Towards On-line Domain-Independent Big Data Learning: Novel Theories and Applications

Feature extraction is an extremely important pre-processing step to pattern recognition, and machine learning problems. This thesis highlights how one can best extract features from the data in an exhaustively online and purely adaptive manner. The solution to this problem is given for both labeled and unlabeled datasets, by presenting a number of novel on-line learning approaches. Specifically, the differential equation method for solving the generalized eigenvalue problem is used to derive a number of novel machine learning and feature extraction algorithms. The incremental eigen-solution method is used to derive a novel incremental extension of linear discriminant analysis (LDA). Further the proposed incremental version is combined with extreme learning machine (ELM) in which the ELM is used as a preprocessor before learning. In this first key contribution, the dynamic random expansion characteristic of ELM is combined with the proposed incremental LDA technique, and shown to offer a significant improvement in maximizing the discrimination between points in two different classes, while minimizing the distance within each class, in comparison with other standard state-of-the-art incremental and batch techniques. In the second contribution, the differential equation method for solving the generalized eigenvalue problem is used to derive a novel state-of-the-art purely incremental version of slow feature analysis (SLA) algorithm, termed the generalized eigenvalue based slow feature analysis (GENEIGSFA) technique. Further the time series expansion of echo state network (ESN) and radial basis functions (EBF) are used as a pre-processor before learning. In addition, the higher order derivatives are used as a smoothing constraint in the output signal. Finally, an online extension of the generalized eigenvalue problem, derived from James Stone’s criterion, is tested, evaluated and compared with the standard batch version of the slow feature analysis technique, to demonstrate its comparative effectiveness. In the third contribution, light-weight extensions of the statistical technique known as canonical correlation analysis (CCA) for both twinned and multiple data streams, are derived by using the same existing method of solving the generalized eigenvalue problem. Further the proposed method is enhanced by maximizing the covariance between data streams while simultaneously maximizing the rate of change of variances within each data stream. A recurrent set of connections used by ESN are used as a pre-processor between the inputs and the canonical projections in order to capture shared temporal information in two or more data streams. A solution to the problem of identifying a low dimensional manifold on a high dimensional dataspace is then presented in an incremental and adaptive manner. Finally, an online locally optimized extension of Laplacian Eigenmaps is derived termed the generalized incremental laplacian eigenmaps technique (GENILE). Apart from exploiting the benefit of the incremental nature of the proposed manifold based dimensionality reduction technique, most of the time the projections produced by this method are shown to produce a better classification accuracy in comparison with standard batch versions of these techniques - on both artificial and real datasets

Compressive Embedding and Visualization using Graphs

Visualizing high-dimensional data has been a focus in data analysis communities for decades, which has led to the design of many algorithms, some of which are now considered references (such as t-SNE for example). In our era of overwhelming data volumes, the scalability of such methods have become more and more important. In this work, we present a method which allows to apply any visualization or embedding algorithm on very large datasets by considering only a fraction of the data as input and then extending the information to all data points using a graph encoding its global similarity. We show that in most cases, using only $\mathcal{O}(\log(N))$ samples is sufficient to diffuse the information to all $N$ data points. In addition, we propose quantitative methods to measure the quality of embeddings and demonstrate the validity of our technique on both synthetic and real-world datasets

Machine Intelligence for Advanced Medical Data Analysis: Manifold Learning Approach

In the current work, linear and non-linear manifold learning techniques, specifically Principle Component Analysis (PCA) and Laplacian Eigenmaps, are studied in detail. Their applications in medical image and shape analysis are investigated. In the first contribution, a manifold learning-based multi-modal image registration technique is developed, which results in a unified intensity system through intensity transformation between the reference and sensed images. The transformation eliminates intensity variations in multi-modal medical scans and hence facilitates employing well-studied mono-modal registration techniques. The method can be used for registering multi-modal images with full and partial data. Next, a manifold learning-based scale invariant global shape descriptor is introduced. The proposed descriptor benefits from the capability of Laplacian Eigenmap in dealing with high dimensional data by introducing an exponential weighting scheme. It eliminates the limitations tied to the well-known cotangent weighting scheme, namely dependency on triangular mesh representation and high intra-class quality of 3D models. In the end, a novel descriptive model for diagnostic classification of pulmonary nodules is presented. The descriptive model benefits from structural differences between benign and malignant nodules for automatic and accurate prediction of a candidate nodule. It extracts concise and discriminative features automatically from the 3D surface structure of a nodule using spectral features studied in the previous work combined with a point cloud-based deep learning network. Extensive experiments have been conducted and have shown that the proposed algorithms based on manifold learning outperform several state-of-the-art methods. Advanced computational techniques with a combination of manifold learning and deep networks can play a vital role in effective healthcare delivery by providing a framework for several fundamental tasks in image and shape processing, namely, registration, classification, and detection of features of interest

Dimensionality Reduction for Classification of Object Weight from Electromyography

Electromyography (EMG) is a simple, non-invasive, and cost-effective technology for measuring muscle activity. However, multi-muscle EMG is also a noisy, complex, and high-dimensional signal. It has nevertheless been widely used in a host of human-machine-interface applications (electrical wheelchairs, virtual computer mice, prosthesis, robotic fingers, etc.) and, in particular, to measure the reach-and-grasp motions of the human hand. Here, we developed an automated pipeline to predict object weight in a reach-grasp-lift task from an open dataset, relying only on EMG data. In doing so, we shifted the focus from manual feature-engineering to automated feature-extraction by using pre-processed EMG signals and thus letting the algorithms select the features. We further compared intrinsic EMG features, derived from several dimensionality-reduction methods, and then ran several classification algorithms on these low-dimensional representations. We found that the Laplacian Eigenmap algorithm generally outperformed other dimensionality-reduction methods. What is more, optimal classification accuracy was achieved using a combination of Laplacian Eigenmaps (simple-minded) and k-Nearest Neighbors (88% F1 score for 3-way classification). Our results, using EMG alone, are comparable to other researchers’, who used EMG and EEG together, in the literature. A running-window analysis further suggests that our method captures information in the EMG signal quickly and remains stable throughout the time that subjects grasp and move the object

Graph Signal Processing: Overview, Challenges and Applications

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing. We then summarize recent developments in developing basic GSP tools, including methods for sampling, filtering or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning. We finish by providing a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE

Functional modeling of high-dimensional data: a Manifold Learning approach

This article belongs to the Special Issue Methodological and Applied Contributions on Stochastic Modelling and ForecastingThis paper introduces stringing via Manifold Learning (ML-stringing), an alternative to the original stringing based on Unidimensional Scaling (UDS). Our proposal is framed within a wider class of methods that map high-dimensional observations to the infinite space of functions,allowing the use of Functional Data Analysis (FDA). Stringing handles general high-dimensional data as scrambled realizations of an unknown stochastic process. Therefore, the essential feature of the method is a rearrangement of the observed values. Motivated by the linear nature of UDS and the increasing number of applications to biosciences (e.g., functional modeling of gene expression arrays and single nucleotide polymorphisms, or the classification of neuroimages) we aim to recover more complex relations between predictors through ML. In simulation studies, it is shown that MLstringing achieves higher-quality orderings and that, in general, this leads to improvements in the functional representation and modeling of the data. The versatility of our method is also illustrated with an application to a colon cancer study that deals with high-dimensional gene expression arrays.This paper shows that ML-stringing is a feasible alternative to the UDS-based version. Also, it opens a window to new contributions to the field of FDA and the study of high-dimensional data.This research was funded in part by Ministerio de Ciencia, Innovación y Universidades grant numbers PID2019-104901RB-I00 and MTM2017-88708-P

Spectral Target Detecting Using Schroedinger Eigenmaps

Applications of optical remote sensing processes include environmental monitoring, military monitoring, meteorology, mapping, surveillance, etc. Many of these tasks include the detection of specific objects or materials, usually few or small, which are surrounded by other materials that clutter the scene and hide the relevant information. This target detection process has been boosted lately by the use of hyperspectral imagery (HSI) since its high spectral dimension provides more detailed spectral information that is desirable in data exploitation. Typical spectral target detectors rely on statistical or geometric models to characterize the spectral variability of the data. However, in many cases these parametric models do not fit well HSI data that impacts the detection performance. On the other hand, non-linear transformation methods, mainly based on manifold learning algorithms, have shown a potential use in HSI transformation, dimensionality reduction and classification. In target detection, non-linear transformation algorithms are used as preprocessing techniques that transform the data to a more suitable lower dimensional space, where the statistical or geometric detectors are applied. One of these non-linear manifold methods is the Schroedinger Eigenmaps (SE) algorithm that has been introduced as a technique for semi-supervised classification. The core tool of the SE algorithm is the Schroedinger operator that includes a potential term that encodes prior information about the materials present in a scene, and enables the embedding to be steered in some convenient directions in order to cluster similar pixels together. A completely novel target detection methodology based on SE algorithm is proposed for the first time in this thesis. The proposed methodology does not just include the transformation of the data to a lower dimensional space but also includes the definition of a detector that capitalizes on the theory behind SE. The fact that target pixels and those similar pixels are clustered in a predictable region of the low-dimensional representation is used to define a decision rule that allows one to identify target pixels over the rest of pixels in a given image. In addition, a knowledge propagation scheme is used to combine spectral and spatial information as a means to propagate the \potential constraints to nearby points. The propagation scheme is introduced to reinforce weak connections and improve the separability between most of the target pixels and the background. Experiments using different HSI data sets are carried out in order to test the proposed methodology. The assessment is performed from a quantitative and qualitative point of view, and by comparing the SE-based methodology against two other detection methodologies that use linear/non-linear algorithms as transformations and the well-known Adaptive Coherence/Cosine Estimator (ACE) detector. Overall results show that the SE-based detector outperforms the other two detection methodologies, which indicates the usefulness of the SE transformation in spectral target detection problems

Spectral methods for multimodal data analysis

Spectral methods have proven themselves as an important and versatile tool in a wide range of problems in the fields of computer graphics, machine learning, pattern recognition, and computer vision, where many important problems boil down to constructing a Laplacian operator and finding a few of its eigenvalues and eigenfunctions. Classical examples include the computation of diffusion distances on manifolds in computer graphics, Laplacian eigenmaps, and spectral clustering in machine learning. In many cases, one has to deal with multiple data spaces simultaneously. For example, clustering multimedia data in machine learning applications involves various modalities or ``views'' (e.g., text and images), and finding correspondence between shapes in computer graphics problems is an operation performed between two or more modalities. In this thesis, we develop a generalization of spectral methods to deal with multiple data spaces and apply them to problems from the domains of computer graphics, machine learning, and image processing. Our main construction is based on simultaneous diagonalization of Laplacian operators. We present an efficient numerical technique for computing joint approximate eigenvectors of two or more Laplacians in challenging noisy scenarios, which also appears to be the first general non-smooth manifold optimization method. Finally, we use the relation between joint approximate diagonalizability and approximate commutativity of operators to define a structural similarity measure for images. We use this measure to perform structure-preserving color manipulations of a given image