Points In Feature Space Research Articles

Variance enhanced K-medoid clustering

This paper proposes new variance enhanced clustering methods to improve the popular K-medoid algorithm by adapting variance information in data clustering. Since measuring similarity between data objects is simpler than mapping data objects to data points in feature space, these pairwise similarity based clustering algorithms can greatly reduce the difficulty in developing clustering based pattern recognition applications. A web-based image clustering system has been developed to demonstrate and show the clustering power and significance of the proposed methods. Synthetic numerical data and real-world image collection are applied to evaluate the performance of the proposed methods on the prototype system. As shown as the web-demonstration, the proposed method, variance enhanced K-medoid model, groups similar images in clusters with various variances according to the distribution of image similarity values.

Spatial prediction of species’ distributions from occurrence-only records: combining point pattern analysis, ENFA and regression-kriging

A computational framework to map species’ distributions (realized density) using occurrence-only data and environmental predictors is presented and illustrated using a textbook example and two case studies: distribution of root vole ( Microtes oeconomus) in the Netherlands, and distribution of white-tailed eagle nests ( Haliaeetus albicilla) in Croatia. The framework combines strengths of point pattern analysis (kernel smoothing), Ecological Niche Factor Analysis (ENFA) and geostatistics (logistic regression-kriging), as implemented in the spatstat, adehabitat and gstat packages of the R environment for statistical computing. A procedure to generate pseudo-absences is proposed. It uses Habitat Suitability Index (HSI, derived through ENFA) and distance from observations as weight maps to allocate pseudo-absence points. This design ensures that the simulated pseudo-absences fall further away from the occurrence points in both feature and geographical spaces. The simulated pseudo-absences can then be combined with occurrence locations and used to build regression-kriging prediction models. The output of prediction are either probabilitiesy of species’ occurrence or density measures. Addition of the pseudo-absence locations has proven effective — the adjusted R-square increased from 0.71 to 0.80 for root vole (562 records), and from 0.69 to 0.83 for white-tailed eagle (135 records) respectively; pseudo-absences improve spreading of the points in feature space and ensure consistent mapping over the whole area of interest. Results of cross validation (leave-one-out method) for these two species showed that the model explains 98% of the total variability in the density values for the root vole, and 94% of the total variability for the white-tailed eagle. The framework could be further extended to Generalized multivariate Linear Geostatistical Models and spatial prediction of multiple species. A copy of the R script and step-by-step instructions to run such analysis are available via contact author’s website.

On the Non-Local Geometry of Turbulence

A multi-scale methodology for the study of the non-local geometry of eddy structures in turbulence is developed. Starting from a given three-dimensional field, this consists of three main steps: extraction, characterization and classification of structures. The extraction step is done in two stages. First, a multi-scale decomposition based on the curvelet transform is applied to the full three-dimensional field, resulting in a finite set of component three-dimensional fields, one per scale. Second, by iso-contouring each component field at one or more iso-contour levels, a set of closed iso-surfaces is obtained that represents the structures at that scale. The characterization stage is based on the joint probability density function (p.d.f.), in terms of area coverage on each individual iso-surface, of two differential-geometry properties, the shape index and curvedness, plus the stretching parameter, a dimensionless global invariant of the surface. Taken together, this defines the geometrical signature of the iso-surface. The classification step is based on the construction of a finite set of parameters, obtained from algebraic functions of moments of the joint p.d.f. of each structure, that specify its location as a point in a multi-dimensional ‘feature space’. At each scale the set of points in feature space represents all structures at that scale, for the specified iso-contour value. This then allows the application, to the set, of clustering techniques that search for groups of structures with a common geometry. Results are presented of a first application of this technique to a passive scalar field obtained from 5123 direct numerical simulation of scalar mixing by forced, isotropic turbulence (Reλ = 265). These show transition, with decreasing scale, from blob-like structures in the larger scales to blob- and tube-like structures with small or moderate stretching in the inertial range of scales, and then toward tube and, predominantly, sheet-like structures with high level of stretching in the dissipation range of scales. Implications of these results for the dynamical behaviour of passive scalar stirring and mixing by turbulence are discussed.

On the non-local geometry of turbulence

A multi-scale methodology for the study of the non-local geometry of eddy structures in turbulence is developed. Starting from a given three-dimensional field, this consists of three main steps: extraction, characterization and classification of structures. The extraction step is done in two stages. First, a multi-scale decomposition based on the curvelet transform is applied to the full three-dimensional field, resulting in a finite set of component three-dimensional fields, one per scale. Second, by iso-contouring each component field at one or more iso-contour levels, a set of closed iso-surfaces is obtained that represents the structures at that scale. The characterization stage is based on the joint probability density function (p.d.f.), in terms of area coverage on each individual iso-surface, of two differential-geometry properties, the shape index and curvedness, plus the stretching parameter, a dimensionless global invariant of the surface. Taken together, this defines the geometrical signature of the iso-surface. The classification step is based on the construction of a finite set of parameters, obtained from algebraic functions of moments of the joint p.d.f. of each structure, that specify its location as a point in a multi-dimensional ‘feature space’. At each scale the set of points in feature space represents all structures at that scale, for the specified iso-contour value. This then allows the application, to the set, of clustering techniques that search for groups of structures with a common geometry. Results are presented of a first application of this technique to a passive scalar field obtained from 5123 direct numerical simulation of scalar mixing by forced, isotropic turbulence (Reλ = 265). These show transition, with decreasing scale, from blob-like structures in the larger scales to blob- and tube-like structures with small or moderate stretching in the inertial range of scales, and then toward tube and, predominantly, sheet-like structures with high level of stretching in the dissipation range of scales. Implications of these results for the dynamical behaviour of passive scalar stirring and mixing by turbulence are discussed.

Self-Organizing Map with Generating and Moving Neurons in Visible Space

Kohonen’s Self-Organizing feature Map (SOM) is used to obtain topology-preserving mapping from high-dimensional feature space to visible space of two or fewer dimensions. The SOM algorithm uses a fixed structure of neurons in visible space and learns a dataset by updating reference points in feature space. The mapping result depends on mapping parameters fixed, which are the number and visible positions of neurons, and parameters of learning, which are the learning rate, total iteration, and the setting of neighboring radii. To obtain a satisfactory result, the user usually must try many combinations of parameters. It is wasteful, however, to set up every possible combination of parameters and to repeatedly run the algorithm from the beginning because the computation cost for learning is large, especially for a large-scale dataset. These problems arise due to the fixing of two types of mapping parameters, i.e., the number and visible positions of neurons. The high computation cost is mainly in the calculation of distances from each sample to all reference points. At the beginning of learning, reference points should be adjusted globally to preserve the topology well because they are initially set far from optimal positions in feature space, e.g. randomly. Such many reference points subdivides feature space into unnecessarily fine Voronoi regions. To avoid this computational waste, it is natural to start learning with a small number of neurons and increase the number of neurons during learning. We propose a new SOM method that varies the number and visible positions of neurons, and thus is applicable also to visible torus and sphere spaces. We apply our proposal to spherical visible space. We use central Voronoi tessellation to move visible positions for two reasons: to tessellate visible space evenly for easy visualization and to level the number of neighboring neurons and better preserve topology. We demonstrate the effect of generating neurons to reduce computation cost and of moving visible positions in visualization and topology preservation.

Power quality disturbance identification using wavelet packet energy entropy and weighted support vector machines

In this paper, wavelet packet energy entropy and weighted support vector machines are used to automatically detect and classify power quality (PQ) disturbances. Electric power quality is an aspect of power engineering that has been with us since the inception of power systems. The types of concerned disturbances include voltage sags, swells, interruptions. Wavelet packet are utilized to denoise the digital signals, to decompose the signals and then to obtain five common features for the sampling PQ disturbance signals. A weighted support vector machine is designed and trained by 5-dimension feature space points for making a decision regarding the type of the disturbance. Simulation cases illustrate the effectiveness.

A theoretical study on six classifier fusion strategies

We look at a single point in feature space, two classes, and L classifiers estimating the posterior probability for class /spl omega//sub 1/. Assuming that the estimates are independent and identically distributed (normal or uniform), we give formulas for the classification error for the following fusion methods: average, minimum, maximum, median, majority vote, and oracle.

Searching in high-dimensional spaces

During the last decade, multimedia databases have become increasingly important in many application areas such as medicine, CAD, geography, and molecular biology. An important research issue in the field of multimedia databases is the content-based retrieval of similar multimedia objects such as images, text, and videos. However, in contrast to searching data in a relational database, a content-based retrieval requires the search of similar objects as a basic functionality of the database system. Most of the approaches addressing similarity search use a so-called feature transformation that transforms important properties of the multimedia objects into high-dimensional points (feature vectors). Thus, the similarity search is transformed into a search of points in the feature space that are close to a given query point in the high-dimensional feature space. Query processing in high-dimensional spaces has therefore been a very active research area over the last few years. A number of new index structures and algorithms have been proposed. It has been shown that the new index structures considerably improve the performance in querying large multimedia databases. Based on recent tutorials [Berchtold and Keim 1998], in this survey we provide an overview of the current state of the art in querying multimedia databases, describing the index structures and algorithms for an efficient query processing in high-dimensional spaces. We identify the problems of processing queries in high-dimensional space, and we provide an overview of the proposed approaches to overcome these problems.

Construction of Neural Network using Cluster Analysis and Voronoi Diagram.

An effective method for designing neural network to classify patterns in the multidimensional feature space is introduced. Voronoi diagram is constructed over points in feature space which represents input teachers in order to realize the desired classification. In order to reduce the size of neural network and to make the learning process efficiently, clustering procedure which enables to manage a number of teachers in a lump is implemented. Two examples demonstrate that the present method gives stable result and a calculation time is smaller than that of back propagation method.

An integrated approach for different attribute types in nearest neighbour classification

AbstractThe basic nearest neighbour algorithm works by storing the training instances and classifying a new case by predicting that it has the same class as its nearest stored instance. To measure the distance between instances, some distance metric needs to be used. In situations when all attributes have numeric values, the conventional nearest neighbour method treats examples as points in feature spaces and uses Euclidean distance as the distance metric. In tasks with only nominal attributes, the simple “over-lap” metric is usually used. To handle classification tasks that have mixed types of attributes, the twodifferentmetrics are simply combined. Work by researchers in the machine learning field has shown that this approach performs poorly. This paper attempts to study a more recently developed distance metric and show that this metric is capable of measuring the importance of different attributes. With the use of discretisation for numeric-valued attributes, this method provides an integrated way in dealing with problem domains with mixtures of attribute types. Through detailed analyses, this paper tries to provide further insights into the understanding of nearest neighbour classification techniques and promote further use of this type of classification algorithm.

Identification of Metallic Spheroids by Classification of Their Electromagnetic Induction Responses

An investigation into the feasibility of applying pattern recognition concepts to the classification of metallic objects by their electromagnetic induction responses was performed. The effect on the response of a limited set of steel spheroids due to various factors such as object shape, size, and orientation was examined and a pattern recognition scheme based on these results was proposed. Implementation of the scheme involved the development of a novel extension to the nearest mean vector type of classifier in which the concept of the class mean as a point in feature space was generalized to be a curve. The resultant pattern recognition scheme was tested on a representative test set which included 815 responses, corresponding to 104 variations in object and orientation. A success rate of greater than 96 percent was achieved. It is noted that the classifier extension developed provides a viable approach to classification of responses that very continuously with respect to a single parameter.

Pattern Trajectory Analysis of Nonstationary Multivariate Data

Multivariate data sets with dependency between observations are described using a feature space representation. The resulting ordered set of points in feature space is termed the pattern trajectory. A set of descriptors of the pattern trajectory has been developed. Time-dependent clusters and transition segments form the basic structural description from which both lower level properties, e.g., cluster position, cluster dispersion, transition rate, and higher level properties, e.g., rebound, periodicity, finite state model, may be derived. Two algorithms have been developed for time-dependent cluster analysis. The time-weighted minimum spanning tree (TWMST) algorithm utilizes a composite space-time distance measure and creates clusters by cutting the longest tree branches. The time-dependent Isodata (TD-ISODATA) algorithm utilizes a global clustering to initiate the segmentation into timedependent cluster cores and transition segments. Examples of the applica tion of these algorithms to nonstationary neuronal spike train data and to simulated animal migration data are described. The pattern trajectory approach appears to offer advantages in the analysis of complex nonstationary data sets where conventional time series techniques are insufficient. Time-dependent clustering provides a means to identify a composite source model.