Variant Of Self-Organizing Map Research Articles

Generalized EmbedSOM on quadtree-structured self-organizing maps

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-directed 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.

Generalized EmbedSOM on quadtree-structured self-organizing maps

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-directed 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.

Generalized EmbedSOM on quadtree-structured self-organizing maps.

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.

Dynamic topology and relevance learning SOM-based algorithm for image clustering tasks

In this paper, the task of unsupervised visual object categorization (UVOC) is addressed. We utilize a variant of Self-organizing Map (SOM) to cluster images in two different scenarios: disjoint (images from Caltech256) and non-disjoint (images from MSRC2) sets. First, we ran several tests to evaluate different image representation techniques: features obtained by a deep convolutional network were compared with those obtained by handcrafted methods, such as SIFT combined with a set of interest point detectors. As expected, we found that deep convolutional network features significantly outperformed its handcrafted counterparts. After choosing the best image representation technique, we compared the state-of-the-art image clustering algorithms with a SOM-based subspace clustering method that identifies automatically the relevant features in the high-dimensional image representations. The results have shown that our method achieves substantially lower clustering error than all competitors in several challenging testing settings.

Reconfigurable VLSI implementation for learning vector quantization with on-chip learning circuit

As an alternative to conventional single-instruction-multiple-data (SIMD) mode solutions with massive parallelism for self-organizing-map (SOM) neural network models, this paper reports a memory-based proposal for the learning vector quantization (LVQ), which is a variant of SOM. A dual-mode LVQ system, enabling both on-chip learning and classification, is implemented by using a reconfigurable pipeline with parallel p-word input (R-PPPI) architecture. As a consequence of the reuse of R-PPPI for solving the most severe computational demands in both modes, power dissipation and Si-area consumption can be dramatically reduced in comparison to previous LVQ implementations. In addition, the designed LVQ ASIC has high flexibility with respect to feature-vector dimensionality and reference-vector number, allowing the execution of many different machine-learning applications. The fabricated test chip in 180 nm CMOS with parallel 8-word inputs and 102 K-bit on-chip memory achieves low power consumption of 66.38 mW (at 75 MHz and 1.8 V) and high learning speed of clock cycles per d-dimensional sample vector where R is the reference-vector number.

MANIFOLD LEARNING AND VISUALIZATION BASED ON DYNAMIC SELF-ORGANIZING MAP

For the data sampled from a low-dimensional nonlinear manifold embedded in a high-dimensional space, such as Swiss roll and S-curve, Self-Organizing Map (SOM) tends to get stuck in local minima and then yield topological defects in the final map. To avoid this problem and obtain more faithful visualization results, a variant of SOM, i.e. Dynamic Self-Organizing Map (DSOM), was presented in this paper. DSOM can dynamically increase the map size, as the training data set is expanded according to its intrinsic neighborhood structure, starting from a small neighborhood in which the data points can lie on or close to a linear patch. According to the locally Euclidean nature of the manifold, the map can be guided onto the manifold surface and then the global faithful visualization results can be achieved step by step. Experimental results show that DSOM can discover the intrinsic manifold structure of the data more faithfully than SOM. In addition, as a new manifold learning method, DSOM can obtain more concise visualization results and be less sensitive to the neighborhood size and the noise than typical manifold learning methods, such as Isometric Mapping (ISOMAP) and Locally Linear Embedding (LLE), which can also be verified by experimental results.

An agent-based simulator driven by variants of Self-Organizing Maps

Abstract This paper introduces an agent-based simulator driven by variants of Self-Organizing Maps (SOMs), specifically designed to model agents learning in economic systems, as well as to render how they interact and the way such interaction can affect the system general behavior. As a consequence, we developed an environment with SOMs nodes treated as agents that are suitable to simulate economic systems and their evolution over time; moreover, in this way we were able to study within the SOM framework the impact of spatial connections on individual decisions. The effectiveness of this framework has been tested in the formalization of a model of economic growth. Agents behavior is simulated when the production efforts are a direct consequence of how individuals (in our simulation: SOM nodes) allocate their time and energies between working and studying, thus defining corresponding consumption and savings patterns. We then tested the model coherence with respect to observable data. The results confirm that, in order to simulate economic systems dynamics, it is relatively easy to mold SOM so that the simulation framework highlights significant patterns. Furthermore, in the examined case being the patterns consistent with the existence of dichotomous growth, i.e. the combination of convergence within regions and divergence among regions, they can be of help to rulers to effectively address their policy intervention.

Multiclass fMRI data decoding and visualization using supervised self-organizing maps

When multivariate pattern decoding is applied to fMRI studies entailing more than two experimental conditions, a most common approach is to transform the multiclass classification problem into a series of binary problems. Furthermore, for decoding analyses, classification accuracy is often the only outcome reported although the topology of activation patterns in the high-dimensional features space may provide additional insights into underlying brain representations. Here we propose to decode and visualize voxel patterns of fMRI datasets consisting of multiple conditions with a supervised variant of self-organizing maps (SSOMs). Using simulations and real fMRI data, we evaluated the performance of our SSOM-based approach. Specifically, the analysis of simulated fMRI data with varying signal-to-noise and contrast-to-noise ratio suggested that SSOMs perform better than a k-nearest-neighbor classifier for medium and large numbers of features (i.e. 250 to 1000 or more voxels) and similar to support vector machines (SVMs) for small and medium numbers of features (i.e. 100 to 600voxels). However, for a larger number of features (>800voxels), SSOMs performed worse than SVMs. When applied to a challenging 3-class fMRI classification problem with datasets collected to examine the neural representation of three human voices at individual speaker level, the SSOM-based algorithm was able to decode speaker identity from auditory cortical activation patterns. Classification performances were similar between SSOMs and other decoding algorithms; however, the ability to visualize decoding models and underlying data topology of SSOMs promotes a more comprehensive understanding of classification outcomes. We further illustrated this visualization ability of SSOMs with a re-analysis of a dataset examining the representation of visual categories in the ventral visual cortex (Haxby et al., 2001). This analysis showed that SSOMs could retrieve and visualize topography and neighborhood relations of the brain representation of eight visual categories. We conclude that SSOMs are particularly suited for decoding datasets consisting of more than two classes and are optimally combined with approaches that reduce the number of voxels used for classification (e.g. region-of-interest or searchlight approaches).

Self-organizing maps whose topologies can be learned with adaptive binary search trees using conditional rotations

Numerous variants of Self-Organizing Maps (SOMs) have been proposed in the literature, including those which also possess an underlying structure, and in some cases, this structure itself can be defined by the user. Although the concepts of growing the SOM and updating it have been studied, the whole issue of using a self-organizing Adaptive Data Structure (ADS) to further enhance the properties of the underlying SOM, has been unexplored. In an earlier work, we impose an arbitrary, user-defined, tree-like topology onto the codebooks, which consequently enforced a neighborhood phenomenon and the so-called tree-based Bubble of Activity (BoA). In this paper, we consider how the underlying tree itself can be rendered dynamic and adaptively transformed. To do this, we present methods by which a SOM with an underlying Binary Search Tree (BST) structure can be adaptively re-structured using Conditional Rotations (CONROT). These rotations on the nodes of the tree are local, can be done in constant time, and performed so as to decrease the Weighted Path Length (WPL) of the entire tree. In doing this, we introduce the pioneering concept referred to as Neural Promotion, where neurons gain prominence in the Neural Network (NN) as their significance increases. We are not aware of any research which deals with the issue of Neural Promotion. The advantage of such a scheme is that the user need not be aware of any of the topological peculiarities of the stochastic data distribution. Rather, the algorithm, referred to as the TTOSOM with Conditional Rotations (TTOCONROT), converges in such a manner that the neurons are ultimately placed in the input space so as to represent its stochastic distribution, and additionally, the neighborhood properties of the neurons suit the best BST that represents the data. These properties have been confirmed by our experimental results on a variety of data sets. We submit that all these concepts are both novel and of a pioneering sort.

NEURAL NETWORK WORLD: OPTIMIZED SPIRAL SPHERICAL SOM (OSS-SOM)

The border effect is one of the problems, which can appear in the application of self-organizing maps (SOM). Different solutions were presented in the literature, but each of them has its drawbacks. In this paper we present a new method for overcoming the border effect - optimized spiral spherical SOM. We also show that standard measure of irregularity is not appropriate and present a modified version - Gaussian measure of irregularity. Our simulations suggest that the new variant of SOM achieves extremely low values of irregularity in comparison to other methods. At the end of the paper we present a software solution for the proposed method.

MONITORING POWER CONSUMPTION USING A GENERALIZED VARIANT OF SELF-ORGANIZING MAP (SOM)

In this paper, we present a new approach for monitoring power consumption in several processes. The generalization of the envSOM algorithm, a variant of Self-Organizing Map (SOM), is used to build an electrical model and visualize the information. The envSOM extended to n hierarchical phases allows us to obtain a more accurate model from real past data. The model is conditioned hierarchically on environmental variables. In this way, time variables can be used to consider seasonality and weekday/hour periodicity. Time variable maps and electrical component planes make it possible to visualize and analyze power consumption. The representation of the Best Matching Unit (BMU) or its trajectory on these maps enables the on-line monitoring.

MIGSOM: Multilevel Interior Growing Self-Organizing Maps for High Dimensional Data Clustering

Understanding the inherent structure of high-dimensional datasets is a very challenging task. This can be tackled from visualization, summarizing or simply clustering points of view. The Self-Organizing Map (SOM) is a powerful and unsupervised neural network to resolve these kinds of problems. By preserving the data topology mapped onto a grid, SOM can facilitate visualization of data structure. However, classical SOM still suffers from the limits of its predefined structure. Growing variants of SOM can overcome this problem, since they have tried to define a network structure with no need an advance a fixed number of output units by dynamic growing architecture. In this paper we propose a new dynamic SOMs called MIGSOM: Multilevel Interior Growing SOMs for high-dimensional data clustering. MIGSOM present a different architecture than dynamic variants presented in the literature. Using an unsupervised training process MIGSOM has the capability of growing map size from the boundaries as well as the interior of the network in order to represent more faithfully the structure present in a data collection. As a result, MIGSOM can have three-dimensional (3-D) structure with different levels of oriented maps developed according to data direction. We demonstrate the potential of the MIGSOM with real-world datasets of high-dimensional properties in terms of topology preserving visualization, vectors summarizing by efficient quantization and data clustering. In addition, MIGSOM achieves better performance compared to growing grid and the classical SOM.

Distance-Preserving SOM: A New Data Visualization Algorithm

As the combination of topology-preserving dimensionality reduction and vector quantization, Self-Organizing Map (SOM) is suitable for visualizing the structure of high-dimensional mass data, which can be used to select more suitable algorithms for subsequent data analysis/processing. However, due to the fixed regular lattice of neurons, SOM has to require some color-coding scheme such as U-matrix to imprint the inter-neuron distance information on the lattice for the aim of visualization. Even so, the structure of the data may often appear in a distorted and unnatural form. In order for the map to visualize the structure of the data faithfully and naturally, the similarity/dissimilarity information should be preserved on the map directly. To do this, a novel variant of SOM, i.e. Distance-Preserving SOM (DPSOM), was presented in this paper. DPSOM can adjust the positions of neurons on the map according to the corresponding distances in the data space, and thus preserve the distance information on the map directly, as Multidimensional Scaling (MDS) does. What’s the most important, DPSOM can automatically avoid the excessive contraction of neurons to one point without any additional parameter, which makes it advantageous over those existing position-adjustable SOMs. Finally, DPSOM can be verified by experimental results well.

Assessment of self-organizing map variants for clustering with application to redistribution of emotional speech patterns

Two well-known variants of the self-organizing map (SOM) that are based on multivariate order statistics are the marginal median SOM and the vector median SOM. In the past, their efficiency was demonstrated for color image quantization. We employ the well-known IRIS and VOWEL data sets and we assess the SOM variants’ performance with respect to the accuracy, the average over all neurons mean squared error between the patterns that were assigned to a neuron and the neuron's weight vector, the Rand index, the Γ statistic, and the overall entropy. All figures of merit favor the marginal median SOM and the vector median SOM against the standard SOM. Based on the aforementioned findings, the marginal median SOM and the vector median SOM are used to redistribute emotional speech patterns from the Danish Emotional Speech database, which were originally classified as being neutral, to the emotional states of hot anger, happiness, sadness, and surprise.

A Pattern Classification Method using Kernel Adaptive-Subspace Self-Organizing Map

Adaptive-Subspace Self-Organizing Map (ASSOM) is a variant of Self-Organizing Map, where each computational unit defines a linear subspace. The subspace in a unit is represented by a set of basis vectors. After training, these units result in a set of subspace detectors. In numerous cases, however, these are not enough to describe a class of patterns because of a linearity. In this letter, the ASSOM on the high-dimensional space with kernel method is proposed in order to achieve efficient classification. By using the kernel method, linear subspaces in the ASSOM can be extended to non-linear subspaces easily. This improves the representation of subspace. The effectiveness of the proposed method is verified by applying it to a well-known problem, or two spirals classification.

The Evolving Tree?A Novel Self-Organizing Network for Data Analysis

The Self-Organizing Map (SOM) is one of the best known and most popular neural network-based data analysis tools. Many variants of the SOM have been proposed, like the Neural Gas by Martinetz and Schulten, the Growing Cell Structures by Fritzke, and the Tree-Structured SOM by Koikkalainen and Oja. The purpose of such variants is either to make a more flexible topology, suitable for complex data analysis problems or to reduce the computational requirements of the SOM, especially the time-consuming search for the best-matching unit in large maps. We propose here a new variant called the Evolving Tree which tries to combine both of these advantages. The nodes are arranged in a tree topology that is allowed to grow when any given branch receives a lot of hits from the training vectors. The search for the best matching unit and its neighbors is conducted along the tree and is therefore very efficient. A comparison experiment with high dimensional real world data shows that the performance of the proposed method is better than some classical variants of SOM.

Variants of self-organizing maps

Self-organizing maps have a bearing on traditional vector quantization. A characteristic that makes them more closely resemble certain biological brain maps, however, is the spatial order of their responses, which is formed in the learning process. A discussion is presented of the basic algorithms and two innovations: dynamic weighting of the input signals at each input of each cell, which improves the ordering when very different input signals are used, and definition of neighborhoods in the learning algorithm by the minimal spanning tree, which provides a far better and faster approximation of prominently structured density functions. It is cautioned that if the maps are used for pattern recognition and decision process, it is necessary to fine tune the reference vectors so that they directly define the decision borders.