Juliana Valencia-Aguirre

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.

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.

Rainfall forecasting based on ensemble empirical mode decomposition and neural networks

In this paper a methodology for rainfall forecasting is presented, using the principle of decomposition and ensemble. In the proposed framework, the employed decomposition technique is the Ensemble Empirical Mode Decomposition (EEMD), which divides the original data into a set of simple components. Each component is modeled with a Feed Forward Neural Network (FNN) as a forecasting tool. Finally, the individual forecasting results for all components are combined to obtain the prediction result of the input signal. Experiments were performed on a real-observed rainfall data, and the attained results were compared against a single FNN model for the raw data, showing an improvement on the system performance.

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.

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.

Silhouette classification by using manifold learning for automated threat detection

Video surveillance systems have become an essential tool to enhance security in both public and private places, especially to prevent potentially dangerous situations. However, these systems usually have a high number of nuisance alarms, when they are aimed at detecting automatically abandoned objects. It was found that people waiting (sitting or standing still) in airports, train stations and bus stops are the main cause of false alarms, as available video surveillance technologies are not focused on recognizing the abandoned objects. In this paper, we present a methodology to recognize abandoned objects. The goal is to determinate if the alarm is caused by an unattended baggage or a stationery person, as the former may pose potential security threats. The R transform, which is a geometric invariant feature descriptor and has low computational complexity, is applied to each of the four patches in which the silhouette of the object to be recognized is divided. Afterwards a covariance matrix representation is calculated from both the original high dimensional space and a low dimensional space obtained with Laplacian Egienmaps, being this matrix a point in a Riemannian Manifold. The proposed methodology is evaluated in a single person dataset and a baggage dataset (gathered from the web) and good performance was obtained.

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.

Visualization and synthesis of data using manifold learning based on Locally Linear Embedding

In this paper we analyze high-dimensional data by means of the manifold learning algorithm Locally Linear Embedding. We employ this method to visually analyze both artificial and real-world datasets lying on nonlinear structures, comparing its transformations against the traditional feature extraction technique Principal Components Analysis. Moreover, we propose a data synthesis scheme based on manifold learning that allows to represent the observations in a low-dimensional space, and then we learn the underlying data structure to properly infer unknown samples. The synthesis results are compared against an interpolation technique that directly estimates unknown samples in the input space. According to the obtained results, the employed manifold learning method improves the data representability, suitably computing low-dimensional transformations of the observations, and properly synthesizing new samples with low relative errors.

Comparación de Métodos de Reducción de Dimensión Basados en Análisis por Localidades

In this paper, a comparison of methods for nonlinear dimensionality reduction is proposed in order to determine which technique preserves better the local properties, without losing the overall structure of the original data. We seek to establish which of these methods is the most appropriate for visualization tasks. The embeddings obtained with each technique are evaluated by two criteria Preservation Neighborhood Error and Preserved Neighbors Average. The methodologies were tested on artificial and real-world data sets which allow us to visually confirm the quality of the embedding. The results obtained show that Maximum variance unfolding computes high quality embeddings, because the optimization problem pretends to preserve exactly the local pair-wise distance between neighbors and conserve the global manifold structure.