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Pollutant source apportionment represents one of the fundamental activities in environmental science. Several efficient chemometric tools are available to the scope, mostly based on multivariate techniques and usually applied to aerosol chemical speciation data. In the present work, an alternative source profiling method is proposed, based on the self-organizing maps (SOM) algorithm. Moreover, the dataset used includes typical criteria pollutants and physical parameters related to airborne particulate matter widely used as a complement of aerosol source apportionment and largely available at a higher time resolution than bulk aerosol samplings, allowing the information on the dynamic behavior of the local airshed to be extended. In this work, data was collected at a coastal location in NW Italy, between January and July 2012. Hourly concentrations of typical gaseous pollutants (SO 2 , NO, NO 2 , benzene, toluene, (m-p)-xylene, o-xylene), black-carbon and particle number concentrations by an optical particle sizer (OPS) were collected. The dataset was integrated with radon-222 activity concentration and meteorological parameters to enrich and refine the information obtained by SOM computation as well as to improve the air pollution source localization. Despite the lower specificity of criteria pollutants, the approach developed was capable of revealing distinct pollution sources such as the urban background traffic, the coal-fired power plant active at the time of the study, and the harbor, in agreement with previous PM-based source apportionment studies carried out locally, while enlightening peculiar dynamical conditions detectable at the sub-daily time scale. The application of the SOM algorithm, with the integration of meteorological parameters and atmospheric radon, proved to be very efficient in unveiling the air pollution sources., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 The Authors. Published by Elsevier Ltd.. All rights reserved.)

Background and Objective: This paper proposes a fully automated and unsupervised stochastic segmentation approach using two-level joint Markov-Gibbs Random Field (MGRF) to detect the vascular system from retinal Optical Coherence Tomography Angiography (OCTA) images, which is a critical step in developing Computer-Aided Diagnosis (CAD) systems for detecting retinal diseases., Methods: Using a new probabilistic model based on a Linear Combination of Discrete Gaussian (LCDG), the first level models the appearance of OCTA images and their spatially smoothed images. The parameters of the LCDG model are estimated using a modified Expectation Maximization (EM) algorithm. The second level models the maps of OCTA images, including the vascular system and other retina tissues, using MGRF with analytically estimated parameters from the input images. The proposed segmentation approach employs modified self-organizing maps as a MAP-based optimizer maximizing the joint likelihood and handles the Joint MGRF model in a new, unsupervised way. This approach deviates from traditional stochastic optimization approaches and leverages non-linear optimization to achieve more accurate segmentation results., Results: The proposed segmentation framework is evaluated quantitatively on a dataset of 204 subjects. Achieving 0.92 ± 0.03 Dice similarity coefficient, 0.69 ± 0.25 95-percentile bidirectional Hausdorff distance, and 0.93 ± 0.03 accuracy, confirms the superior performance of the proposed approach., Conclusions: The conclusions drawn from the study highlight the superior performance of the proposed unsupervised and fully automated segmentation approach in detecting the vascular system from OCTA images. This approach not only deviates from traditional methods but also achieves more accurate segmentation results, demonstrating its potential in aiding the development of CAD systems for detecting retinal diseases., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier B.V. All rights reserved.)

Interest in unsupervised learning architectures has been rising. Besides being biologically unnatural, it is costly to depend on large labeled data sets to get a well-performing classification system. Therefore, both the deep learning community and the more biologically-inspired models community have focused on proposing unsupervised techniques that can produce adequate hidden representations which can then be fed to a simpler supervised classifier. Despite great success with this approach, an ultimate dependence on a supervised model remains, which forces the number of classes to be known beforehand, and makes the system depend on labels to extract concepts. To overcome this limitation, recent work has been proposed that shows how a self-organizing map (SOM) can be used as a completely unsupervised classifier. However, to achieve success it required deep learning techniques to generate high quality embeddings. The purpose of this work is to show that we can use our previously proposed What-Where encoder in tandem with the SOM to get an end-to-end unsupervised system that is Hebbian. Such system, requires no labels to train nor does it require knowledge of which classes exist beforehand. It can be trained online and adapt to new classes that may emerge. As in the original work, we use the MNIST data set to run an experimental analysis and verify that the system achieves similar accuracies to the best ones reported thus far. Furthermore, we extend the analysis to the more difficult Fashion-MNIST problem and conclude that the system still performs., (© 2023. The Author(s).)

Cell mechanical properties have been proposed as label free markers for diagnostic purposes in diseases such as cancer. Cancer cells show altered mechanical phenotypes compared to their healthy counterparts. Atomic Force Microscopy (AFM) is a widely utilized tool to study cell mechanics. These measurements often need skilful users, physical modelling of mechanical properties and expertise in data interpretation. Together with the need to perform many measurements for statistical significance and to probe wide enough areas in tissue structures, the application of machine learning and artificial neural network techniques to automatically classify AFM datasets has received interest recently. We propose the use of self-organizing maps (SOMs) as unsupervised artificial neural network applied to mechanical measurements performed via AFM on epithelial breast cancer cells treated with different substances that affect estrogen receptor signalling. We show changes in mechanical properties due to treatments, as estrogen softened the cells, while resveratrol led to an increase in cell stiffness and viscosity. These data were then used as input for SOMs. Our approach was able to distinguish between estrogen treated, control and resveratrol treated cells in an unsupervised manner. In addition, the maps enabled investigation of the relationship of the input variables., (© 2023. The Author(s).)

Conventional drug discovery methods rely primarily on in-vitro experiments with a target molecule and an extensive set of small molecules to choose the suitable ligand. The exploration space for the selected ligand being huge; this approach is highly time-consuming and requires high capital for facilitation. Virtual screening, a computational technique used to reduce this search space and identify lead molecules, can speed up the drug discovery process. This paper proposes a ligand-based virtual screening method using an artificial neural network called self-organizing map (SOM). The proposed work uses two SOMs to predict the active and inactive molecules separately. This SOM based technique can uniquely label a small molecule as active, inactive, and undefined as well. This can reduce the number of false positives in the screening process and improve recall; compared to support vector machine and random forest based models. Additionally, by exploiting the parallelism present in the learning and classification phases of a SOM, a graphics processing unit (GPU) based model yields much better execution time. The proposed GPU-based SOM tool can successfully evaluate a large number of molecules in training and screening phases. The source code of the implementation and related files are available at https://github.com/jayarajpbalakrishnan/2_SOM_SCREEN., (© 2021. The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.)

Improvements in computing capacity have allowed computers today to execute increasingly complex tasks. One of the main benefits of these improvements is the possibility of developing machine learning algorithms, of which the fields of application are extensive and varied. However, an area in which this type of algorithms acquires an increasing relevance is structural health monitoring (SHM), where inspection strategies and guided wave-based approaches make the evaluation of the structural conditions of an aircraft, vessel or building among others possible, by detecting and classifying existing damages. The use of sensors, data acquisition systems (DAQ) and computation has also allowed these damage detection and classification tasks to be carried out automatically. Despite today's advances, it is still necessary to continue with the development of more robust, reliable, and low-cost structural health monitoring systems. For this reason, this work contemplates three key points: (i) the configuration of a data acquisition system for signal gathering from an an active piezoelectric (PZT) sensor network; (ii) the development of a damage classification methodology based on signal processing techniques (normalization and PCA), from which the models that describe the structural conditions of the plate are built; and (iii) the use of machine learning algorithms, more specifically, three variants of the self-organizing maps called CPANN (counterpropagation artificial neural network), SKN (supervised Kohonen) and XYF (X-Y fused Kohonen). The data obtained allowed one to carry out an experimental validation of the damage classification methodology, to determine the presence of damages in two aluminum plates of different sizes, where masses were added to change the vibrational responses captured by the sensor network and a composite (CFRP) plate with real damages, such as delamination and cracks. This classification methodology allowed one to obtain excellent results by validating the usefulness of the SKN and XYF networks in damage classification tasks, showing overall accuracies of 73.75% and 72.5%, respectively, according to the cross-validation process. These percentages are higher than those obtained in comparison with other neural networks such as: kNN, discriminant analysis, classification trees, partial least square discriminant analysis, and backpropagation neural networks, when the cross-validation process was applied.

When fourier transform infrared spectroscopy (FTIR) techniques combined with multivariate calibration are used to measure the key process features or analyte concentrations during batch process, model adaption is indispensable for maintaining the predictability of a primary calibration model in new secondary batches. Many model adaption methods conforming to the actual application scenario of batch process have been proposed. Here we report on a novel standard-free model adaption method without reference measurement called variable selection strategy with self-organizing maps (VSSOM). It uses self-organizing maps (SOM) to classify the whole spectral variables into multiple classes according to the spectra from primary batch and secondary batch, respectively; and the corresponding primary feature subsets and secondary feature subsets are formed firstly. Secondly, candidate feature subsets without empty elements are generated by operating intersection between any primary feature subsets and any secondary feature subsets. Thirdly, the candidate feature subset with minimum root mean square error of cross-validation (RMSECV) for the primary calibration set is selected as the optimal feature subset. In this manner, the optimal feature subset can be identified from the candidate feature subsets. In other words, VSSOM aims to create a stable and consistent feature subset across different batches provided that it selects better features within the intersection sets between primary feature subsets and any secondary feature subsets. Two batch process datasets (γ-polyglutamic acid fermentation and paeoniflorin extraction) are presented for comparing the VSSOM method with No transfer partial least squares (PLS), boxcar signal transfer (BST), successive projection algorithm (SPA), transfer component analysis (TCA) and domain-invariant iterative partial least squares (DIPALS). Experimental results show that VSSOM has superior performance and comparable prediction performance in all the scenarios., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2021 Elsevier B.V. All rights reserved.)

Advances in measurement technology are producing increasingly time-resolved environmental exposure data. We aim to gain new insights into exposures and their potential health impacts by moving beyond simple summary statistics (e.g., means, maxima) to characterize more detailed features of high-frequency time series data. This study proposes a novel variant of the Self-Organizing Map (SOM) algorithm called Dynamic Time Warping Self-Organizing Map (DTW-SOM) for unsupervised pattern discovery in time series. This algorithm uses DTW, a similarity measure that optimally aligns interior patterns of sequential data, both as the similarity measure and training guide of the neural network. We applied DTW-SOM to a panel study monitoring indoor and outdoor residential temperature and particulate matter air pollution (PM 2.5 ) for 10 patients with asthma from 7 households near Salt Lake City, UT; the patients were followed for up to 373 days each. Compared to previous SOM algorithms using timestamp alignment on time series data, the DTW-SOM algorithm produced fewer quantization errors and more detailed diurnal patterns. DTW-SOM identified the expected typical diurnal patterns in outdoor temperature which varied by season, as well diurnal patterns in PM 2.5 which may be related to daily asthma outcomes. In summary, DTW-SOM is an innovative feature engineering method that can be applied to highly time-resolved environmental exposures assessed by sensors to identify typical diurnal (or hourly or monthly) patterns and provide new insights into the health effects of environmental exposures., (© 2021. The Author(s).)

Human learning and intelligence work differently from the supervised pattern recognition approach adopted in most deep learning architectures. Humans seem to learn rich representations by exploration and imitation, build causal models of the world, and use both to flexibly solve new tasks. We suggest a simple but effective unsupervised model which develops such characteristics. The agent learns to represent the dynamical physical properties of its environment by intrinsically motivated exploration and performs inference on this representation to reach goals. For this, a set of self-organizing maps which represent state-action pairs is combined with a causal model for sequence prediction. The proposed system is evaluated in the cartpole environment. After an initial phase of playful exploration, the agent can execute kinematic simulations of the environment's future and use those for action planning. We demonstrate its performance on a set of several related, but different one-shot imitation tasks, which the agent flexibly solves in an active inference style., Competing Interests: The authors declare that there are no conflicts of interest regarding the publication of this study., (Copyright © 2021 Martin Stetter and Elmar W. Lang.)

Self-Organizing Maps (SOMs) are extensively used for data clustering and dimensionality reduction. However, if applications are to fully benefit from SOM based techniques, high-speed processing is demanding, given that data tends to be both highly dimensional and yet "big". Hence, a fully parallel architecture for the SOM is introduced to optimize the system's data processing time. Unlike most literature approaches, the architecture proposed here does not contain sequential steps - a common limiting factor for processing speed. The architecture was validated on FPGA and evaluated concerning hardware throughput and the use of resources. Comparisons to the state of the art show a speedup of 8.91× over a partially serial implementation, using less than 15% of hardware resources available. Thus, the method proposed here points to a hardware architecture that will not be obsolete quickly., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2021 Elsevier Ltd. All rights reserved.)

Summary: We implemented the Self-Organizing Maps algorithm running efficiently on GPUs, and also provide several clustering methods of the resulting maps. We provide scripts and a use case to cluster macro-molecular conformations generated by molecular dynamics simulations., Availability and Implementation: The method is available on GitHub and distributed as a pip package., (© The Author(s) 2020. Published by Oxford University Press.)

With the rapid advances of various single-cell technologies, an increasing number of single-cell datasets are being generated, and the computational tools for aligning the datasets which make subsequent integration or meta-analysis possible have become critical. Typically, single-cell datasets from different technologies cannot be directly combined or concatenated, due to the innate difference in the data, such as the number of measured parameters and the distributions. Even datasets generated by the same technology are often affected by the batch effect. A computational approach for aligning different datasets and hence identifying related clusters will be useful for data integration and interpretation in large scale single-cell experiments. Our proposed algorithm called JSOM, a variation of the Self-organizing map, aligns two related datasets that contain similar clusters, by constructing two maps-low-dimensional discretized representation of datasets-that jointly evolve according to both datasets. Here we applied the JSOM algorithm to flow cytometry, mass cytometry, and single-cell RNA sequencing datasets. The resulting JSOM maps not only align the related clusters in the two datasets but also preserve the topology of the datasets so that the maps could be used for further analysis, such as clustering., Competing Interests: The authors have declared that no competing interests exist.

Motivation: One of the main challenges in applying graph convolutional neural networks (CNNs) on gene-interaction data is the lack of understanding of the vector space to which they belong, and also the inherent difficulties involved in representing those interactions on a significantly lower dimension, viz Euclidean spaces. The challenge becomes more prevalent when dealing with various types of heterogeneous data. We introduce a systematic, generalized method, called iSOM-GSN, used to transform 'multi-omic' data with higher dimensions onto a 2D grid. Afterwards, we apply a CNN to predict disease states of various types. Based on the idea of Kohonen's self-organizing map, we generate a 2D grid for each sample for a given set of genes that represent a gene similarity network., Results: We have tested the model to predict breast and prostate cancer using gene expression, DNA methylation and copy number alteration. Prediction accuracies in the 94-98% range were obtained for tumor stages of breast cancer and calculated Gleason scores of prostate cancer with just 14 input genes for both cases. The scheme not only outputs nearly perfect classification accuracy, but also provides an enhanced scheme for representation learning, visualization, dimensionality reduction and interpretation of multi-omic data., Availability and Implementation: The source code and sample data are available via a Github project at https://github.com/NaziaFatima/iSOM_GSN., Supplementary Information: Supplementary data are available at Bioinformatics online., (© The Author(s) 2020. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

Protein phosphorylation is a vital physiological process, which plays a critical role in controlling survival differentiation, cell growth, metabolism and apoptosis. The accurate identification of whether a protein will be phosphorylated solely from protein sequence is especially useful for both basic research and drug development. In this study, a new predictor specifically designed for the prediction of human phosphorylated proteins is proposed. The proposed method first train two supervised kernel self-organizing maps (SKSOMs): one is trained with feature from protein physiochemical composition view, while the other is trained with feature from protein evolutionary information view. Then, the two trained SKSOMs are ensembled to perform the final prediction. Rigorous computational experiments show that the proposed method achieves 78.75 % and 0.561 on ACC and MCC, which are 6.96 % and 12.5 % higher than that of the state-of-the-art predictor. Overall, the study demonstrated a new sensitive avenue to identify human phosphorylated proteins and could be readily extended to recognize phosphorylated proteins for other species., (© 2020 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.)

EmbedSOM is a simple and fast dimensionality reduction algorithm, originally developed for its applications in single-cell cytometry data analysis. We present an updated version of EmbedSOM, viewed as an algorithm for landmark-based embedding enrichment, and demonstrate that it works well even with manifold-learning techniques other than the self-organizing maps. Using this generalization, we introduce an inwards-growing variant of self-organizing maps that is designed to mitigate some earlier identified deficiencies of EmbedSOM output. Finally, we measure the performance of the generalized EmbedSOM, compare several variants of the algorithm that utilize different landmark-generating functions, and showcase the functionality on single-cell cytometry datasets from recent studies., Competing Interests: No competing interests were disclosed., (Copyright: © 2019 Kratochvíl M et al.)

Motivation: Non-coding RNAs (ncRNAs) play important roles in many biological processes and are involved in many diseases. Their identification is an important task, and many tools exist in the literature for this purpose. However, almost all of them are focused on the discrimination of coding and ncRNAs without giving more biological insight. In this paper, we propose a new reliable method called IRSOM, based on a supervised Self-Organizing Map (SOM) with a rejection option, that overcomes these limitations. The rejection option in IRSOM improves the accuracy of the method and also allows identifing the ambiguous transcripts. Furthermore, with the visualization of the SOM, we analyze the rejected predictions and highlight the ambiguity of the transcripts., Results: IRSOM was tested on datasets of several species from different reigns, and shown better results compared to state-of-art. The accuracy of IRSOM is always greater than 0.95 for all the species with an average specificity of 0.98 and an average sensitivity of 0.99. Besides, IRSOM is fast (it takes around 254 s to analyze a dataset of 147 000 transcripts) and is able to handle very large datasets., Availability and Implementation: IRSOM is implemented in Python and C++. It is available on our software platform EvryRNA (http://EvryRNA.ibisc.univ-evry.fr).

There has been an increasing interest in multi-view approaches based on their ability to manage data from several sources. However, regarding unsupervised learning, most multi-view approaches are clustering algorithms suitable for analyzing vector data. Currently, only a relatively few SOM algorithms can manage multi-view dissimilarity data, despite their usefulness. This paper proposes two new families of batch SOM algorithms for multi-view dissimilarity data: multi-medoids SOM and relational SOM, both designed to give a crisp partition and learn the relevance weight for each dissimilarity matrix by optimizing an objective function, aiming to preserve the topological properties of the map data. In both families, the weight represents the relevance of each dissimilarity matrix for the learning task being computed, either locally, for each cluster, or globally, for the whole partition. The proposed algorithms were compared with already in the literature single-view SOM and set-medoids SOM for multi-view dissimilarity data. According to the experiments using 14 datasets for F-measure, NMI, Topographic Error, and Silhouette, the relevance weights of the dissimilarity matrices must be considered. In addition, the multi-medoids and relational SOM performed better than the set-medoids SOM. An application study was also carried out on a dermatology dataset, where the proposed methods have the best performance. [ABSTRACT FROM AUTHOR]

The k nearest neighbor is one of the most important and simple procedures for data classification task. The k NN, as it is called, requires only two parameters: the number of k and a similarity measure. However, the algorithm has some weaknesses that make it impossible to be used in real problems. Since the algorithm has no model, an exhaustive comparison of the object in classification analysis and all training dataset is necessary. Another weakness is the optimal choice of k parameter when the object analyzed is in an overlap region. To mitigate theses negative aspects, in this work, a hybrid algorithm is proposed which uses the Self-Organizing Maps (SOM) artificial neural network and a classifier that uses similarity measure based on information. Since SOM has the properties of vector quantization, it is used as a Prototype Generation approach to select a reduced training dataset for the classification approach based on the nearest neighbor rule with informativeness measure, named i NN. The SOM i NN combination was exhaustively experimented and the results show that the proposed approach presents important accuracy in databases where the border region does not have the object classes well defined.

Recent efforts to develop large-scale brain and neurocognitive architectures have paid relatively little attention to the use of self-organizing maps (SOMs). Part of the reason for this is that most conventional SOMs use a static encoding representation: each input pattern or sequence is effectively represented as a fixed point activation pattern in the map layer, something that is inconsistent with the rhythmic oscillatory activity observed in the brain. Here we develop and study an alternative encoding scheme that instead uses sparsely-coded limit cycles to represent external input patterns/sequences. We establish conditions under which learned limit cycle representations arise reliably and dominate the dynamics in a SOM. These limit cycles tend to be relatively unique for different inputs, robust to perturbations, and fairly insensitive to timing. In spite of the continually changing activity in the map layer when a limit cycle representation is used, map formation continues to occur reliably. In a two-SOM architecture where each SOM represents a different sensory modality, we also show that after learning, limit cycles in one SOM can correctly evoke corresponding limit cycles in the other, and thus there is the potential for multi-SOM systems using limit cycles to work effectively as hetero-associative memories. While the results presented here are only first steps, they establish the viability of SOM models based on limit cycle activity patterns, and suggest that such models merit further study., (Copyright © 2014 Elsevier Ltd. All rights reserved.)

The number of markers measured in both flow and mass cytometry keeps increasing steadily. Although this provides a wealth of information, it becomes infeasible to analyze these datasets manually. When using 2D scatter plots, the number of possible plots increases exponentially with the number of markers and therefore, relevant information that is present in the data might be missed. In this article, we introduce a new visualization technique, called FlowSOM, which analyzes Flow or mass cytometry data using a Self-Organizing Map. Using a two-level clustering and star charts, our algorithm helps to obtain a clear overview of how all markers are behaving on all cells, and to detect subsets that might be missed otherwise. R code is available at https://github.com/SofieVG/FlowSOM and will be made available at Bioconductor., (© 2015 International Society for Advancement of Cytometry.)

Motivation: Self-organizing maps (SOMs) are readily available bioinformatics methods for clustering and visualizing high-dimensional data, provided that such biological information is previously transformed to fixed-size, metric-based vectors. To increase the usefulness of SOM-based approaches for the analysis of genomic sequence data, novel representation methods are required that automatically and objectively transform aligned nucleotide sequences into numeric vectors, dealing with both nucleotide ambiguity and gaps derived from sequence alignment., Results: Six different codification variants based on Euclidean space, just like SOM processing, have been tested using two SOM models: the classical Kohonen's SOM and growing cell structures. They have been applied to two different sets of sequences: 32 sequences of small sub-unit ribosomal RNA from organisms belonging to the three domains of life, and 44 sequences of the reverse transcriptase region of the pol gene of human immunodeficiency virus type 1 belonging to different groups and sub-types. Our results show that the most important factor affecting the accuracy of sequence clustering is the assignment of an extra weight to the presence of alignment-derived gaps. Although each of the codification variants shows a different level of taxonomic consistency, the results are in agreement with sequence-based phylogenetic reconstructions and anticipate a broad applicability of this codification method., (© The Author 2014. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.)

A metabolic system is composed of inherently interconnected metabolic precursors, intermediates, and products. The analysis of untargeted metabolomics data has conventionally been performed through the use of comparative statistics or multivariate statistical analysis-based approaches; however, each falls short in representing the related nature of metabolic perturbations. Herein, we describe a complementary method for the analysis of large metabolite inventories using a data-driven approach based upon a self-organizing map algorithm. This workflow allows for the unsupervised clustering, and subsequent prioritization of, correlated features through Gestalt comparisons of metabolic heat maps. We describe this methodology in detail, including a comparison to conventional metabolomics approaches, and demonstrate the application of this method to the analysis of the metabolic repercussions of prolonged cocaine exposure in rat sera profiles.

A recent research area in unsupervised learning is the combination of representation learning with deep neural networks and data clustering. The success of deep learning for supervised tasks is widely established. However, recent research has demonstrated how neural networks are able to learn representations to improve clustering in their intermediate feature space, using specific regularizations. By considering representation learning and clustering as a joint task, models learn clustering-friendly spaces and outperform two-stage approaches where dimensionality reduction and clustering are performed separately. Recently, this idea has been extended to topology-preserving clustering models, known as self-organizing maps (SOM). This work is a thorough study on the deep embedded self-organizing map (DESOM), a model composed of an autoencoder and a SOM layer, training jointly the code vectors and network weights to learn SOM-friendly representations. In other words, SOM induces a form a regularization to improve the quality of quantization and topology in latent space. After detailing the architecture, loss and training algorithm, we study hyperparameters with a series of experiments. Different SOM-based models are evaluated in terms of clustering, visualization and classification on benchmark datasets. We study benefits and trade-offs of joint representation learning and self-organization. DESOM achieves competitive results, requires no pretraining and produces topologically organized visualizations. [ABSTRACT FROM AUTHOR]

It is important to identify DNA motifs in promoter regions to understand the mechanism of gene regulation. Computational approaches for finding DNA motifs are well recognized as useful tools to biologists, which greatly help in saving experimental time and cost in wet laboratories. Self-organizing maps (SOMs), as a powerful clustering tool, have demonstrated good potential for problem solving. However, the current SOM-based motif discovery algorithms unfairly treat data samples lying around the cluster boundaries by assigning them to one of the nodes, which may result in unreliable system performance. This paper aims to develop a robust framework for discovering DNA motifs, where fuzzy SOMs, with an integration of fuzzy c-means membership functions and a standard batch-learning scheme, are employed to extract putative motifs with varying length in a recursive manner. Experimental results on eight real datasets show that our proposed algorithm outperforms the other searching tools such as SOMBRERO, SOMEA, MEME, AlignACE, and WEEDER in terms of the F-measure and algorithm reliability. It is observed that a remarkable 24.6% improvement can be achieved compared to the state-of-the-art SOMBRERO. Furthermore, our algorithm can produce a 20% and 6.6% improvement over SOMBRERO and SOMEA, respectively, in finding multiple motifs on five artificial datasets.

We present novel graph-based visualizations of self-organizing maps for unsupervised functional magnetic resonance imaging (fMRI) analysis. A self-organizing map is an artificial neural network model that transforms high-dimensional data into a low-dimensional (often a 2-D) map using unsupervised learning. However, a postprocessing scheme is necessary to correctly interpret similarity between neighboring node prototypes (feature vectors) on the output map and delineate clusters and features of interest in the data. In this paper, we used graph-based visualizations to capture fMRI data features based upon 1) the distribution of data across the receptive fields of the prototypes (density-based connectivity); and 2) temporal similarities (correlations) between the prototypes (correlation-based connectivity). We applied this approach to identify task-related brain areas in an fMRI reaction time experiment involving a visuo-manual response task, and we correlated the time-to-peak of the fMRI responses in these areas with reaction time. Visualization of self-organizing maps outperformed independent component analysis and voxelwise univariate linear regression analysis in identifying and classifying relevant brain regions. We conclude that the graph-based visualizations of self-organizing maps help in advanced visualization of cluster boundaries in fMRI data enabling the separation of regions with small differences in the timings of their brain responses.

A self-organizing map (SOM) is a self-organized projection of high-dimensional data onto a typically 2-dimensional (2-D) feature map, wherein vector similarity is implicitly translated into topological closeness in the 2-D projection. However, when there are more neurons than input patterns, it can be challenging to interpret the results, due to diffuse cluster boundaries and limitations of current methods for displaying interneuron distances. In this brief, we introduce a new cluster reinforcement (CR) phase for sparsely-matched SOMs. The CR phase amplifies within-cluster similarity in an unsupervised, data-driven manner. Discontinuities in the resulting map correspond to between-cluster distances and are stored in a boundary (B) matrix. We describe a new hierarchical visualization of cluster boundaries displayed directly on feature maps, which requires no further clustering beyond what was implicitly accomplished during self-organization in SOM training. We use a synthetic benchmark problem and previously published microbial community profile data to demonstrate the benefits of the proposed methods.

Increasing amounts of data are collected in sports due to technological progress. From a typical soccer game, for instance, the positions of the 22 players and the ball can be recorded 25 times per second, resulting in approximately 135.000 datasets. Without computational assistance it is almost impossible to extract relevant information from the complete data. This contribution introduces a hierarchical architecture of artificial neural networks to find tactical patterns in those positional data. The results from the classification using the hierarchical setup were compared to the results gained by an expert manually classifying the different categories. Short and long game initiations can be detected with relative high accuracy leading to the conclusion that the hierarchical architecture is capable of recognizing different tactical patterns and variations in these patterns. Remaining problems are discussed and ideas concerning further improvements of classification are indicated., (Copyright © 2011 Elsevier B.V. All rights reserved.)

To deal with the task assignment problem of multi-AUV systems under kinematic constraints, which means steering capability constraints for underactuated AUVs or other vehicles likely, an improved task assignment algorithm is proposed combining the Dubins Path algorithm with improved SOM neural network algorithm. At first, the aimed tasks are assigned to the AUVs by the improved SOM neural network method based on workload balance and neighborhood function. When there exists kinematic constraints or obstacles which may cause failure of trajectory planning, task re-assignment will be implemented by changing the weights of SOM neurals, until the AUVs can have paths to reach all the targets. Then, the Dubins paths are generated in several limited cases. The AUV's yaw angle is limited, which results in new assignments to the targets. Computation flow is designed so that the algorithm in MATLAB and Python can realize the path planning to multiple targets. Finally, simulation results prove that the proposed algorithm can effectively accomplish the task assignment task for a multi-AUV system. [ABSTRACT FROM AUTHOR]

A powerful method in the analysis of datasets where there are many natural clusters with varying statistics such as different sizes, shapes, density distribution, overlaps, etc., is the use of self-organizing maps (SOMs). However, further processing tools, such as visualization and interactive clustering, are often necessary to capture the clusters from the learned SOM knowledge. A recent visualization scheme (CONNvis) and its interactive clustering utilize the data topology for SOM knowledge representation by using a connectivity matrix (a weighted Delaunay graph), CONN. In this paper, we propose an automated clustering method for SOMs, which is a hierarchical agglomerative clustering of CONN. We determine the number of clusters either by using cluster validity indices or by prior knowledge on the datasets. We show that, for the datasets used in this paper, data-topology-based hierarchical clustering can produce better partitioning than hierarchical clustering based solely on distance information.

A self-organizing map (SOM) algorithm can generate a topographic map from a high-dimensional stimulus space to a low-dimensional array of units. Because a topographic map preserves neighborhood relationships between the stimuli, the SOM can be applied to certain types of information processing such as data visualization. During the learning process, however, topological defects frequently emerge in the map. The presence of defects tends to drastically slow down the formation of a globally ordered topographic map. To remove such topological defects, it has been reported that an asymmetric neighborhood function is effective, but only in the simple case of mapping one-dimensional stimuli to a chain of units. In this paper, we demonstrate that even when high-dimensional stimuli are used, the asymmetric neighborhood function is effective for both artificial and real-world data. Our results suggest that applying the asymmetric neighborhood function to the SOM algorithm improves the reliability of the algorithm. In addition, it enables processing of complicated, high-dimensional data by using this algorithm.

The original self-organizing feature map did not define any probability distribution on the input space. However, the advantages of introducing probabilistic methodologies into self-organizing map models were soon evident. This has led to a wide range of proposals which reflect the current emergence of probabilistic approaches to computational intelligence. The underlying estimation theories behind them derive from two main lines of thought: the expectation maximization methodology and stochastic approximation methods. Here, we present a comprehensive view of the state of the art, with a unifying perspective of the involved theoretical frameworks. In particular, we examine the most commonly used continuous probability distributions, self-organization mechanisms, and learning schemes. Special emphasis is given to the connections among them and their relative advantages depending on the characteristics of the problem at hand. Furthermore, we evaluate their performance in two typical applications of self-organizing maps: classification and visualization.

The self-organizing map (SOM) is a powerful method for manifold learning because of producing a 2-D spatially ordered quantization of a higher dimensional data space on a rigid lattice and adaptively determining optimal approximation of the (unknown) density distribution of the data. However, a postprocessing visualization scheme is often required to capture the data manifold. A recent visualization scheme CONNvis, which is shown effective for clustering, uses a topology representing graph that shows detailed local data distribution within receptive fields. This brief proposes that this graph representation can be adapted to show local distances. The proposed graphs of local density and local distances provide tools to analyze the correlation between these two information and to merge them in various ways to achieve an advanced visualization. The brief also gives comparisons for several synthetic data sets.

This study proposes new developmental stages for Callithrix jacchus, using K-Means algorithm and an artificial neural network-self-organising maps (SOM) as computational tools, based on weight and age. Eight developmental stages are proposed: Infant I, II and III, Juvenile I and II, Sub adult, Young adult and Older adult. This classification is consistent with the first appearance of several behavioural and physiological characteristics and thus may have generality in defining critical developmental periods. It also reveals differences in male and female development and establishes a stage for the onset of the final adult life cycle. This classification is also important to understanding the biology of the ontogenetic development of common marmosets, providing new insights for the management and care of captive animals and improving age estimate indicators when specimens are captured in long term monitoring of free ranging groups.

There is an increasing interest in clustering time course gene expression data to investigate a wide range of biological processes. However, developing a clustering algorithm ideal for time course gene express data is still challenging. As timing is an important factor in defining true clusters, a clustering algorithm shall explore expression correlations between time points in order to achieve a high clustering accuracy. Moreover, inter-cluster gene relationships are often desired in order to facilitate the computational inference of biological pathways and regulatory networks. In this paper, a new clustering algorithm called CurveSOM is developed to offer both features above. It first presents each gene by a cubic smoothing spline fitted to the time course expression profile, and then groups genes into clusters by applying a self-organizing map-based clustering on the resulting splines. CurveSOM has been tested on three well-studied yeast cell cycle datasets, and compared with four popular programs including Cluster 3.0, GENECLUSTER, MCLUST, and SSClust. The results show that CurveSOM is a very promising tool for the exploratory analysis of time course expression data, as it is not only able to group genes into clusters with high accuracy but also able to find true time-shifted correlations of expression patterns across clusters.

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.

Cluster analysis is one of the crucial steps in gene expression pattern (GEP) analysis. It leads to the discovery or identification of temporal patterns and coexpressed genes. GEP analysis involves highly dimensional multivariate data which demand appropriate tools. A good alternative for grouping many multidimensional objects is self-organizing maps (SOM), an unsupervised neural network algorithm able to find relationships among data. SOM groups and maps them topologically. However, it may be difficult to identify clusters with the usual visualization tools for SOM. We propose a simple algorithm to identify and visualize clusters in SOM (the RP-Q method). The RP is a new node-adaptive attribute that moves in a two dimensional virtual space imitating the movement of the codebooks vectors of the SOM net into the input space. The Q statistic evaluates the SOM structure providing an estimation of the number of clusters underlying the data set. The SOM-RP-Q algorithm permits the visualization of clusters in the SOM and their node patterns. The algorithm was evaluated in several simulated and real GEP data sets. Results show that the proposed algorithm successfully displays the underlying cluster structure directly from the SOM and is robust to different net sizes.

We present a statistical analysis of a large set of absorption spectra of phytoplankton, measured in natural samples collected from ocean water, in conjunction with detailed pigment concentrations. We processed the absorption spectra with a sophisticated neural network method suitable for classifying complex phenomena, the so-called self-organizing maps (SOM) proposed by Kohonen [Kohonen, Self Organizing Maps (Springer-Verlag, 1984)]. The aim was to compress the information embedded in the data set into a reduced number of classes characterizing the data set, which facilitates the analysis. By processing the absorption spectra, we were able to retrieve well-known relationships among pigment concentrations and to display them on maps to facilitate their interpretation. We then showed that the SOM enabled us to extract pertinent information about pigment concentrations normalized to chlorophyll a. We were able to propose new relationships between the fucoxanthin/Tchl-a ratio and the derivative of the absorption spectrum at 510 nm and between the Tchl-b/Tchl-a ratio and the derivative at 640 nm. Finally, we demonstrate the possibility of inverting the absorption spectrum to retrieve the pigment concentrations with better accuracy than a regression analysis using the Tchl-a concentration derived from the absorption at 440 nm. We also discuss the data coding used to build the self-organizing map. This methodology is very general and can be used to analyze a large class of complex data.

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 topographic maps, 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-organizing map (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 beta (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.

In many real-world applications, data cannot be accurately represented by vectors. In those situations, one possible solution is to rely on dissimilarity measures that enable a sensible comparison between observations. Kohonen's self-organizing map (SOM) has been adapted to data described only through their dissimilarity matrix. This algorithm provides both nonlinear projection and clustering of nonvector data. Unfortunately, the algorithm suffers from a high cost that makes it quite difficult to use with voluminous data sets. In this paper, we propose a new algorithm that provides an important reduction in the theoretical cost of the dissimilarity SOM without changing its outcome (the results are exactly the same as those obtained with the original algorithm). Moreover, we introduce implementation methods that result in very short running times. Improvements deduced from the theoretical cost model are validated on simulated and real-world data (a word list clustering problem). We also demonstrate that the proposed implementation methods reduce the running time of the fast algorithm by a factor up to three over a standard implementation.

Contiguity analysis is a straightforward generalization of linear discriminant analysis in which the partition of elements is replaced by a more general graph structure. Applied to the graph induced by a Self Organizing Map (SOM), contiguity analysis provides a set of linear projectors leading to a planar representation as close as possible to the SOM. As expected, such projectors may only concern local parts of the SOMs. They allow us to visualize the shapes of the clusters (convex hulls of the projections of the elements belonging to a cluster) and the pattern of the elements within each cluster. In some contexts, it is possible to project the bootstrap replicates of the elements, and therefore to produce confidence areas for elements via a standard partial bootstrap procedure.

Self-Organizing Maps have been applied in various industrial applications and have proven to be a valuable data mining tool. In order to fully benefit from their potential, advanced visualization techniques assist the user in analyzing and interpreting the maps. We propose two new methods for depicting the SOM based on vector fields, namely the Gradient Field and Borderline visualization techniques, to show the clustering structure at various levels of detail. We explain how this method can be used on aggregated parts of the SOM that show which factors contribute to the clustering structure, and show how to use it for finding correlations and dependencies in the underlying data. We provide examples on several artificial and real-world data sets to point out the strengths of our technique, specifically as a means to combine different types of visualizations offering effective multidimensional information visualization of SOMs.

Although graph matching and graph edit distance computation have become areas of intensive research recently, the automatic inference of the cost of edit operations has remained an open problem. In the present paper, we address the issue of learning graph edit distance cost functions for numerically labeled graphs from a corpus of sample graphs. We propose a system of self-organizing maps (SOMs) that represent the distance measuring spaces of node and edge labels. Our learning process is based on the concept of self-organization. It adapts the edit costs in such a way that the similarity of graphs from the same class is increased, whereas the similarity of graphs from different classes decreases. The learning procedure is demonstrated on two different applications involving line drawing graphs and graphs representing diatoms, respectively.

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.

Color quantization (CQ) is an image processing task popularly used to convert true color images to palletized images for limited color display devices. To minimize the contouring artifacts introduced by the reduction of colors, a new competitive learning (CL) based scheme called the frequency sensitive self-organizing maps (FS-SOMs) is proposed to optimize the color palette design for CQ. FS-SOM harmonically blends the neighborhood adaptation of the well-known self-organizing maps (SOMs) with the neuron dependent frequency sensitive learning model, the global butterfly permutation sequence for input randomization, and the reinitialization of dead neurons to harness effective utilization of neurons. The net effect is an improvement in adaptation, a well-ordered color palette, and the alleviation of underutilization problem, which is the main cause of visually perceivable artifacts of CQ. Extensive simulations have been performed to analyze and compare the learning behavior and performance of FS-SOM against other vector quantization (VQ) algorithms. The results show that the proposed FS-SOM outperforms classical CL, Linde, Buzo, and Gray (LBG), and SOM algorithms. More importantly, FS-SOM achieves its superiority in reconstruction quality and topological ordering with a much greater robustness against variations in network parameters than the current art SOM algorithm for CQ. A most significant bit (MSB) biased encoding scheme is also introduced to reduce the number of parallel processing units. By mapping the pixel values as sign-magnitude numbers and biasing the magnitudes according to their sign bits, eight lattice points in the color space are condensed into one common point density function. Consequently, the same processing element can be used to map several color clusters and the entire FS-SOM network can be substantially scaled down without severely scarifying the quality of the displayed image. The drawback of this encoding scheme is the additional storage overhead, which can be cut down by leveraging on existing encoder in an overall lossy compression scheme.

This paper presents a new algorithm to compare substructural epitopes in protein binding cavities. Through the comparison of binding cavities accommodating well characterized ligands with cavities whose actual guests are yet unknown, it is possible to draw some conclusions on the required shape of a putative ligand likely to bind to the latter cavities. To detect functional relationships among proteins, their binding-site exposed physicochemical characteristics are described by assigning generic pseudocenters to the functional groups of the amino acids flanking the particular active site. The cavities are divided into small local regions of four pseudocenters having the shape of a pyramid with triangular basis. To find similar local regions, an emergent self-organizing map is used for clustering. Two local regions within the same cluster are similar and form the basis for the superpositioning of the corresponding cavities to score this match. First results show that the similarities between enzymes with the same EC number can be found correctly. Enzymes with different EC numbers are detected to have no common substructures. These results indicate the benefit of this method and motivate further studies.

The launch of large-scale chicken expressed sequence tags (EST) projects has placed the chicken in the lead for the number of EST sequences in agriculturally important animals. More than 451,000 chicken ESTs derived from over 158 libraries have been deposited in the NCBI dbEST database as of December 2003. But how many genes these ESTs represent and how they are expressed in different chicken tissues/organs remain undetermined. In the present research, we developed a human gene-based strategy for census of chicken orthologous genes and identification of their expression patterns. Among 34,157 human coding genes used in the study, BLAST analysis revealed that 11,066 genes provisionally matched 248,628 chicken ESTs. Based on the average EST abundance of the orthologous genes, the current public repository of chicken ESTs could represent approximately 20,000 provisional genes. Analysis of gene expression in 14 single tissues/organs showed that approximately 15% of genes were expressed exclusively in single tissue/organ whereas the remaining approximately 85% of genes were co-expressed in two or more tissues/organs. A majority (91.15%) of genes expressed in chicken embryos were also expressed at post-hatch stages, indicating that most genes activated in chicken embryos could serve housekeeping functions. Self-organizing maps (SOM) analysis organized 8807 provisional genes in selected chicken tissues into 98 clusters with each cluster being indicative of common regulatory factors and pathways. A total of 969 provisional orthologous genes were identified as preferentially expressed genes (PEGs) in various chicken tissues/organs (LOD>3.0). No doubt, the present study on gene expression patterns will provide insight into dynamics of metabolic pathways and tissue/organ programming and reprogramming in chickens.

Modeling non-linear descriptor-target activity/property relationships with many dependent descriptors has been a long-standing challenge in the design of biologically active molecules. In an effort to address this problem, we couple the supervised self-organizing map with the genetic algorithm. Although self-organizing maps are non-linear and topology-preserving techniques that hold great potential for modeling and decoding relationships, the large number of descriptors in typical quantitative structure-activity relationship or quantitative structure-property relationship analysis may lead to spurious correlation(s) and/or difficulty in the interpretation of resulting models. To reduce the number of descriptors to a manageable size, we chose the genetic algorithm for descriptor selection because of its flexibility and efficiency in solving complex problems. Feasibility studies were conducted using six different datasets, of moderate-to-large size and moderate-to-great diversity; each with a different biological endpoint. Since favorable training set statistics do not necessarily indicate a highly predictive model, the quality of all models was confirmed by withholding a portion of each dataset for external validation. We also address the variability introduced onto modeling through dataset partitioning and through the stochastic nature of the combined genetic algorithm supervised self-organizing map method using the z-score and other tests. Experiments show that the combined method provides comparable accuracy to the supervised self-organizing map alone, but using significantly fewer descriptors in the models generated. We observed consistently better results than partial least squares models. We conclude that the combination of genetic algorithms with the supervised self-organizing map shows great potential as a quantitative structure-activity/property relationship modeling tool.