Genaro Daza-Santacoloma

Global and local choice of the number of nearest neighbors in locally linear embedding

Highlights? We propose a new method for automatically computing the number of neighbors in LLE. ? We analyze the global and local properties of the embedding results. ? We study manifolds where the density and the intrinsic dimensionality of the neighborhoods are variable. ? Artificial and real-world datasets were tested. The crux in the locally linear embedding algorithm is the selection of the number of nearest neighbors k. Some previous techniques have been developed for finding this parameter based on embedding quality measures. Nevertheless, they do not achieve suitable results when they are tested on several kind of manifolds. In this work is presented a new method for automatically computing the number of neighbors by means of analyzing global and local properties of the embedding results. Besides, it is also proposed a second strategy for choosing the parameter k, on manifolds where the density and the intrinsic dimensionality of the neighborhoods are changeful. The first proposed technique, called preservation neighborhood error, calculates a unique value of k for the whole manifold. Moreover, the second method, named local neighborhood selection, computes a suitable number of neighbors for each sample point in the manifold. The methodologies were tested on artificial and real-world datasets which allow us to visually confirm the quality of the embedding. According to the results our methods aim to find suitable values of k and appropriated embeddings.

Dynamic Feature Extraction: an Application to Voice Pathology Detection

Abstract In pattern recognition, observations are often represented by the so called static features, that is, numeric values that represent some kind of attribute from observations, which are assumed constant with respect to an associated dimension or dimensions (e.g. time, space, and so on). Nevertheless, we can represent the objects to be classified by means of another kind of measurements that do change over some associated dimension: these are called dynamic features. A dynamic feature can be represented by either a vector or a matrix for each observation. The advantage of using such an extended form is the inclusion of new information that gives abetter representation of the object. The main goal in this work is to extend traditional Principal Component Analysis (normally applied on static features) to a classification task using a dynamic representation. The method was applied to detect the presence of pathology in the speech using two different voice disorders databases, obtaining high classificat...

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.

Kernel based hand gesture recognition using kinect sensor

Category 4. A machine learning based methodology is proposed to recognize a predefined set of hand gestures using depth images. For such purpose, a RGBD sensor (Microsoft kinect) is employed to track the hand position. Thus, a preprocessing stage is presented to subtract the region of interest from depth images. Moreover, a learning algorithm based on kernel methods is used to discover the relationships among samples, properly describing the studied gestures. Proposed methodology aims to obtain a representation space which allow us to identify the dynamic of hand movements. Attained results show how our approach presents a suitable performance for detecting different hand gestures. As future work, we are interested in recognize more complex human activities, in order to support the development of human-computer interface systems.

Locally linear embedding based on correntropy measure for visualization and classification

Linear dimensionality reduction (DR) is a widely used technique in pattern recognition to control the dimensionality of input data, but it does neither preserve discriminability nor is capable of discovering nonlinear degrees of freedom present in natural observations. More recently, nonlinear dimensionality reduction (NLDR) algorithms have been developed taking advantage of the fact that data may lie on an embedded nonlinear manifold within an high dimensional feature space. Nevertheless, if the input data is corrupted (noise and outliers), most of nonlinear techniques specially Locally Linear Embedding (LLE) do not produce suitable embedding results. The culprit is the Euclidean distance (cost function in LLE) that does not correctly represent the dissimilarity between objects, increasing the error because of corrupted observations. In this work, the Euclidean distance is replaced by the correntropy induced metric (CIM), which is particularly useful to handle outliers. Moreover, we also extend NLDR to handle manifold divided into separated groups or several manifolds at the same time by employing class label information (CLI), yielding a discriminative representation of data on low dimensional space. Correntropy LLE+CLI approach is tested for visualization and classification on noisy artificial and real-world data sets. The obtained results confirm the capabilities of the discussed approach reducing the negative effects of outliers and noise on the low dimensional space. Besides, it outperforms the other NLDR techniques, in terms of classification accuracy.

Automatic Choice of the Number of Nearest Neighbors in Locally Linear Embedding

Locally linear embedding (LLE) is a method for nonlinear dimensionality reduction, which calculates a low dimensional embedding with the property that nearby points in the high dimensional space remain nearby and similarly co-located with respect to one another in the low dimensional space [1]. LLE algorithm needs to set up a free parameter, the number of nearest neighbors k . This parameter has a strong influence in the transformation. In this paper is proposed a cost function that quantifies the quality of the embedding results and computes an appropriate k . Quality measure is tested on artificial and real-world data sets, which allow us to visually confirm whether the embedding was correctly calculated.

A Gaussian Process Emulator for Estimating the Volume of Tissue Activated During Deep Brain Stimulation

The volume of tissue activated (VTA) is a well established approach to model the effects of deep brain stimulation (DBS), and previous studies have pointed to its potential benefits in clinical applications. However, the elevated computational cost of the standard technique for VTA estimation limits its suitability for practical use. In this study we developed a novel methodology to reduce the cost of VTA estimation. Our approach combines multicompartment axon models coupled to the stimulating electric field with a Gaussian emulator. We achieved a remarkable reduction in the average time required for VTA estimation, without the loss of accuracy and other limitations entailed by alternative methods used to attain similar benefits, such as activation threshold curves.

Automatic epileptic seizure prediction based on scalp EEG and ECG signals

The epilepsy is a common neurological disease caused by a neuronal electric activity imbalance in any side of the brain, named epileptic focus. The epilepsy is characterized by recurrent and sudden seizures. Recently, researchers found that approximately 50% of epileptic patients feel auras (subjective phenomenon which precedes and indicates an epileptic seizure onset) associated to a physiological anomaly. In this research, a non-invasive seizure prediction methodology is developed in order to improve the quality of life of the patients with epilepsy, alerting them about potential seizure and avoiding falls, injuries, wounds or even death. The research addresses the recognition of patterns in electroencephalographic (EEG) and electrocardiographic (ECG) signals taken from 7 patients with focal epilepsy whom are treated at the Instituto de Epilepsia y Parkinson del Eje Cafetero-NEUROCENTRO-. The biosignals were independently analyzed, at least 15 minutes before the seizure onset and in periods with no seizure were considered. The methodology considers the generation of features computed over the discrete wavelet transform of the EEG signal and others related to the heart rate variability in the ECG signal. Using feature selection techniques such as Sequential Forward Selection (SFS) with classification algorithms as cost functions (linear-Bayes and k-nearest neighbors classifier), we found which features have the most relevant information about pre-ictal state and which of them are the most appropriated for seizure forecasting, therefore we found that ECG signal could be a potential resource for predicting epileptic seizures, and we concluded that there are patterns in EEG and ECG signals that, via machine learning algorithms, can predict the epileptic seizure onset.

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.