R-SVD dictionary learning algorithm

R-SVD (Rotate-SVD) is an algorithm for dictionary learning in the sparsity model, inspired by a type of statistical shape analysis, called Procrustes method. It consists in applying Euclidean transformations to a set of vectors (atoms in our case) to yield a new set with the goal of optimizing the model fitting measure. While maintaining the alternating scheme, R-SVD algorithm splits the dictionary into several groups of atoms and applies the Orthogonal Procrustes analysis simultaneously to all the atoms in each group capturing more complex data structures and being more efficient. The technique is able to find an optimal dictionary after few iterations of the scheme.

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ID Dimension for Data Analysis

When dealing with datasets comprising high-dimensional points, it is usually advantageous to discover some data structure. A fundamental information needed to this aim is the minimum number of parameters required to describe the data while minimizing the information loss. This number, usually called intrinsic dimension ($\texttt{i.d.}$), can be interpreted as the dimension of the manifold from which the input data are supposed to be drawn.

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Compression of ECG Signals

Electrocardiogram (ECG) signals are essential in the diagnosis of heart diseases. Their acquisition consists in applying from 4 to 10 electrodes on the body, and for long recordings the signals can be acquired even over 24 hours, thus producing a large volume of data to be stored on portable devices. Moreover, the progress in technology allows an improvement of the acquisition precision (e.g. sampling rate, resolution), leading to a further grow of the amount of digital ECG data. We tackled the problem of ECG signal compression using sparsity recovery techinques.

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Face Recognition Systems

The face recognition problem has been widely studied in the last decades. This interest is motivated by the numerous applications it involves, such as human- computer interaction (HCI), content-based image retrieval (CBIR), security systems and access control systems. Unfortunately most of the existing methods behave very well under controlled conditions, but their performance drop down significantly when dealing with uncontrolled conditions. We design a FRS, namely the k-LiMapS_HFR, which faces in a novel way the above mentioned hurdles. It is a holistic sparse representation method that, after having automatically cropped the face images and projected them in the LDA space, attains the sparse solution adopting the l0- pseudonorm optimization called k-LiMapS.

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Algorithms for sparse recovery

We provide a fast iterative method for finding sparse solutions to underdetermined linear systems. It is based on a fixed-point iteration scheme which combines nonconvex Lipschitzian-type mappings with canonical orthogonal projectors. The former are aimed at uniformly enhancing the sparseness level by shrinkage effects, the latter are used to project back onto the space of feasible solutions. The iterative process is driven by an increasing sequence of a scalar parameter that mainly contributes to approach the sparsest solutions.

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Computational modelling of human gaze behaviour

If observed gaze-shifts are generated by an underlying stochastic process the distribution functions and the temporal dynamics of eye movements should be completely specified by the stochastic process. By analysing the long-tail distributions resulting from the analysis of eye-tracking data, we have proposed the foraging hypothesis as an explanation.

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