Conventional Self-organizing Map Research Articles

Improving the performance of self-organizing map using reweighted zero-attracting method

In this paper, we introduce a novel approach to enhance the accuracy and convergence behavior of Self-Organizing Maps (SOM) by incorporating a reweighted zero-attracting term into the loss function. We evaluated two SOM versions: conventional SOM and robust adaptive SOM (RASOM). The enhanced versions, reweighted zero-attracting SOM (RZA-SOM) and reweighted zero-attracting RASOM (RZA-RASOM), include an l1 norm in the error function to add a zero-attractor term, which improves weight coefficient adjustments while preserving topology. The models were assessed for convergence speed and misadjustment under sparsity assumptions of the true coefficient matrix, and their robustness was tested under conditions of increased non-zero taps. Using six different datasets, we compared the performance of RZA-SOM and RZA-RASOM against conventional SOM and RA-SOM in terms of accuracy, quantization error, and topology preservation. Experimental results consistently demonstrated that RZA-SOM and RZA-RASOM surpassed the performance of conventional SOM and RA-SOM.

Adaptive Self-Organizing Map Using Optimal Control

The self-organizing map (SOM), which is a type of artificial neural network (ANN), was formulated as an optimal control problem. Its objective function is to minimize the mean quantization error, and the state equation is the weight updating equation of SOM. Based on the objective function and the state equations, the Hamiltonian equation based on Pontryagin’s minimum principle (PMP) was formed. This study presents two models of SOM formulated as an optimal control problem. In the first model, called SOMOC1, the design is based on the state equation representing the weight updating equation of the best matching units of the SOM nodes in each iteration, whereas in the second model, called SOMOC2, it considers the weight updating equation of all the nodes in the SOM as the state updating equation. The learning rate is treated as the control variable. Based on the solution of the switching function, a bang-bang control was applied with a high and low learning rate. The proposed SOMOC2 model performs better than the SOMOC1 model and conventional SOM as it considers all the nodes in the Hamiltonian equation, and the switching function obtained from it is influenced by all the states, which provides one costate variable for each. The costate determines the marginal cost of violating the constraint by the state equations, and the switching function is influenced by this, hence producing a greater improvement in terms of the mean quantization error at the final iteration. It was found that the solution leads to an infinite order singular arc. The possible solutions for the suitable learning rates during the singular arc period are discussed in this study.

Maximum correntropy self-organizing map for waveform classification

The self-organizing map (SOM) is a well-known unsupervised classification method for seismic facies analysis. The conventional SOM networks and their mutation methods are mostly based on the Euclidean distance measurement, which estimates the global similarity between the input data and weights of neuron. Such measurement is suitable for signals with a Gaussian distribution but may not work well for seismic data for which the dominant structural features (e.g., stratigraphic layers, faults, channels, and salt bodies) typically appear some specially distributed patterns. Therefore, we propose to modify the SOM by introducing a new distance measurement criterion based on the maximum correntropy. The correntropy is mainly used to measure the local similarity between variables, especially for non-Gaussian signals, and therefore is more suitable than the Euclidean distance to adaptively characterize the seismic structural similarities for seismic classification tasks. Validations on two synthetic data sets indicate that the proposed method yields more accurate classification results and is more robust to noise than the traditional SOM algorithm. Comparison experiments on a field data example also demonstrate that the proposed method can delineate the distribution of seismic facies more effectively and stably than the traditional one.

A faster dynamic convergency approach for self-organizing maps

This paper proposes a novel variable learning rate to address two main challenges of the conventional Self-Organizing Maps (SOM) termed VLRSOM: high accuracy with fast convergence and low topological error. We empirically showed that the proposed method exhibits faster convergence behavior. It is also more robust in topology preservation as it maintains an optimal topology until the end of the maximum iterations. Since the learning rate adaption and the misadjustment parameter depends on the calculated error, the VLRSOM will avoid the undesired results by exploiting the error response during the weight updation. Then the learning rate is updated adaptively after the random initialization at the beginning of the training process. Experimental results show that it eliminates the tradeoff between the rate of convergence and accuracy and maintains the data's topological relationship. Extensive experiments were conducted on different types of datasets to evaluate the performance of the proposed method. First, we experimented with synthetic data and handwritten digits. For each data set, two experiments with a different number of iterations (200 and 500) were performed to test the stability of the network. The proposed method was further evaluated using four benchmark data sets. These datasets include Balance, Wisconsin Breast, Dermatology, and Ionosphere. In addition, a comprehensive comparative analysis was performed between the proposed method and three other SOM techniques: conventional SOM, parameter-less self-organizing map (PLSOM2), and RA-SOM in terms of accuracy, quantization error (QE), and topology error (TE). The results indicated the proposed approach produced superior results to the other three methods.

Monitoring of casting quality using principal component analysis and self-organizing map

The monitoring of casting quality is very important to ensure the safe operation of casting processes. In this paper, in order to improve the accurate detection of casting defects, a combined method based on principal component analysis (PCA) and self-organizing map (SOM) is presented. The proposed method reduces the dimensionality of the original data by the projection of the data onto a smaller subspace through PCA. It uses Hotelling’s T2 and Q statistics as essential features for characterizing the process functionality. The SOM is used to improve the separation between casting defects. It computes the metric distances based similarity, using the T2 and Q (T2Q) statistics as input. A comparative study between conventional SOM, SOM with reduced data, and SOM with selected features is examined. The proposed method is used to identify the running conditions of the low pressure lost foam casting process. The monitoring results indicate that the SOM based on T2Q as feature vectors remains important comparatively to conventional SOM and SOM based on reduced data.

Hardware implementation of an active learning self-organizing neural network to predict the power fluctuation events of a photovoltaic grid-tied system

Power fluctuations happens due to highly stochastic solar irradiance nature and this could cause unwanted power quality issues in photovoltaic (PV) system. First predicting the PV output then mitigating the fluctuation by using energy storage system is one of the most effective power fluctuation mitigation method. Incremental learning algorithm such as incremental self-organizing map can be used to actively learn and predict power output. Although significant improvement in terms of mitigated events can be achieved in this kind of system, it still suffers from prediction accuracy due to the highly fluctuating PV profile. In this paper, a time-series unsupervised learning algorithm namely the Time-Series Self-Organizing Incremental Neural Network (TS-SOINN) is proposed to better predict the highly stochastic PV output. It incorporates a novel weighted memory layer to give higher emphasis to recent observation and improves data overlap issues in the conventional self-organizing map algorithm. In the simulation results, the TS-SOINN achieves prediction rate of 93.81% which outperforms the latest unsupervised incremental learning algorithm, M-SOINN by 33.44% and the TS-SOINN mitigated 89.13% power fluctuation events whereas M-SOINN only mitigated 79.62% events. In addition, the TS-SOINN is implemented in Altera Stratix V GS Field Programmable Gate Array (FPGA) board to run real-time prediction. This hardware architecture is able to increase new node and remove inactive nodes throughout the real-time prediction. The hardware TS-SOINN is integrated with mitigation engine to smoothen out power fluctuation events in PV grid-tied system, the experimental results show that the proposed system mitigated 83.33% of power fluctuation events at the grid and the battery state-of-charge maintains within 30%-100%.

Some measures to impact on the performance of Kohonen self-organizing map

In the field of unsupervised learning, Self-Organizing Map (SOM) has attracted the attention of many researchers. SOM is a popular algorithm in the area of data clustering; in this paper, new algorithms are developed to find the initial weights, to assign those initial weights to the SOM grid and a new way to determine the number of clusters in the SOM algorithm. Also, a new performance measure MSRI (Modified Semantic Relevant Index) has been introduced for the SOM algorithm. For the class label datasets, the performance criteria like Classification Accuracy (CA), Quantization error (QE) and Convergence time (CT) are used to compare the proposed SOM algorithm with existing SOM algorithms. Here the existing SOM algorithms like Enhanced SOM (ESOM), SOM Particle Swarm Optimization (SOMPSO), ESOMPSO and conventional SOM are used. In addition, MSRI is used to compare the proposed SOM with the existing SOM algorithms. We have also used different image classification datasets to compare our proposed SOM and existing SOM algorithm with CA, QE, CT, and MSRI. For the non-class label dataset, the criteria like QE, CT and MSRI are employed to analyze the performance of proposed SOM with the conventional SOM algorithm. The gene index is also used to validate the number of clusters obtained by the proposed SOM algorithm. It is found that our proposed SOM algorithm has shown better performance in all cases.

Hybrid multi-mode machine learning-based fault diagnosis strategies with application to aircraft gas turbine engines

In this work, a novel data-driven fault diagnostic framework is developed by using hybrid multi-mode machine learning strategies to monitor system health status. The coexistence of multi-mode and concurrent faults and their adverse coupling effects pose serious limitations for developing reliable diagnostic methodologies. A novel framework is proposed by exploiting inherent embedded health information contained in the I/O sensor data. The proposed hybrid strategies consist of optimal integration of recurrent neural network-based feature generation and self-organizing map diagnostic modules. To construct reliable fault diagnostic modules, a systematic clustering and modeling methodology is developed that has two primary advantages: (i) it does not require any a priori knowledge of data set characteristics or system mathematical model, and (ii) it does address and resolve the key limitations and challenges in conventional self-organizing map approaches. The effectiveness of our proposed framework is validated by utilizing sensor data including healthy and various degradation modes in application to compressor and turbine of an aircraft gas turbine engine. Comparisons with other machine learning-based methods in the literature are provided to demonstrate the performance and superiority of our proposed framework in fault diagnostic accuracy, false alarm rates, and in dealing with multi-mode and concurrent fault scenarios.

Evolution of SOMs’ Structure and Learning Algorithm: From Visualization of High-Dimensional Data to Clustering of Complex Data

In this paper, we briefly present several modifications and generalizations of the concept of self-organizing neural networks—usually referred to as self-organizing maps (SOMs)—to illustrate their advantages in applications that range from high-dimensional data visualization to complex data clustering. Starting from conventional SOMs, Growing SOMs (GSOMs), Growing Grid Networks (GGNs), Incremental Grid Growing (IGG) approach, Growing Neural Gas (GNG) method as well as our two original solutions, i.e., Generalized SOMs with 1-Dimensional Neighborhood (GeSOMs with 1DN also referred to as Dynamic SOMs (DSOMs)) and Generalized SOMs with Tree-Like Structures (GeSOMs with T-LSs) are discussed. They are characterized in terms of (i) the modification mechanisms used, (ii) the range of network modifications introduced, (iii) the structure regularity, and (iv) the data-visualization/data-clustering effectiveness. The performance of particular solutions is illustrated and compared by means of selected data sets. We also show that the proposed original solutions, i.e., GeSOMs with 1DN (DSOMs) and GeSOMS with T-LSs outperform alternative approaches in various complex clustering tasks by providing up to 20 % increase in the clustering accuracy. The contribution of this work is threefold. First, algorithm-oriented original computer-implementations of particular SOM’s generalizations are developed. Second, their detailed simulation results are presented and discussed. Third, the advantages of our earlier-mentioned original solutions are demonstrated.

Improving positioning accuracy based on self‐organizing map (SOM) and inter‐vehicular communication

AbstractLow‐cost global positioning system (GPS) receivers installed in most vehicles and smart devices typically display tens of meters of error in their location data. A large amount of research effort has been made to increase the positioning accuracy of GPS receivers mostly by reducing errors with the help of auxiliary devices and/or methodologies such as differential GPSs, assisted GPSs, real‐time kinematic positioning, computer vision, etc, which result in a certain amount of cost increase. In this paper, we propose a new cooperative vehicular localization scheme based on vehicle‐to‐vehicle communication. The proposed scheme first estimates the distances between neighboring vehicles using the weighted least square of double difference scheme and uses a novel machine learning technique called constrained self‐organizing map (C‐SOM) with a set of adjusted GPS fixes to generate the final estimates of GPS locations with considerably lower errors. We also propose a new method of presenting training samples to address the issue of convergence failure that arises from the constraints imposed on the inter‐vehicular distances. We present simulation results that demonstrate the superior performance of the proposed scheme over both the conventional SOM and the distributed location estimate algorithm.

Robust adaptive learning approach to self-organizing maps

The Self-Organizing Map (SOM) has attracted much research in diverse fields of study, where it has been successfully applied to a wide range of artificial intelligence applications. In this paper, a new intelligent adaptive learning SOM, in contrast with the conventional SOM algorithm, is presented. The proposed SOM overcomes the disadvantages of the conventional SOM by deriving a new variable learning rate that can adaptively achieve the optimal weights and obtain the winner neurons with a shorter learning process time. To quantify the performance, the proposed SOM was compared with various unsupervised algorithms to examine how well the network weight update equation adapts and reaches the optimum weights with fewer iterations. Extensive experiments were conducted using eight different databases from the UCI and KEEL repositories. The proposed SOM algorithm was further compared with the conventional SOM, GF-SOM, PLSOM, and PLSOM2 algorithms. The proposed SOM algorithm showed superiority in terms of the convergence rate, Quantization Error (QE), Topology Error (TE) preserving map, and accuracy during the classification process.

An intelligent real-time power management system with active learning prediction engine for PV grid-tied systems

In this paper, an incremental unsupervised neural network algorithm namely memory self-organizing incremental neural network (M-SOINN) is proposed to first predict the output power and subsequently detect the occurrence of power fluctuation events in a photovoltaic microgrid system. The M-SOINN uses clustering technique to form the data map, identifies the most similar patterns to predict the photovoltaic output power and then detects power fluctuation events. A novel memory layer is incorporated to establish the time-series learning. By using real life environment data, the proposed M-SOINN based real-time prediction engine detects power fluctuation events with a high detection rate of 92.69% and it outperforms the conventional self-organizing map (SOM), k-nearest neighbour (KNN), focused time delay neural network (FTDNN), and nonlinear autoregressive with exogenous input (NARX) networks. The system is simulated in the PSCAD environment and later experimentally. The proposed M-SOINN is then integrated into a power management system to mitigate power fluctuation events of the photovoltaic grid-tied system. Results show that the proposed power management system reduces 79.62% of power fluctuation events with an energy loss of 2.16% and battery state-of-charge maintains within 30%–100%. The proposed system outperforms hourly rule-based controller and the ramp rate controller by 44.02% and 27.57%, respectively in terms of the mitigated power fluctuation events.

Personal sleep pattern visualization using sequence-based kernel self-organizing map on sound data.

We propose a method to discover sleep patterns via clustering of sound events recorded during sleep. The proposed method extends the conventional self-organizing map algorithm by kernelization and sequence-based technologies to obtain a fine-grained map that visualizes the distribution and changes of sleep-related events. We introduced features widely applied in sound processing and popular kernel functions to the proposed method to evaluate and compare performance. The proposed method provides a new aspect of sleep monitoring because the results demonstrate that sound events can be directly correlated to an individual's sleep patterns. In addition, by visualizing the transition of cluster dynamics, sleep-related sound events were found to relate to the various stages of sleep. Therefore, these results empirically warrant future study into the assessment of personal sleep quality using sound data.

An artificial intelligence approach fit for tRNA gene studies in the era of big sequence data.

Unsupervised data mining capable of extracting a wide range of knowledge from big data without prior knowledge or particular models is a timely application in the era of big sequence data accumulation in genome research. By handling oligonucleotide compositions as high-dimensional data, we have previously modified the conventional self-organizing map (SOM) for genome informatics and established BLSOM, which can analyze more than ten million sequences simultaneously. Here, we develop BLSOM specialized for tRNA genes (tDNAs) that can cluster (self-organize) more than one million microbial tDNAs according to their cognate amino acid solely depending on tetra- and pentanucleotide compositions. This unsupervised clustering can reveal combinatorial oligonucleotide motifs that are responsible for the amino acid-dependent clustering, as well as other functionally and structurally important consensus motifs, which have been evolutionarily conserved. BLSOM is also useful for identifying tDNAs as phylogenetic markers for special phylotypes. When we constructed BLSOM with 'species-unknown' tDNAs from metagenomic sequences plus 'species-known' microbial tDNAs, a large portion of metagenomic tDNAs self-organized with species-known tDNAs, yielding information on microbial communities in environmental samples. BLSOM can also enhance accuracy in the tDNA database obtained from big sequence data. This unsupervised data mining should become important for studying numerous functionally unclear RNAs obtained from a wide range of organisms.

An Effective Color Quantization Method Using Octree-Based Self-Organizing Maps

Color quantization is an essential technique in color image processing, which has been continuously researched. It is often used, in particular, as preprocessing for many applications. Self-Organizing Map (SOM) color quantization is one of the most effective methods. However, it is inefficient for obtaining accurate results when it performs quantization with too few colors. In this paper, we present a more effective color quantization algorithm that reduces the number of colors to a small number by using octree quantization. This generates more natural results with less difference from the original image. The proposed method is evaluated by comparing it with well-known quantization methods. The experimental results show that the proposed method is more effective than other methods when using a small number of colors to quantize the colors. Also, it takes only 71.73% of the processing time of the conventional SOM method.

Batch SOM algorithms for interval-valued data with automatic weighting of the variables

Interval-valued data is most utilized to represent either the uncertainty related to a single measurement, or the variability of the information inherent to a group rather than an individual. In this paper, we focus on Kohonen self-organizing maps (SOMs) for interval-valued data, and design a new Batch SOM algorithm that optimizes an explicit objective function. This algorithm can handle, respectively, suitable City-Block, Euclidean and Hausdorff distances with the purpose to compare interval-valued data during the training of the SOM. Moreover, most often conventional batch SOM algorithms consider that all variables are equally important in the training of the SOM. However, in real situations, some variables may be more or less important or even irrelevant for this task. Thanks to a parameterized definition of the above-mentioned distances, we propose also an adaptive version of the new algorithm that tackles this problem with an additional step where a relevance weight is automatically learned for each interval-valued variable. Several examples with synthetic and real interval-valued data sets illustrate the usefulness of the two novel batch SOM algorithms.

AN EFFECTIVE COLOR QUANTIZATION METHOD USING COLOR IMPORTANCE-BASED SELF-ORGANIZING MAPS

Color quantization is an important process for image processing and various applications. Up to now, many color quantization methods have been proposed. The self-organizing maps (SOM) method is one of the most effective color quantization methods, which gives excellent color quantization results. However, it is slow, so it is not suitable for real-time applications. In this paper, we present a color importance{based SOM color quantization method. The proposed method dynamically adjusts the learning rate and the radius of the neighborhood using color importance. This makes the proposed method faster than the conventional SOM-based color quantization method. We compare the proposed method to 10 well-known color quantization methods to evaluate performance. The methods are compared by measuring mean absolute error (MAE), mean square error (MSE), and processing time. The experimental results show that the proposed method is effective and excellent for color quantization. Not only does the proposed method provide the best results compared to the other methods, but it uses only 67.18% of the processing time of the conventional SOM method.

CG-containing oligonucleotides and transcription factor-binding motifs are enriched in human pericentric regions.

Unsupervised data mining capable of extracting a wide range of information from big sequence data without prior knowledge or particular models is highly desirable in an era of big data accumulation for research on genes, genomes and genetic systems. By handling oligonucleotide compositions in genomic sequences as high-dimensional data, we have previously modified the conventional SOM (self-organizing map) for genome informatics and established BLSOM for oligonucleotide composition, which can analyze more than ten million sequences simultaneously and is thus suitable for big data analyses. Oligonucleotides often represent motif sequences responsible for sequence-specific binding of proteins such as transcription factors. The distribution of such functionally important oligonucleotides is probably biased in genomic sequences, and may differ among genomic regions. When constructing BLSOMs to analyze pentanucleotide composition in 50-kb sequences derived from the human genome in this study, we found that BLSOMs did not classify human sequences according to chromosome but revealed several specific zones, which are enriched for a class of CG-containing pentanucleotides; these zones are composed primarily of sequences derived from pericentric regions. The biological significance of enrichment of these pentanucleotides in pericentric regions is discussed in connection with cell type- and stage-dependent formation of the condensed heterochromatin in the chromocenter, which is formed through association of pericentric regions of multiple chromosomes.

Learning-regulated context relevant topographical map.

Kohonen's self-organizing map (SOM) is used to map high-dimensional data into a low-dimensional representation (typically a 2-D or 3-D space) while preserving their topological characteristics. A major reason for its application is to be able to visualize data while preserving their relation in the high-dimensional input data space as much as possible. Here, we are seeking to go further by incorporating semantic meaning in the low-dimensional representation. In a conventional SOM, the semantic context of the data, such as class labels, does not have any influence on the formation of the map. As an abstraction of neural function, the SOM models bottom-up self-organization but not feedback modulation which is also ubiquitous in the brain. In this paper, we demonstrate a hierarchical neural network, which learns a topographical map that also reflects the semantic context of the data. Our method combines unsupervised, bottom-up topographical map formation with top-down supervised learning. We discuss the mathematical properties of the proposed hierarchical neural network and demonstrate its abilities with empirical experiments.

Self-organizing maps based on limit cycle attractors

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.