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.     

Application of Kohonen's self-organizing feature map algorithm to cortical maps of orientation and direction preference

Cortical maps of orientation preference in cats, ferrets and monkeys contain numerous half-rotation point singularities. Experimental data have shown that direction preference also has a smooth representation in these maps, with preferences being for the most part orthogonal to the axis of preferred orientation. As a result, the orientation singularities induce an extensive set of linear fractures in the direction map. These fractures run between and connect nearby point orientation singularities. Their existence appears to pose a puzzle for theories that postulate that cortical maps maximize continuity of representation, because the fractures could be avoided if the orientation map contained full-rotation singularities. Here we show that a dimension-reduction model of cortical map formation, which implements principles of continuity and completeness, produces an arrangement of linear direction fractures connecting point orientation singularities which is similar to that observed experimentally. We analyse the behaviour of this model and suggest reasons why the model maps contain half-rotation rather than full-rotation orientation singularities.     

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.     

Chromosomal regions in prostatic carcinomas studied by comparative genomic hybridization, hierarchical cluster analysis and self-organizing feature maps.

Comparative genomic hybridization (CGH) is an established genetic method which enables a genome-wide survey of chromosomal imbalances. For each chromosome region, one obtains the information whether there is a loss or gain of genetic material, or whether there is no change at that place. Therefore, large amounts of data quickly accumulate which must be put into a logical order. Cluster analysis can be used to assign individual cases (samples) to different clusters of cases, which are similar and where each cluster may be related to a different tumour biology. Another approach consists in a clustering of chromosomal regions by rewriting the original data matrix, where the cases are written as rows and the chromosomal regions as columns, in a transposed form. In this paper we applied hierarchical cluster analysis as well as two implementations of self-organizing feature maps as classical and neuronal tools for cluster analysis of CGH data from prostatic carcinomas to such transposed data sets. Self-organizing maps are artificial neural networks with the capability to form clusters on the basis of an unsupervised learning rule. We studied a group of 48 cases of incidental carcinomas, a tumour category which has not been evaluated by CGH before. In addition we studied a group of 50 cases of pT2N0-tumours and a group of 20 pT3N0-carcinomas. The results show in all case groups three clusters of chromosomal regions, which are (i) normal or minimally affected by losses and gains, (ii) regions with many losses and few gains and (iii) regions with many gains and few losses. Moreover, for the pT2N0- and pT3N0-groups, it could be shown that the regions 6q, 8p and 13q lay all on the same cluster (associated with losses), and that the regions 9q and 20q belonged to the same cluster (associated with gains). For the incidental cancers such clear correlations could not be demonstrated.     

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.     

Estimating the number of clusters in multivariate data by self-organizing maps

Determining the structure of data without prior knowledge of the number of clusters or any information about their composition is a problem of interest in many fields, such as image analysis, astrophysics, biology, etc. Partitioning a set of n patterns in a p-dimensional feature space must be done such that those in a given cluster are more similar to each other than the rest. As there are approximately Kn/K! possible ways of partitioning the patterns among K clusters, finding the best solution is very hard when n is large. The search space is increased when we have no a priori number of partitions. Although the self-organizing feature map (SOM) can be used to visualize clusters, the automation of knowledge discovery by SOM is a difficult task. This paper proposes region-based image processing methods to post-processing the U-matrix obtained after the unsupervised learning performed by SOM. Mathematical morphology is applied to identify regions of neurons that are similar. The number of regions and their labels are automatically found and they are related to the number of clusters in a multivariate data set. New data can be classified by labeling it according to the best match neuron. Simulations using data sets drawn from finite mixtures of p-variate normal densities are presented as well as related advantages and drawbacks of the method.     

Avoiding overfitting in multilayer perceptrons with feeling-of-knowing using self-organizing maps

Overfitting in multilayer perceptron (MLP) training is a serious problem. The purpose of this study is to avoid overfitting in on-line learning. To overcome the overfitting problem, we have investigated feeling-of-knowing (FOK) using self-organizing maps (SOMs). We propose MLPs with FOK using the SOMs method to overcome the overfitting problem. In this method, the learning process advances according to the degree of FOK calculated using SOMs. The mean square error obtained for the test set using the proposed method is significantly less than that in a conventional MLP method. Consequently, the proposed method avoids overfitting.     

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.     

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.     

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.     

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.     

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.