Carlos Daniel Acosta-Medina

Regularization parameter choice in locally linear embedding

Locally linear embedding (LLE) is a recent unsupervised learning algorithm for non-linear dimensionality reduction of high dimensional data. One advantage of this algorithm is that just two parameters are needed to be set by user: the number of nearest neighbors and a regularization parameter. The choice of the regularization parameter plays an important role in the embedding results. In this paper, an automated method for choosing this parameter is proposed. Besides, in order to objectively qualify the performance of the embedding results, a new measure of embedding quality is suggested. Our approach is experimentally verified on 9 artificial data sets and 2 real world data sets. Numerical results are compared against two methods previously found in the state of art.

Relevance analysis of stochastic biosignals for identification of pathologies

This paper presents a complementary study of the methodology for diagnosing of pathologies, based on relevance analysis of stochastic (time-variant) features that are extracted from t-f representations of biosignal recordings. Dimension reduction is carried out by adapting in time commonly used latent variable techniques for a given relevance function, as evaluation measure of time-variant transformation. Examples of both unsupervised and supervised training are deliberated for distinguishing the set of most relevant stochastic features. Besides, two different combining approaches for feature selection are studied. Firstly, when the considered input set comprises a single type of stochastic features, that is, having the same principle of generation. Secondly, when the whole input set of parameters is taken into consideration no matter of their physical meaning. For validation purposes, the methodology is tested for the concrete case of diagnosing of obstructive sleep apnea. Achieved results related to performed accuracy and dimension reduction are comparable with respect to other outcomes reported in the literature, and thus clearly showing that proposed methodology can be focused on finding alternative methods minimizing the parameters used for pathology diagnosing.

Video analysis based on Multi-Kernel Representation with automatic parameter choice

In this work, we analyze video data by learning both the spatial and temporal relationships among frames. For this purpose, the nonlinear dimensionality reduction algorithm, Laplacian Eigenmaps, is improved using a multiple kernel learning framework, and it is assumed that the data can be modeled by means of two different graphs: one considering the spatial information (i.e., the pixel intensity similarities) and the other one based on the frame temporal order. In addition, a formulation for automatic tuning of the required free parameters is stated, which is based on a tradeoff between the contribution of each information source (spatial and temporal). Moreover, we proposed a scheme to compute a common representation in a low-dimensional space for data lying in several manifolds, such as multiple videos of similar behaviors. The proposed algorithm is tested on real-world datasets, and the obtained results allow us to confirm visually the quality of the attained embedding. Accordingly, discussed approach is suitable for data representability when considering cyclic movements.

Multiple manifold learning by nonlinear dimensionality reduction

Methods for nonlinear dimensionality reduction have been widely used for different purposes, but they are constrained to single manifold datasets. Considering that in real world applications, like video and image analysis, datasets with multiple manifolds are common, we propose a framework to find a low-dimensional embedding for data lying on multiple manifolds. Our approach is inspired on the manifold learning algorithm Laplacian Eigenmaps - LEM, computing the relationships among samples of different datasets based on an intra manifold comparison to unfold properly the data underlying structure. According to the results, our approach shows meaningful embeddings that outperform the results obtained by the conventional LEM algorithm and a previous close related work that analyzes multiple manifolds.

Quadratic Problem Formulation with Linear Constraints for Normalized Cut Clustering

This work describes a novel quadratic formulation for solving the normalized cuts-based clustering problem as an alternative to spectral clustering approaches. Such formulation is done by establishing simple and suitable constraints, which are further relaxed in order to write a quadratic functional with linear constraints. As a meaningful result of this work, we accomplish a deterministic solution instead of using a heuristic search. Our method reaches comparable performance against conventional spectral methods, but spending significantly lower processing time.

An Improved Multi-Class Spectral Clustering Based on Normalized Cuts

In this work, we present an improved multi-class spectral clustering (MCSC) that represents an alternative to the standard k-way normalized clustering, avoiding the use of an iterative algorithm for tuning the orthogonal matrix rotation. The performance of proposed method is compared with the conventional MCSC and k-means in terms of different clustering quality indicators. Results are accomplished on commonly used toy data sets with hardly separable classes, as well as on an image segmentation database. In addition, as a clustering indicator, a novel unsupervised measure is introduced to quantify the performance of the proposed method. The proposed method spends lower processing time than conventional spectral clustering approaches.

Image synthesis based on manifold learning

A new methodology for image synthesis based on manifold learning is proposed. We employ a local analysis of the observations in a low-dimensional space computed by Locally Linear Embedding, and then we synthesize unknown images solving an inverse problem, which normally is ill-posed. We use some regularization procedures in order to prevent unstable solutions. Moreover, the Least Squares-Support Vector Regression (LS-SVR) method is used to estimate new samples in the embedding space. Furthermore, we also present a new methodology for multiple parameter choice in LS-SVR based on Generalized Cross-Validation. Our methodology is compared to a high-dimensional data interpolation method, and a similar approach that uses low-dimensional space representations to improve the input data analysis. We test the synthesis algorithm on databases that allow us to confirm visually the quality of the results. According to the experiments our method presents the lowest average relative errors with stable synthesis results.

Finite Rank Series Modeling for Discrimination of Non-stationary Signals

The analysis of time-variant biosignals for classification tasks, usually requires a modeling that may handel their different dynamics and non–stationary components. Although determination of proper stationary data length and the model parameters remains as an open issue. In this work, time–variant signal decomposition through Finite Rank Series Modeling is carried out, aiming to find the model parameters. Three schemes are tested for OSA detection based on HRV recordings: SSA and DLM as linear decompositions and EDS as non–linear decomposition. Results show that EDS decomposition presents the best performance, followed by SSA. As a conclusion, it can be inferred that adding complexity at the linear model the trend is approximate to a simple non–linear model.

Human Activity Recognition by Class Label LLE

Human motion analysis has emerged as an important area of research for different fields and applications. However, analyzing image and video sequences to perform tasks such as action recognition, becomes a challenge due to the high dimensionality of this type of data, not mentioning the restrictions in the recording conditions (lighting, angle, distances, etc). In that sense, we propose a framework for human action recognition, which involves a preprocessing stage that decreases the influence of the record conditions in the analysis. Further, our proposal is based on a new supervised feature extraction technique that includes class label information in the mapping process, to enhance both the underlying data structure unfolding and the margin of separability among classes. Proposed methodology is tested on a benchmark dataset. Attained results show how our approach obtains a suitable performance using straightforward classifiers.

Time-Frequency Based Feature Extraction for Non-Stationary Signal Classification

Biosignal recordings are useful for extracting information about the functional state of an organism. For this reason, such recordings are widely used as tools for supporting medical decision. Nevertheless, reaching a diagnostic decision based on biosignal recordings normally requires analysis of long data records by specialized medical personnel. In several cases, specialized medical attention is unavailable, due to the high quantity of patients and data to analyze. Besides, the access to this kind of service may be difficult in remote places. As a result, the quality of medical service is deteriorated. In this sense, automated decision support systems are an important aid for improving pathology diagnosis and treatment, specially when long data records are involved. The successful performance of automatic decision systems strongly depends on the adequate choice of features. Therefore, non-stationarity is one of the most important problems to take into account. Non-stationarity is an inherent property of biosignals, as the underlying biological system has a time dependant response to environmental excitations. Specially, changes in physiological conditions and pathologies may produce significant variations. It has been found that non-stationary conditions give rise to changes in the spectral content of the biosignal (Hassanpour et al., 2004; Quiceno-Manrique et al., 2010; Sepulveda-Cano et al., 2011; Subasi, 2007; Tarvainen et al., 2009; Tzallas et al., 2008). Therefore, time-frequency (t–f) features have been previously proposed for examining the dynamic properties of the spectral parameters during transient physiological or pathological episodes. It is expected that t–f features reveal the correlation between the t–f characteristics of abnormal non-stationary behavior (Debbal & Bereksi-Reguig, 2007). For this reason, t–f methods should outperform conventional methods of frequency analysis (Tzallas et al., 2008). Besides, t–f features are expected to behave slowly enough along the time axis, so the usual stationary restrictions imposed on short-term intervals should work out better than when straightforwardly analyzing over the raw input biosignal. Among t–f features, time-frequency representations (TFR) are one of the most common and widely used features. TFRs are the most complete characterization method for non-stationary biosignals, as they display the energy distribution of a signal in time and frequency domains. Several TFR estimators have been proposed, which can be classified as non-parametric (linear and quadratic) and parametric (Marchant, 2003; Poulimenos & Fassois, 2006). The selection of 13