Side information in robust principal component analysis: algorithms and applications

Dimensionality reduction and noise removal are fundamental machine learning tasks that are vital to artificial intelligence applications. Principal component analysis has long been utilised in computer vision to achieve the above mentioned goals. Recently, it has been enhanced in terms of robustness to outliers in robust principal component analysis. Both convex and non-convex programs have been developed to solve this new formulation, some with exact convergence guarantees. Its effectiveness can be witnessed in image and video applications ranging from image denoising and alignment to background separation and face recognition. However, robust principal component analysis is by no means perfect. This dissertation identifies its limitations, explores various promising options for improvement and validates the proposed algorithms on both synthetic and real-world datasets. Common algorithms approximate the NP-hard formulation of robust principal component analysis with convex envelopes. Though under certain assumptions exact recovery can be guaranteed, the relaxation margin is too big to be squandered. In this work, we propose to apply gradient descent on the Burer-Monteiro bilinear matrix factorisation to squeeze this margin given available subspaces. This non-convex approach improves upon conventional convex approaches both in terms of accuracy and speed. On the other hand, oftentimes there is accompanying side information when an observation is made. The ability to assimilate such auxiliary sources of data can ameliorate the recovery process. In this work, we investigate in-depth such possibilities for incorporating side information in restoring the true underlining low-rank component from gross sparse noise. Lastly, tensors, also known as multi-dimensional arrays, represent real-world data more naturally than matrices. It is thus advantageous to adapt robust principal component analysis to tensors. Since there is no exact equivalence between tensor rank and matrix rank, we employ the notions of Tucker rank and CP rank as our optimisation objectives. Overall, this dissertation carefully defines the problems when facing real-world computer vision challenges, extensively and impartially evaluates the state-of-the-art approaches, proposes novel solutions and provides sufficient validations on both simulated data and popular real-world datasets for various mainstream computer vision tasks.Open Acces

Tensor Regression

Regression analysis is a key area of interest in the field of data analysis and machine learning which is devoted to exploring the dependencies between variables, often using vectors. The emergence of high dimensional data in technologies such as neuroimaging, computer vision, climatology and social networks, has brought challenges to traditional data representation methods. Tensors, as high dimensional extensions of vectors, are considered as natural representations of high dimensional data. In this book, the authors provide a systematic study and analysis of tensor-based regression models and their applications in recent years. It groups and illustrates the existing tensor-based regression methods and covers the basics, core ideas, and theoretical characteristics of most tensor-based regression methods. In addition, readers can learn how to use existing tensor-based regression methods to solve specific regression tasks with multiway data, what datasets can be selected, and what software packages are available to start related work as soon as possible. Tensor Regression is the first thorough overview of the fundamentals, motivations, popular algorithms, strategies for efficient implementation, related applications, available datasets, and software resources for tensor-based regression analysis. It is essential reading for all students, researchers and practitioners of working on high dimensional data.Comment: 187 pages, 32 figures, 10 table

Towards solving the riddle of forgetting in functional amnesia: recent advances and current opinions

Staniloiu A, Markowitsch HJ. Towards solving the riddle of forgetting in functional amnesia: recent advances and current opinions. Frontiers in Psychology. 2012;3:403.Remembering the past is a core feature of human beings, enabling them to maintain a sense of wholeness and identity and preparing them for the demands of the future. Forgetting operates in a dynamic neural connection with remembering, allowing the elimination of unnecessary or irrelevant information overload and decreasing interference. Stress and traumatic experiences could affect this connection, resulting in memory disturbances, such as functional amnesia. An overview of clinical, epidemiological, neuropsychological, and neurobiological aspects of functional amnesia is presented, by preponderantly resorting to own data from patients with functional amnesia. Patients were investigated medically, neuropsychologically, and neuroradiologically. A detailed report of a new case is included to illustrate the challenges posed by making an accurate differential diagnosis of functional amnesia, a condition that may encroach on the boundaries between psychiatry and neurology. Several mechanisms may play a role in "forgetting" in functional amnesia, such as retrieval impairments, consolidating defects, motivated forgetting, deficits in binding and reassembling details of the past, deficits in establishing a first person autonoetic connection with personal events, and loss of information. In a substantial number of patients, we observed a synchronization abnormality between a frontal lobe system, important for autonoetic consciousness, and a temporo-amygdalar system, important for evaluation and emotions, which provides empirical support for an underlying mechanism of dissociation (a failure of integration between cognition and emotion). This observation suggests a mnestic blockade in functional amnesia that is triggered by psychological or environmental stress and is underpinned by a stress hormone mediated synchronization abnormality during retrieval between processing of affect-laden events and fact-processing