and cancer data. For all the data, except for the cancer data, better performance could be obtained in terms of quantitative and topological errors. In addition, we could see that the trustworthiness and continuity, referring to the quality of neighborhood preservation, could be improved by the self-enhancement learning. Finally, we used modern dimensionality reduction methods and compared their results with those obtained by the self-enhancement learning. The results obtained by the self-enhancement were not superior to but comparable with those obtained by the modern dimensionality reduction methods.     

An efficient approach to the travelling salesman problem using self-organizing maps

This paper presents an approach to the well-known Travelling Salesman Problem (TSP) using Self-Organizing Maps (SOM). The SOM algorithm has interesting topological information about its neurons configuration on cartesian space, which can be used to solve optimization problems. Aspects of initialization, parameters adaptation, and complexity analysis of the proposed SOM based algorithm are discussed. The results show an average deviation of 3.7% from the optimal tour length for a set of 12 TSP instances.     

Clustering of ant communities and indicator species analysis using self-organizing maps

To understand the complex relationships that exist between ant assemblages and their habitats, we performed a self-organizing map (SOM) analysis to clarify the interactions among ant diversity, spatial distribution, and land use types in Fukuoka City, Japan. A total of 52 species from 12 study sites with nine land use types were collected from 1998 to 2012. A SOM was used to classify the collected data into three clusters based on the similarities between the ant communities. Consequently, each cluster reflected both the species composition and habitat characteristics in the study area. A detrended correspondence analysis (DCA) corroborated these findings, but removal of unique and duplicate species from the dataset in order to avoid sampling errors had a marked effect on the results; specifically, the clusters produced by DCA before and after the exclusion of specific data points were very different, while the clusters produced by the SOM were consistent. In addition, while the indicator value associated with SOMs clearly illustrated the importance of individual species in each cluster, the DCA scatterplot generated for species was not clear. The results suggested that SOM analysis was better suited for understanding the relationships between ant communities and species and habitat characteristics.     

Metabolite-based clustering and visualization of mass spectrometry data using one-dimensional self-organizing maps

Background  

One of the goals of global metabolomic analysis is to identify metabolic markers that are hidden within a large background of data originating from high-throughput analytical measurements. Metabolite-based clustering is an unsupervised approach for marker identification based on grouping similar concentration profiles of putative metabolites. A major problem of this approach is that in general there is no prior information about an adequate number of clusters.     

An analysis of Kohonen's self-organizing maps using a system of energy functions

In this paper a new method for analyzing Kohonen's self-organizing feature maps is presented. The method makes use of a system of energy functions, one energy function for each processing unit. It is shown that the training process is equivalent to minimizing each energy function subject to constraints. The analysis is used to prove the formation of topologically correct maps when the inherent dimensionality of the input patterns matches that of the network. The energy equations can be used to compute the steady-state weight values of the network. In addition, the analysis allows bounds on the training parameters to be determined. Finally, examples of energy landscapes are presented to graphically show the behavior of the network.     

Practical application of self-organizing maps to interrelate biodiversity and functional data in NGS-based metagenomics

Next-generation sequencing (NGS) technologies have enabled the application of broad-scale sequencing in microbial biodiversity and metagenome studies. Biodiversity is usually targeted by classifying 16S ribosomal RNA genes, while metagenomic approaches target metabolic genes. However, both approaches remain isolated, as long as the taxonomic and functional information cannot be interrelated. Techniques like self-organizing maps (SOMs) have been applied to cluster metagenomes into taxon-specific bins in order to link biodiversity with functions, but have not been applied to broad-scale NGS-based metagenomics yet. Here, we provide a novel implementation, demonstrate its potential and practicability, and provide a web-based service for public usage. Evaluation with published data sets mimicking varyingly complex habitats resulted into classification specificities and sensitivities of close to 100% to above 90% from phylum to genus level for assemblies exceeding 8 kb for low and medium complexity data. When applied to five real-world metagenomes of medium complexity from direct pyrosequencing of marine subsurface waters, classifications of assemblies above 2.5 kb were in good agreement with fluorescence in situ hybridizations, indicating that biodiversity was mostly retained within the metagenomes, and confirming high classification specificities. This was validated by two protein-based classifications (PBCs) methods. SOMs were able to retrieve the relevant taxa down to the genus level, while surpassing PBCs in resolution. In order to make the approach accessible to a broad audience, we implemented a feature-rich web-based SOM application named TaxSOM, which is freely available at http://www.megx.net/toolbox/taxsom. TaxSOM can classify reads or assemblies exceeding 2.5 kb with high accuracy and thus assists in linking biodiversity and functions in metagenome studies, which is a precondition to study microbial ecology in a holistic fashion.     

Modelling of batch fermentation and estimation of state variables using self-organizing feature maps

Summary A self-organizing feature map was used for modelling of batch yeast cultures. The model was constructed by training the neural network with experimental data of the specific rates. Estimates of state variables were obtained from the neural network model and differential mass balance equations via integration. They were compared with the experimental data. The neural network model showed a good modelling accuracy and interpolation capability.