Matrix completion and extrapolation via kernel regression

Matrix completion and extrapolation (MCEX) are dealt with here over reproducing kernel Hilbert spaces (RKHSs) in order to account for prior information present in the available data. Aiming at a faster and low-complexity solver, the task is formulated as a kernel ridge regression. The resultant MCEX algorithm can also afford online implementation, while the class of kernel functions also encompasses several existing approaches to MC with prior information. Numerical tests on synthetic and real datasets show that the novel approach performs faster than widespread methods such as alternating least squares (ALS) or stochastic gradient descent (SGD), and that the recovery error is reduced, especially when dealing with noisy data

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

Random Feature-based Online Multi-kernel Learning in Environments with Unknown Dynamics

Kernel-based methods exhibit well-documented performance in various nonlinear learning tasks. Most of them rely on a preselected kernel, whose prudent choice presumes task-specific prior information. Especially when the latter is not available, multi-kernel learning has gained popularity thanks to its flexibility in choosing kernels from a prescribed kernel dictionary. Leveraging the random feature approximation and its recent orthogonality-promoting variant, the present contribution develops a scalable multi-kernel learning scheme (termed Raker) to obtain the sought nonlinear learning function `on the fly,' first for static environments. To further boost performance in dynamic environments, an adaptive multi-kernel learning scheme (termed AdaRaker) is developed. AdaRaker accounts not only for data-driven learning of kernel combination, but also for the unknown dynamics. Performance is analyzed in terms of both static and dynamic regrets. AdaRaker is uniquely capable of tracking nonlinear learning functions in environments with unknown dynamics, and with with analytic performance guarantees. Tests with synthetic and real datasets are carried out to showcase the effectiveness of the novel algorithms.Comment: 36 page

Efficient Optimization Algorithms for Nonlinear Data Analysis

Identification of low-dimensional structures and main sources of variation from multivariate data are fundamental tasks in data analysis. Many methods aimed at these tasks involve solution of an optimization problem. Thus, the objective of this thesis is to develop computationally efficient and theoretically justified methods for solving such problems. Most of the thesis is based on a statistical model, where ridges of the density estimated from the data are considered as relevant features. Finding ridges, that are generalized maxima, necessitates development of advanced optimization methods. An efficient and convergent trust region Newton method for projecting a point onto a ridge of the underlying density is developed for this purpose. The method is utilized in a differential equation-based approach for tracing ridges and computing projection coordinates along them. The density estimation is done nonparametrically by using Gaussian kernels. This allows application of ridge-based methods with only mild assumptions on the underlying structure of the data. The statistical model and the ridge finding methods are adapted to two different applications. The first one is extraction of curvilinear structures from noisy data mixed with background clutter. The second one is a novel nonlinear generalization of principal component analysis (PCA) and its extension to time series data. The methods have a wide range of potential applications, where most of the earlier approaches are inadequate. Examples include identification of faults from seismic data and identification of filaments from cosmological data. Applicability of the nonlinear PCA to climate analysis and reconstruction of periodic patterns from noisy time series data are also demonstrated. Other contributions of the thesis include development of an efficient semidefinite optimization method for embedding graphs into the Euclidean space. The method produces structure-preserving embeddings that maximize interpoint distances. It is primarily developed for dimensionality reduction, but has also potential applications in graph theory and various areas of physics, chemistry and engineering. Asymptotic behaviour of ridges and maxima of Gaussian kernel densities is also investigated when the kernel bandwidth approaches infinity. The results are applied to the nonlinear PCA and to finding significant maxima of such densities, which is a typical problem in visual object tracking.Siirretty Doriast

Scalable Learning Adaptive to Unknown Dynamics and Graphs

University of Minnesota Ph.D. dissertation.June 2019. Major: Electrical/Computer Engineering. Advisor: Georgios B. Giannakis. 1 computer file (PDF); xii, 174 pages.With the scale of information growing every day, the key challenges in machine learning include the high-dimensionality and sheer volume of feature vectors that may consist of real and categorical data, as well as the speed and the typically streaming format of data acquisition that may also entail outliers and misses. The latter may be present, either unintentionally or intentionally, in order to cope with scalability, privacy, and adversarial behavior. These challenges provide ample opportunities for algorithmic and analytical innovations in online and nonlinear subspace learning approaches. Among the available nonlinear learning tools, those based on kernels have merits that are well documented. However, most rely on a preselected kernel, whose prudent choice presumes task-specific prior information that is generally not available. It is also known that kernel-based methods do not scale well with the size or dimensionality of the data at hand. Besides data science, the urgent need for scalable tools is a core issue also in network science that has recently emerged as a means of collectively understanding the behavior of complex interconnected entities. The rich spectrum of application domains comprises communication, social, financial, gene-regulatory, brain, and power networks, to name a few. Prominent tasks in all network science applications are those of topology identification and inference of nodal processes evolving over graphs. Most contemporary graph-driven inference approaches rely on linear and static models that are simple and tractable, but also presume that the nodal processes are directly observable. To cope with these challenges, the present thesis first introduces a novel online categorical subspace learning approach to track the latent structure of categorical data `on the fly.' Leveraging the random feature approximation, it then develops an adaptive online multi-kernel learning approach (termed AdaRaker), which accounts not only for data-driven learning of the kernel combination, but also for the unknown dynamics. Performance analysis is provided in terms of both static and dynamic regrets to quantify the novel learning function approximation. In addition, the thesis introduces a kernel-based topology identification approach that can even account for nonlinear dependencies among nodes and across time. To cope with nodal processes that may not be directly observable in certain applications, tensor-based algorithms that leverage piecewise stationary statistics of nodal processes are developed, and pertinent identifiability conditions are established. To facilitate real-time operation and inference of time-varying networks, an adaptive tensor decomposition based scheme is put forth to track the topologies of time-varying networks. Last but not least, the present thesis offers a unifying framework to deal with various learning tasks over possibly dynamic networks. These tasks include dimensionality reduction, classification, and clustering. Tests on both synthetic and real datasets from the aforementioned application domains are carried out to showcase the effectiveness of the novel algorithms throughout

Radar and RGB-depth sensors for fall detection: a review

This paper reviews recent works in the literature on the use of systems based on radar and RGB-Depth (RGB-D) sensors for fall detection, and discusses outstanding research challenges and trends related to this research field. Systems to detect reliably fall events and promptly alert carers and first responders have gained significant interest in the past few years in order to address the societal issue of an increasing number of elderly people living alone, with the associated risk of them falling and the consequences in terms of health treatments, reduced well-being, and costs. The interest in radar and RGB-D sensors is related to their capability to enable contactless and non-intrusive monitoring, which is an advantage for practical deployment and users’ acceptance and compliance, compared with other sensor technologies, such as video-cameras, or wearables. Furthermore, the possibility of combining and fusing information from The heterogeneous types of sensors is expected to improve the overall performance of practical fall detection systems. Researchers from different fields can benefit from multidisciplinary knowledge and awareness of the latest developments in radar and RGB-D sensors that this paper is discussing