Andrés Eduardo Castro-Ospina

Multiple Kernel Learning for Spectral Dimensionality Reduction

This work introduces a multiple kernel learning (MKL) approach for selecting and combining different spectral methods of dimensionality reduction (DR). From a predefined set of kernels representing conventional spectral DR methods, a generalized kernel is calculated by means of a linear combination of kernel matrices. Coefficients are estimated via a variable ranking aimed at quantifying how much each variable contributes to optimize a variance preservation criterion. All considered kernels are tested within a kernel PCA framework. The experiments are carried out over well-known real and artificial data sets. The performance of compared DR approaches is quantified by a scaled version of the average agreement rate between K-ary neighborhoods. Proposed MKL approach exploits the representation ability of every single method to reach a better embedded data for both getting more intelligible visualization and preserving the structure of data.

A Kernel-Based Representation to Support 3D MRI Unsupervised Clustering

A new kernel-based image representation is proposed on this paper aiming to support clustering tasks on 3D magnetic resonances images. The approach establishes an effective way to encode inter-slice similarities, so that the main shape information is kept on a lower dimensional space. Additionally, a spectral clustering technique is employed to estimate a compact embedding space where natural groups are easily detectable. Proposed approach outperforms the conventional voxel-wise sum of squared differences on clustering the gender category. Additionally, a pair of eigenvectors describing accurately the subject age is found.

Novel heuristic search for ventricular arrhythmia detection using normalized cut clustering

Processing of the long-term ECG Holter recordings for accurate arrhythmia detection is a problem that has been addressed in several approaches. However, there is not an outright method for heartbeat classification able to handle problems such as the large amount of data and highly unbalanced classes. This work introduces a heuristic-search-based clustering to discriminate among ventricular cardiac arrhythmias in Holter recordings. The proposed method is posed under the normalized cut criterion, which iteratively seeks for the nodes to be grouped into the same cluster. Searching procedure is carried out in accordance to the introduced maximum similarity value. Since our approach is unsupervised, a procedure for setting the initial algorithm parameters is proposed by fixing the initial nodes using a kernel density estimator. Results are obtained from MIT/BIH arrhythmia database providing heartbeat labelling. As a result, proposed heuristic-search-based clustering shows an adequate performance, even in the presence of strong unbalanced classes.

Analysis of Motor Imaginary BCI Within Multi-environment Scenarios Using a Mixture of Classifiers

Brain-computer interface (BCI) is a system that provides communication between human beings and machines through an analysis of human brain neural activity. Several studies on BCI systems have been carried out in controlled environments, however, a functional BCI should be able to achieve an adequate performance in real environments. This paper presents a comparative study on alternative classification options to analyze motor imaginary BCI within multi-environment real scenarios based on mixtures of classifiers. The proposed methodology is as follows: The imaginary movement detection is carried out by means of feature extraction and classification, in the first stage; feature set is obtained from wavelet transform, empirical mode decomposition, entropy, variance and rates between minimum and maximum, in the second stage, where several classifier combinations are applied. The system is validated using a database, which was constructed using the Emotiv Epoc+ with 14 channels of electroencephalography (EEG) signals. These were acquired from three subject in 3 different environments with the presence and absence of disturbances. According to the different effects of the disturbances analyzed in the three environments, the performance of the mixture of classifiers presented better results when compared to the individual classifiers, making it possible to provide guidelines for choosing the appropriate classification algorithm to incorporate into a BCI system.

Automatic Graph Building Approach for Spectral Clustering

Spectral clustering techniques have shown their capability to identify the data relationships using graph analysis, achieving better accuracy than traditional algorithms as k-means. Here, we propose a methodology to build automatically a graph representation over the input data for spectral clustering based approaches by taking into account the local and global sample structure. Regarding this, both the Euclidean and the geodesic distances are used to identify the main relationships between a given point and neighboring samples around it. Then, given the information about the local data structure, we estimate an affinity matrix by means of Gaussian kernel. Synthetic and real-world datasets are tested. Attained results show how our approach outperforms, in most of the cases, benchmark methods.

Developments on Solutions of the Normalized-Cut-Clustering Problem Without Eigenvectors

Normalized-cut clustering (NCC) is a benchmark graph-based approach for unsupervised data analysis. Since its traditional formulation is a quadratic form subject to orthogonality conditions, it is often solved within an eigenvector-based framework. Nonetheless, in some cases the calculation of eigenvectors is prohibitive or unfeasible due to the involved computational cost – for instance, when dealing with high dimensional data. In this work, we present an overview of recent developments on approaches to solve the NCC problem with no requiring the calculation of eigenvectors. Particularly, heuristic-search and quadratic-formulation-based approaches are studied. Such approaches are elegantly deduced and explained, as well as simple ways to implement them are provided.

Optimization of the University Transportation by Contraction Hierarchies Method and Clustering Algorithms

This research work focuses on the study of different models of solution reflected in the literature, which treat the optimization of the routing of vehicles by nodes and the optimal route for the university transport service. With the recent expansion of the facilities of a university institution, the allocation of the routes for the transport of its students, became more complex. As a result, geographic information systems (GIS) tools and operations research methodologies are applied, such as graph theory and vehicular routing problems, to facilitate mobilization and improve the students transport service, as well as optimizing the transfer time and utilization of the available transport units. An optimal route management procedure has been implemented to maximize the level of service of student transport using the K-means clustering algorithm and the method of node contraction hierarchies, with low cost due to the use of free software.

Automatic graph pruning based on kernel alignment for spectral clustering

A graph pruning approach, Kernel Alignment based Graph Pruning (KAGP), is proposed.KAGP enhances both the local and global data consistencies.KAGP enhances the clustering performance in most of the cases.KAGP avoids the need of a comprehensive user knowledge about its free parameters.KAGP is a suitable alternative to support spectral clustering algorithms. Display Omitted Detection of data structures in spectral clustering approaches becomes a difficult task when dealing with complex distributions. Moreover, there is a need of a real user prior knowledge about the influence of the free parameters when building the graph. Here, we introduce a graph pruning approach, termed Kernel Alignment based Graph Pruning (KAGP), within a spectral clustering framework that enhances both the local and global data consistencies for a given input similarity. The KAGP allows revealing hidden data structures by finding relevant pair-wise relationships among samples. So, KAGP estimates the loss of information during the pruning process in terms of a kernel alignment-based cost function. Besides, we encode the sample similarities using a compactly supported kernel function that allows obtaining a sparse data representation to support spectral clustering techniques. Attained results shows that KAGP enhances the clustering performance in most of the cases. In addition, KAGP avoids the need for a comprehensive user knowledge regarding the influence of its free parameters.

On the Spectral Clustering for Dynamic Data

Spectral clustering has shown to be a powerful technique for grouping and/or rank data as well as a proper alternative for unlabeled problems. Particularly, it is a suitable alternative when dealing with pattern recognition problems involving highly hardly separable classes. Due to its versatility, applicability and feasibility, this clustering technique results appealing for many applications. Nevertheless, conventional spectral clustering approaches lack the ability to process dynamic or time-varying data. Within a spectral framework, this work presents an overview of clustering techniques as well as their extensions to dynamic data analysis.

Spectral Clustering Using Compactly Supported Graph Building

Clustering techniques demand on suitable models of data structures to infer the main samples patterns. Nonetheless, detection of data structures becomes a difficult task when dealing with nonlinear data relationships and complex distributions. Here, to support clustering tasks, we introduce a new graph building strategy based on a compactly supported kernel technique. Thus, our approach makes relevant pair-wise sample relationships by finding a sparse kernel matrix that codes the main sample connections. Clustering performance is assessed on synthetic and real-world data sets. Obtained results show that the proposed method enhances the data interpretability and separability by revealing relevant data relationships into a graph-based representation.