Topological Feature Map Research Articles

Sieci neuronowe do mapowania archeologicznych artefaktów litowych

An analytical non-destructive strategy to chemically characterize lithic artefacts has been developed. Around 100 archaeological lithic materials found in Neolithic-Chalcolithic sites in the Mediterranean region of the Iberian Peninsula and nowadays stored in different museums of the Valencian Community (Spain), were studied. The materials belong to different typologies of rock (diabase, sillimanite, ophite and amphibolite) and were analysed employing portable energy dispersive X-ray fluorescence spectroscopy (pXRF) directly in the rock surface. The obtained data were processed through neural networks protocol, specifically the so-called Kohonen networks or Self Organised Maps (SOM), to map the geologic samples. This self-organized topological feature maps are suitable to deal with multidimensional representations and map them in a two-dimensional space of neurons, following an unsupervised learning protocol. SOM is used to reduce multidimensional data onto lower-dimensional spaces and clustering procedures. As a result, SOM create spatially organized representations, which enhance the discovery of correlations between data. In this case the method has enabled the evaluation of elemental markers related to each rock type behaving as a fine hidden pattern detector and so understand the possible advantages and disadvantages of the analytical method employed to define provenance issues. The attribution suggested by statistics is mainly driven by the composition of rocks essential minerals which are linked to the different petrogenetic conditions. The results showed that in most of the cases the distribution and dispersion of the chemical profile depend of the kind of rock, and clearly suggest that a good way to identify stone tools raw material procurement is to look for elemental markers, being the prior step to create an approximation to ancient exchange networks and their evolution in a diachronic axis.

Learning a complex network representation for shape classification

Shape contour is a key low-level characteristic, making shape description an important aspect in many computer vision problems, with several challenges such as variations in scale, rotation, and noise. In this paper, we introduce an approach for shape analysis and classification from binary images based on representations learned by applying Randomized Neural Networks (RNNs) on feature maps derived from a Complex Network (CN) framework. Our approach models the contour in a complex network and computes their topological measures using a dynamic evolution strategy. This evolution of the CN provides significant information into the physical aspects of the shape’s contour. Therefore, we propose embedding the topological measures computed from the dynamics of the CN evolution into a matrix representation, which we have named the Topological Feature Map (TFM). Then, we employ the RNN to learn representations from the TFM through a sliding window strategy. The proposed representation is formed by the learned weights between the hidden and output layers of the RNN. Our experimental results show performance improvements in shape classification using the proposed method across two generic shape datasets. We also applied our approach to the recognition of plant leaves, achieving high performance in this challenging task. Furthermore, the proposed approach has demonstrated robustness to noise and invariance to transformations in scale and orientation of the shapes.

Spatial-temporal flood inundation nowcasts by fusing machine learning methods and principal component analysis

• Build a novel forecast model (PCA-SOM-NARX) by statistical & machine learning tools. • 2-dimensional SOBEK simulates the full-scale flooding processes of rainfall patterns. • PCA extracts principal components to present spatial distributions of inundation. • SOM clusters inundation data to form a spatial–temporal topological feature map. • PCA-SOM-NARX makes reliable and accurate multi-step-ahead regional flood nowcasts. The frequency and severity of floods have noticeably increased worldwide in the last decades due to climate change and urbanization. This study aims to build an urban flood warning system for reducing the impact of flood disasters. A great number of storm-induced rainfall data were collected in Taipei, Taiwan, and the corresponding 2-D inundation maps were simulated for illustrating urban rainfall-flood inundation processes. We proposed a novel urban flood forecast methodology framed by machine learning and statistical techniques to mine the spatial–temporal features between rainfall patterns and inundation maps for making multi-step-ahead regional flood inundation forecasts. The proposed methodology (PCA-SOM-NARX) integrated the advantages of Principal Component Analysis (PCA), Self-Organizing Map (SOM), and Nonlinear Autoregressive with Exogenous Inputs (NARX). PCA was used to extract principal components representing the different spatial distributions of urban inundation. SOM was used to cluster high dimensional inundation datasets to form a two-dimensional topological feature map. NARX was used to establish multi-step-ahead flood forecast models for the next hour at a 10-minute scale. The results show that the PCA-SOM-NARX approach not only produced more stable and accurate multi-step-ahead forecasts on flood inundation depth but was also more indicative of the spatial distribution of inundation caused by torrential rain events, compared to the SOM-NARX approach (the benchmark). The results demonstrate the proposed methodology can adequately grasp the inundation status associated with different rainfall distributions to reliably and accurately forecast regional flood inundation depths, which can help decision makers respond to flooding earlier and mitigate flood disasters.

Classification of breast masses in mammograms using geometric and topological feature maps and shape distribution

Breast cancer is the second most common cancer in the world, being more common among women and representing 24.2% of new cases each year. Mammography is currently the best technique for early detection of non-palpable breast lesions. Due to the need to create new more computationally efficient techniques, this paper presents a methodology for mass classification from mammographic images based on their geometric and topological features. For each image, two spatial feature maps named distance map and surface map are computed. These features describe the mass geometry and topology, respectively. Also, shape descriptors based on distances histograms are used to characterize the shape of the masses. The purpose of this comparison is to discriminate its malignancy and benignity patterns. The high-boost filter is applied to enhance the masses, since the difference between them and the breast tissue or other components of them is very subtle. Mammograms digitized from the Digital Database for Screening Mammography (DDSM) were used for the testing of this methodology, corresponding to 794 ROIs that were separated into groups by density, according to BI-RADS classification. The best results for accuracy, sensitivity, and specificity were 93.70%, 96.29%, and 91.05%, respectively, for density 2 and 90.18%, 91.01%, and 89.94% for all images. The results obtained demonstrate that the sets of features successfully discriminate mass standards, even with the exceptions and obstacles that characterize and classify the masses through their shape.

Saliency prediction by Mahalanobis distance of topological feature on deep color components

A new saliency prediction method via extracting topological feature and calculating Mahalanobis distance on deep color components is presented in this paper. Specifically, four selectable schemes of color components are considered and a deep convolutional network is used to learn the best scheme. Then the topological feature maps of an input image are extracted on the learned color components by the analysis of connectivity and adjacency. To achieve the final saliency map, a new fusion method is proposed by calculating the Mahalanobis distance between the feature maps and their means with their covariance matrices rather than summating the feature maps linearly. The numerical and visual evaluation shows that a competitive performance compared with fourteen state-of-the-art models is achieved by the proposed method.

Feature recognition and shape design in sneakers

Due to the improvements associated with our modern lifestyle, both personal preferences and commercial market value should be considered when undertaking the challenge of new product development. Thus, a crucial research topic is how to design a customized product for consumers. In this study, a feature recognition and shape-design process for basketball sneakers was established that integrated Kansei engineering and artificial neural networks (ANNs), in combination with famous point guards in the National Basketball Association (NBA), as the basis for constructing a topological feature map for sneakers. We used questionnaires to get 20 fans in NBA games to assign a rating value in Kansei adjectives to evaluate 50 basketball shoes and to identify the top 10 NBA point guards. The fans’ perspectives combined the psychological and physical scales for the top 10 point guards to establish a gross relationship between sneakers and the point guards. Based on competitive learning in the self-organizing map (SOM), the similarities of the inputs from the Kansei perspective concerning NBA point guards and sneakers can be reduced in their dimensions and grouped into six clusters. A back propagation network (BPN) is proposed to verify the mapping of sneakers onto point guards. The results were validated by comparing them with the target neurons based on SOM feature map. A MATLAB program was developed using SOM and BPN algorithms to verify the groups of sneakers accompanying the point guards. Then, the system can categorize the sneakers that match the players. A feature-based, shape-morphing process for the design of a new style of sneaker was implemented. A model to blend the features was constructed in SolidWorks CAD by choosing any two different shapes from the SOM map. This research was used to add the vast variety of shapes and design of sneakers from the selected SOM feature map to help designers create many different styles in a short period of time.

New Strategy for Optimizing Water Application under Trickle Irrigation

The determination of water application parameters for creating an optimal soil moisture profile represents a complex nonlinear optimization problem which renders traditional optimization into a cumbersome procedure. For this reason, an alternative methodology is proposed which combines a numerical subsurface flow model and artificial neural networks (ANN) for solving the problem in two, fully separate steps. The first step employs the flow model for calculating a large number of wetting profiles (output), obtained from a systematic variation of both water application and initial soil moisture (input). The resulting matrix of corresponding input/output values is used for training the ANN. The second step, the application of the fully trained ANN, then provides the irrigation parameters which range from a specified initial soil moisture to a desired crop-specific soil moisture profile. In order to avoid substantial disadvantages associated with the common feedforward backpropagation approach, a self-organizing topological feature map is implemented to perform this task. After a comprehensive sensitivity analysis, the new methodology is applied to the outcome of an irrigation experiment. The convincing results recommend the new methodology as a positive contribution towards an improved irrigation efficiency.

A general probability estimation approach for neural comp.

We describe an analytical framework for the adaptations of neural systems that adapt its internal structure on the basis of subjective probabilities constructed by computation of randomly received input signals. A principled approach is provided with the key property that it defines a probability density model that allows studying the convergence of the adaptation process. In particular, the derived algorithm can be applied for approximation problems such as the estimation of probability densities or the recognition of regression functions. These approximation algorithms can be easily extended to higher-dimensional cases. Certain neural network models can be derived from our approach (e.g., topological feature maps and associative networks).

Analysis of infant cries for the early detection of hearing impairment

The basic hypothesis is that cry vocalizations of hearing-impaired infants differ from those of their counterparts with normal hearing abilities due to the lack of auditory feedback. This assumption, based on observations made by clinical experts, is investigated by means of auditory experiments with naive and expert listeners, and by signal analysis of the cries. The listening experiment shows that it is possible for experts to auditorily classify cries for both infant groups, based on the voice related and melodic cry features. The cries of profoundly hearing-impaired infants are different regarding their perceived sound, rhythm and melody. The sound may well be correlated to spectral characteristics, and melodic and rhythmic parameters are extracted which differ significantly for the two infant groups. The findings are discussed in the context of a cry production model. The extracted signal parameters enable an automatic classification of the cries by means of topological feature maps, which may later be used as the basis for an early supplementary diagnostic tool.

Competitive learning and vector quantization in digital VLSI systems

This paper reviews implementations of competitive learning algorithms in digital VLSI circuits and systems, including recent results from our laboratory on neural circuits for efficient learning computations and for vector quantization. Digital circuits for competitive learning, especially those operating with low-power requirements, are currently important for their applications in computationally efficient speech and image compression by vector quantization, as required, for example, in portable multimedia terminals. A summary of competitive learning models is presented to indicate the type of VLSI computations required, and the effects of weight quantization are discussed. Circuit representations of computational primitives for learning and evaluation of distortion metrics by digital circuits are also reviewed. The present state of VLSI implementations of hard and soft competitive learning algorithms are discussed, as well as those for topological feature maps. Recent results are also presented from simulations of frequency-sensitive competitive learning concerning sensitivity of these algorithms to limited precision in VLSI learning computations. Applications of these learning algorithms to unsupervised feature extraction and to vector quantization are also described.

Analog VLSI Circuits for Competitive Learning Networks

An investigation is made concerning implementations of competitive learning algorithms in analog VLSI circuits and systems. Analog and low power digital circuits for competitive learning are currently important for their applications in computationally-efficient speech and image compression by vector quantization, as required for example in portable multi-media terminals. A summary of competitive learning models is presented to indicate the type of VLSI computations required, and the effects of weight quantization are discussed. Analog circuit representations of computational primitives for learning and evaluation of distortion metrics are discussed. The present state of VLSI implementations of hard and soft competitive learning algorithms are described, as well as those for topological feature maps. Tolerance of learning algorithms to observed analog circuit properties is reported. New results are also presented from simulations of frequency-sensitive and soft competitive learning concerning sensitivity of these algorithms to precision in VLSI learning computations. Applications of these learning algorithms to unsupervised feature extraction and to vector quantization of speech and images are also described.

TOPOLOGICAL FEATURE MAPS ON PARALLEL COMPUTERS

Analysis of skewed memory schemes for parallel implementation of Kohonen’s topological feature maps are presented in this paper. It is found that linear skewing is more general and more effective for this problem as compared with other memory skewing schemes. Implementations on parallel machines and performance results will also be presented.

Asymptotic level density in topological feature maps

The Kohonen algorithm entails a topology conserving mapping of an input pattern space X subsetR(n) characterized by an a priori probability distribution P(x), xinX, onto a discrete lattice of neurons r with virtual positions w(r)inX. Extending results obtained by Ritter (1991) the authors show in the one-dimensional case for an arbitrary monotonously decreasing neighborhood function h(|r-r'|) that the point density D(W(r)) of the virtual net is a polynomial function of the probability density P(x) with D(w(r))~P(alpha)(w(r)). Here the distortion exponent is given by alpha=(1+12R)/3(1+6R) and is determined by the normalized second moment R of the neighborhood function. A Gaussian neighborhood interaction is discussed and the analytical results are checked by means of computer simulations.

Representation of Molecular Electrostatic Potentials by Topological Feature Maps

Representation of Molecular Electrostatic Potentials by Topological Feature Maps

A parallel topological feature map in APL

One can distinguish two different approaches of neural networks the supervised networks and the self organizing or unsupervised neural networks. The first type of neural nets is supplied with an ideal result regarding the input. During the learning procedure, the neural net adjusts weighting factors of the links between neurons so that the input feature vectors map to the ideal output. Those nets are used for example in robotics, where the ideal result is well known: it is the position the robot should be placed in. For the cases where no ideal result is known, the second type of neural nets, the so called self-learning Topological Feature Map (TFM) is appropriate. This paper will introduce such a neural net based on the idea of Kohonen's TFM. The original algorithm was extremely sequential and therefore not suitable for an APL implementation. The parallelization of the algorithm led to important improvements in speed and convergence to the global optimum.

Vector quantization with complexity costs

Vector quantization is a data compression method by which a set of data points is encoded by a reduced set of reference vectors: the codebook. A vector quantization strategy is discussed that jointly optimizes distortion errors and the codebook complexity, thereby determining the size of the codebook. A maximum entropy estimation of the cost function yields an optimal number of reference vectors, their positions, and their assignment probabilities. The dependence of the codebook density on the data density for different complexity functions is investigated in the limit of asymptotic quantization levels. How different complexity measures influence the efficiency of vector quantizers is studied for the task of image compression. The wavelet coefficients of gray-level images are quantized, and the reconstruction error is measured. The approach establishes a unifying framework for different quantization methods like K-means clustering and its fuzzy version, entropy constrained vector quantization or topological feature maps, and competitive neural networks.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Complexity Optimized Data Clustering by Competitive Neural Networks

Data clustering is a complex optimization problem with applications ranging from vision and speech processing to data transmission and data storage in technical as well as in biological systems. We discuss a clustering strategy that explicitly reflects the tradeoff between simplicity and precision of a data representation. The resulting clustering algorithm jointly optimizes distortion errors and complexity costs. A maximum entropy estimation of the clustering cost function yields an optimal number of clusters, their positions, and their cluster probabilities. Our approach establishes a unifying framework for different clustering methods like K-means clustering, fuzzy clustering, entropy constrained vector quantization, or topological feature maps and competitive neural networks.

Trace feature map: a model of episodic associative memory.

An approach to episodic associative memory is presented, which has several desirable properties as a human memory model. The design is based on topological feature map representation of data. An ordinary feature map is a classifier, mapping an input vector onto a topologically meaningful location on the map. A trace feature map, in addition, creates a memory trace on that location. The traces can be stored episodically in a single presentation, and retrieved with a partial cue. Nearby traces overlap, which results in plausible memory interference behavior. Performance degrades gracefully as the memory is overloaded. More recent traces are easier to recall as are traces that are unique in the memory.

A “ PAC ” Algorithm for Making Feature Maps

Kohonen and others have devised network algorithms for computing so-called topological feature maps. We describe a new algorithm, called the CDF-Inversion(CDFI) Algorithm, that can be used to learn feature maps and, in the process, approximate an unknown probability distribution to within any specified accuracy. The primary advantages of the algorithm over previous feature-map algorithms are that it is simple enough to analyze mathematically for correctness and efficiency, and that it distributes the points of the map evenly, in a sense that can be made rigorous. Like other vector-quantization algorithms it is potentially useful for many applications, including monitoring and statistical modeling. While not a network algorithm, the CDFI algorithm is well-suited to implementation on parallel computers.

Self-organization of associative memory and pattern classification: recurrent signal processing on topological feature maps

Self-organization of associative memory and pattern classification: recurrent signal processing on topological feature maps