Recursive principal components analysis.

A recurrent linear network can be trained with Oja's constrained Hebbian learning rule. As a result, the network learns to represent the temporal context associated to its input sequence. The operation performed by the network is a generalization of Principal Components Analysis (PCA) to time-series, called Recursive PCA. The representations learned by the network are adapted to the temporal statistics of the input. Moreover, sequences stored in the network may be retrieved explicitly, in the reverse order of presentation, thus providing a straight-forward neural implementation of a logical stack.     

TreeSOM: Cluster analysis in the self-organizing map.

Clustering problems arise in various domains of science and engineering. A large number of methods have been developed to date. The Kohonen self-organizing map (SOM) is a popular tool that maps a high-dimensional space onto a small number of dimensions by placing similar elements close together, forming clusters. Cluster analysis is often left to the user. In this paper we present the method TreeSOM and a set of tools to perform unsupervised SOM cluster analysis, determine cluster confidence and visualize the result as a tree facilitating comparison with existing hierarchical classifiers. We also introduce a distance measure for cluster trees that allows one to select a SOM with the most confident clusters.     

Component-based visual clustering using the self-organizing map.

In this paper we present a new method for visual clustering of multi-component images such as trademarks, using the topological properties of the self-organizing map, and show how it can be used for similarity retrieval from a database. The method involves two stages: firstly, the construction of a 2D map based on features extracted from image components, and secondly the derivation of a Component Similarity Vector from a query image, which is used in turn to derive a 2D map of retrieved images. The retrieval effectiveness of this novel component-based shape matching approach has been evaluated on a set of over 10 000 trademark images, using a spatially-based precision-recall measure. Our results suggest that our component-based matching technique performs markedly better than matching using whole-image clustering, and is relatively insensitive to changes in input parameters such as network size.     

A principal components analysis of the Autism Diagnostic Interview-Revised

OBJECTIVE: To develop factors based on the Autism Diagnostic Interview-Revised (ADI-R) that index separate components of the autism phenotype that are genetically relevant and validated against standard measures of the constructs. METHOD: ADIs and ADI-Rs of 292 individuals with autism were subjected to a principal components analysis using VARCLUS. The resulting variable clusters were validated against standard measures. RESULTS: Six clusters of variables emerged: spoken language, social intent, compulsions, developmental milestones, savant skills and sensory aversions. Five of the factors were significantly correlated with the validating measures and had good internal consistency, face validity, and discriminant and construct validity. Most intraclass correlations between siblings were adequate for use in genetic studies. CONCLUSION: The ADI-R contains correlated clusters of variables that are valid, genetically relevant, and that can be used in a variety of studies.     

Grid topologies for the self-organizing map

The original Self-Organizing Feature Map (SOFM) has been extended in many ways to suit different goals and application domains. However, the topologies of the map lattice that we can found in literature are nearly always square or, more rarely, hexagonal. In this paper we study alternative grid topologies, which are derived from the geometrical theory of tessellations. Experimental results are presented for unsupervised clustering, color image segmentation and classification tasks, which show that the differences among the topologies are statistically significant in most cases, and that the optimal topology depends on the problem at hand. A theoretical interpretation of these results is also developed.     

Spherical self-organizing map using efficient indexed geodesic data structure.

The two-dimensional (2D) Self-Organizing Map (SOM) has a well-known "border effect". Several spherical SOMs which use lattices of the tessellated icosahedron have been proposed to solve this problem. However, existing data structures for such SOMs are either not space efficient or are time consuming when searching the neighborhood. We introduce a 2D rectangular grid data structure to store the icosahedron-based geodesic dome. Vertices relationships are maintained by their positions in the data structure rather than by immediate neighbor pointers or an adjacency list. Increasing the number of neurons can be done efficiently because the overhead caused by pointer updates is reduced. Experiments show that the spherical SOM using our data structure, called a GeoSOM, runs with comparable speed to the conventional 2D SOM. The GeoSOM also reduces data distortion due to removal of the boundaries. Furthermore, we developed an interface to project the GeoSOM onto the 2D plane using a cartographic approach, which gives users a global view of the spherical data map. Users can change the center of the 2D data map interactively. In the end, we compare the GeoSOM to the other spherical SOMs by space complexity and time complexity.     

Adaptive filtering with the self-organizing map: a performance comparison.

In this paper we provide an in-depth evaluation of the SOM as a feasible tool for nonlinear adaptive filtering. A comprehensive survey of existing SOM-based and related architectures for learning input-output mappings is carried out and the application of these architectures to nonlinear adaptive filtering is formulated. Then, we introduce two simple procedures for building RBF-based nonlinear filters using the Vector-Quantized Temporal Associative Memory (VQTAM), a recently proposed method for learning dynamical input-output mappings using the SOM. The aforementioned SOM-based adaptive filters are compared with standard FIR/LMS and FIR/LMS-Newton linear transversal filters, as well as with powerful MLP-based filters in nonlinear channel equalization and inverse modeling tasks. The obtained results in both tasks indicate that SOM-based filters can consistently outperform powerful MLP-based ones.     

A programmable triangular neighborhood function for a Kohonen self-organizing map implemented on chip

An efficient transistor level implementation of a flexible, programmable triangular function (TF) that can be used as a triangular neighborhood function (TNF) in ultra-low power, self-organizing maps (SOMs) realized as application-specific integrated circuit (ASIC) is presented. The proposed TNF block is a component of a larger neighborhood mechanism, whose role is to determine the distance between the winning neuron and all neighboring neurons. Detailed simulations carried out for the software model of such network show that the TNF forms a good approximation of the gaussian neighborhood function (GNF), while being implemented in a much easier way in hardware. The overall mechanism is very fast. In the CMOS 0.18 μm technology, distances to all neighboring neurons are determined in parallel, within the time not exceeding 11 ns, for an example neighborhood range, R, of 15. The TNF blocks in particular neurons require another 6 ns to calculate the output values directly used in the adaptation process. This is also performed in parallel in all neurons. As a result, after determining the winning neuron, the entire map is ready for the adaptation after the time not exceeding 17 ns, even for large numbers of neurons. This feature allows for the realization of ultra low power SOMs, which are hundred times faster than similar SOMs realized on PC. The signal resolution at the output of the TNF block has a dominant impact on the overall energy consumption as well as the silicon area. Detailed system level simulations of the SOM show that even for low resolutions of 3 to 6 bits, the learning abilities of the SOM are not affected. The circuit performance has been verified by means of transistor level Hspice simulations carried out for different transistor models and different values of supply voltage and the environment temperature - a typical procedure completed in case of commercial chips that makes the obtained results reliable.     

Looking inside self-organizing map ensembles with resampling and negative correlation learning

In this work, we focus on the problem of training ensembles or, more generally, a set of self-organizing maps (SOMs). In the light of new theory behind ensemble learning, in particular negative correlation learning (NCL), the question arises if SOM ensemble learning can benefit from non-independent learning when the individual learning stages are interlinked by a term penalizing correlation in errors. We can show that SOMs are well suited as weak ensemble components with a small number of neurons. Using our approach, we obtain efficiently trained SOM ensembles outperforming other reference learners. Due to the transparency of SOMs, we can give insights into the interrelation between diversity and sublocal accuracy inside SOMs. We are able to shed light on the diversity arising over a combination of several factors: explicit versus implicit as well as inter-diversities versus intra-diversities. NCL fully exploits the potential of SOM ensemble learning when the single neural networks co-operate at the highest level and stability is satisfied. The reported quantified diversities exhibit high correlations to the prediction performance.     

Efficiently updating and tracking the dominant kernel principal components.

The dominant set of eigenvectors of the symmetrical kernel Gram matrix is used in many important kernel methods (like e.g. kernel Principal Component Analysis, feature approximation, denoising, compression, prediction) in the machine learning area. Yet in the case of dynamic and/or large-scale data, the batch calculation nature and computational demands of the eigenvector decomposition limit these methods in numerous applications. In this paper we present an efficient incremental approach for fast calculation of the dominant kernel eigenbasis, which allows us to track the kernel eigenspace dynamically. Experiments show that our updating scheme delivers a numerically stable and accurate approximation for eigenvalues and eigenvectors at every iteration in comparison to the batch algorithm.     

Plastic mine detecting radar system using complex-valued self-organizing map that deals with multiple-frequency interferometric images.

Ground penetrating radars (GPR's) have been often applied to underground object imaging. However, conventional radar systems do not work sufficiently to detect anti-personnel plastic landmines. We propose a novel radar imaging system, which processes adaptively interferometric front-end data obtained at multiple-frequency points. The system deals with interferometric images using complex-valued self-organizing map (C-SOM). We demonstrate a successful visualization of a plastic mine buried near the ground surface.     

A loss function approach to model selection in nonlinear principal components

The nonlinear transformation of the input variables that characterises the first nonlinear principal component is modelled as a linear sum of radially-symmetric kernel functions. It is shown that the parameters of the variance maximising transformation may be obtained through the minimisation of a loss function measuring departure from homogeneity. An alternating least squares algorithm is given. This is used as the basis of a cross-validation routine for model selection.     

Localization of the event-related potential novelty response as defined by principal components analysis

Recent research indicates that novel stimuli elicit at least two distinct components, the Novelty P3 and the P300. The P300 is thought to be elicited when a context updating mechanism is activated by a wide class of deviant events. The functional significance of the Novelty P3 is uncertain. Identification of the generator sources of the two components could provide additional information about their functional significance. Previous localization efforts have yielded conflicting results. The present report demonstrates that the use of principal components analysis (PCA) results in better convergence with knowledge about functional neuroanatomy than did previous localization efforts. The results are also more convincing than that obtained by two alternative methods, MUSIC-RAP and the Minimum Norm. Source modeling on 129-channel data with BESA and BrainVoyager suggests the P300 has sources in the temporal-parietal junction whereas the Novelty P3 has sources in the anterior cingulate.     

Image denoising using self-organizing map-based nonlinear independent component analysis.

This paper proposes the use of self-organizing maps (SOMs) to the blind source separation (BSS) problem for nonlinearly mixed signals corrupted with multiplicative noise. After an overview of some signal denoising approaches, we introduce the generic independent component analysis (ICA) framework, followed by a survey of existing neural solutions on ICA and nonlinear ICA (NLICA). We then detail a BSS method based on SOMs and intended for image denoising applications. Considering that the pixel intensities of raw images represent a useful signal corrupted with noise, we show that an NLICA-based approach can provide a satisfactory solution to the nonlinear BSS (NLBSS) problem. Furthermore, a comparison between the standard SOM and a modified version, more suitable for dealing with multiplicative noise, is made. Separation results obtained from test and real images demonstrate the feasibility of our approach.     

Neuropathological heterogeneity in Alzheimer’s disease: A study of 80 cases using principal components analysis

Three hypotheses have been proposed to explain neuropathological heterogeneity in Alzheimer’s disease (AD): the presence of distinct subtypes (‘subtype hypothesis’), variation in the stage of the disease (‘phase hypothesis’) and variation in the origin and progression of the disease (‘compensation hypothesis’). To test these hypotheses, variation in the distribution and severity of senile plaques (SP) and neurofibrillary tangles (NFT) was studied in 80 cases of AD using principal components analysis (PCA). Principal components analysis using the cases as variables (Q‐type analysis) suggested that individual differences between patients were continuously distributed rather than the cases being clustered into distinct subtypes. In addition, PCA using the abundances of SP and NFT as variables (R‐type analysis) suggested that variations in the presence and abundance of lesions in the frontal and occipital lobes, the cingulate gyrus and the posterior parahippocampal gyrus were the most important sources of heterogeneity consistent with the presence of different stages of the disease. In addition, in a subgroup of patients, individual differences were related to apolipoprotein E (ApoE) genotype, the presence and severity of SP in the frontal and occipital cortex being significantly increased in patients expressing apolipoprotein (Apo)E allele ?4. It was concluded that some of the neuropathological heterogeneity in our AD cases may be consistent with the ‘phase hypothesis’. A major factor determining this variation in late‐onset cases was ApoE genotype with accelerated rates of spread of the pathology in patients expressing allele ?4.