### Contact

 Giuliano Grossi (Assistant Professor) Dipartimento di Informatica - Università degli Studi di Milano via Celoria 18, I-20133 Milano - Italy Phone: +39 02503.16262 Email: grossi@di.unimi.it Lab: phuselab.di.unimi.it

### Teaching activity

current (Italian)
past

- Metodi per l'elaborazione dei segnali (Laurea Magistrale in Informatica)

- Sistemi e Segnali (Laurea Triennale in Informatica)

- Programmazione in Matlab (Scuola di Fisica Medica)

- Laboratorio di programmazione Java (Laurea Triennale in Informatica)

- Elaborazione numericadei segnali (Laurea Triennale in Informatica)

- Elaborazione di segnali stocastici (Laurea Magistrale in Informatica)

### Research interests

Sparse recovery and regularization methods in signal processing
LiMapS, k-LiMapS: We proposed 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. It is shown that the minima are locally asymptotically stable for a specific smooth l0-norm. Furthermore, it is shown that the points yielded by this iterative strategy are related to the optimal solutions measured in terms of a suitable smooth l1-norm. Numerical simulations on phase transition show that the performances of the proposed technique overcome those yielded by well known methods for sparse recovery.
In the figure we report the 3D phase transitions of LiMapS and other sparsity solvers, such as OMP, CoSaMP, SL0, LASSO and BP. The figure clearly shows the existence of a sharp phase transition that partitions the phase space into a unrecoverable region, with vanishing exact-recovery probability, from an recoverable region in which the probability to recover the optimal sparse vector will eventually approach to one. Qualitatively, it is evident that LiMapS algorithm reaches the best results, having the largest area of high recoverability.
R-SVD: In the sparse representation models, the design of overcomplete dictionaries plays a key role for the effectiveness and applicability in different domains. Recent research has produced several dictionary learning approaches, being proven that dictionaries learnt by data examples significantly outperform structured ones, e.g. wavelet transforms. In this context, learning consists in adapting the dictionary atoms to a set of training signals in order to promote a sparse representation that minimizes the reconstruction error. Finding the best fitting dictionary remains a very difficult task, leaving the question still open. A well-established heuristic method for tackling this problem is an iterative alternating scheme, adopted for instance in the well-known K-SVD algorithm. Essentially, it consists in repeating two stages; the former promotes sparse coding of the training set and the latter adapts the dictionary to reduce the error. In this context we presented R-SVD, a new method that, while maintaining the alternating scheme, adopts the Orthogonal Procrustes analysis to update the dictionary atoms suitably arranged into groups. Comparative experiments on synthetic data prove the effectiveness of R-SVD with respect to well known dictionary learning algorithms such as K-SVD, ILS-DLA and the online method OSDL. Moreover, experiments on natural data such as ECG compression, EEG sparse representation, and image modeling confirm the R-SVD robustness and wide applicability.
ECG compression: Long duration recordings of ECG signals require high compression ratios, in particular when storing on portable devices. Most of the ECG compression methods in literature are based on wavelet transform while only few of them rely on sparsity promotion models. We proposed a novel ECG signal compression framework based on sparse representation using a set of ECG segments as natural basis. This approach exploits the signal regularity, i.e. the repetition of common patterns, in order to achieve high compression ratio (CR). We applied k-LiMapS as fine- tuned sparsity solver algorithm guaranteeing the required signal reconstruction quality (PRD). The idea behind the method relies on basis elements drawn from the initial transitory of a signal itself, and the sparsity promotion process applied to its subsequent blocks grabbed by a sliding window. The saved coefficients rescaled in a convenient range, quantized and compressed by a lossless entropy-based algorithm. Extensive experiments of our method and of four competitors (namely ARLE, Rajoub, SPIHT, TRE) have been conducted on all the 48 records of MIT-BIH Arrhythmia Database. Our method achieves average performances that are 3 times higher than the competitor results. In particular the compression ratio gap between our method and the others increases with the PRD growing.

Face recognition via sparse decomposition
SSPP problem: Single Sample Per Person (SSPP) Face Recognition is receiving a significant attention due to the challenges it opens especially when conceived for real applications under unconstrained environments. We proposed a solution combining the effectiveness of deep convolutional neural networks (DCNN) feature characterization, the discriminative capability of linear discriminant analysis (LDA), and the efficacy of a sparsity based classifier built on the k-LiMapS algorithm. Experiments on the public LFW dataset prove the method robustness to solve the SSPP problem, outperforming several state-of-the-art methods.
FR framework (very few images per subject): For decades, face recognition (FR) has attracted a lot of attention, and several systems have been successfully developed to solve this problem. However, the issue deserves further research e®ort so as to reduce the still existing gap between the computer and human ability in solving it. Among the others, one of the human skills concerns his ability in naturally conferring a degree of reliability" to the face identi ̄cation he carried out. We believe that providing a FR system with this feature would be of great help in real application contexts, making more °exible and treatable the identi ̄cation process. In this spirit, we propose a completely automatic FR system robust to possible adverse illuminations and facial expression variations that provides together with the identity the corresponding degree of reliability. The method promotes sparse coding of multi-feature representations with LDA projections for dimensionality reduction, and uses a multistage classi ̄er. The method has been evaluated in the challenging condition of having few (3–5) images per subject in the gallery. Extended experiments on several challenging databases (frontal faces of Extended YaleB, BANCA, FRGC v2.0, and frontal faces of Multi-PIE) show that our method outperforms several state-of-the-art sparse coding FR systems, thus demon- strating its e®ectiveness and generalizability.

Stochastic models in affective computing
Deep models for the affective space We draw on a simulationist approach to the analysis of facially displayed emotions - e.g., in the course of a face-to-face interaction between an expresser and an observer. At the heart of such perspective lies the enactment of the perceived emotion in the observer. We propose a novel probabilistic framework based on a deep latent representation of a continuous affect space, which can be exploited for both the estimation and the enactment of affective states in a multimodal space (visible facial expressions and physiological signals). The rationale behind the approach lies in the large body of evidence from affective neuroscience showing that when we observe emotional facial expressions, we react with congruent facial mimicry. Further, in more complex situations, affect understanding is likely to rely on a comprehensive representation grounding the reconstruction of the state of the body associated with the displayed emotion. We show that our approach can address such problems in a unified and principled perspective, thus avoiding ad hoc heuristics while minimising learning efforts. Results so far achieved have been assessed by exploiting a publicly available dataset.

Parallel algorithms on GPU-based architectures
ParCOSNET: Several problems in network biology and medicine can be cast into a framework where entities are represented through partially labeled networks, and the aim is inferring the labels usually binary of the unlabeled part. Connections represent functional or genetic similarity between entities, while the labellings often are highly unbalanced, that is one class is largely under-represented: for instance in the automated protein function prediction (AFP) for most Gene Ontology terms only few proteins are annotated, or in the disease-gene prioritization problem only few genes are actually known to be involved in the etiology of a given disease. Imbalance-aware approaches to accurately predict node labels in biological networks are thereby required. Furthermore, such methods must be scalable, since input data can be large-sized as, for instance, in the context of multi-species protein networks.
We proposed a novel semi-supervised parallel enhancement of COSNET, an imbalance-aware algorithm build on Hopfield neural model recently suggested to solve the AFP problem. By adopting an efficient representation of the graph and assuming a sparse network topology, we empirically show that it can be efficiently applied to networks with millions of nodes. The key strategy to speed up the computations is to partition nodes into independent sets so as to process each set in parallel by exploiting the power of GPU accelerators. This parallel technique ensures the convergence to asymptotically stable attractors, while preserving the asynchronous dynamics of the original model. Detailed experiments on real data and artificial big instances of the problem highlight scalability and efficiency of the proposed method.
By parallelizing COSNET we achieved on average a speed-up of 180x in solving the AFP problem in the S. cerevisiae, Mus musculus and Homo sapiens organisms, while lowering memory requirements. In addition, to show the potential applicability of the method to huge biomolecular networks, we predicted node labels in artificially generated sparse networks involving hundreds of thousands to millions of nodes.
Accelerated VP8 ME: We developed an efficient cooperative interaction between multicore (CPU) and manycore (GPU) resources in the design of a high-performance video encoder. The proposed technique, applied to the well-establi\-shed and highly optimized VP8 encoding format, can achieve a significant speed-up with respect to the mostly optimized software encoder (up to $\times$6), with minimum degradation of the visual quality and low processing latency. This result has been obtained through a highly optimized CPU-GPU interaction, the exploitation of specific GPU features, and a modified search algorithm specifically adapted to the GPU execution model. Several experimental results are reported and discussed, confirming the effectiveness of the proposed technique. The presented approach, though implemented for the VP8 standard, is of general interest, as it could be applied to any other video encoding scheme.

### Projects

[2013-2016]
European project FP7-ICT-2013-11: Future Networks. Project title: Network Functions as-a-Service over Virtualised Infrastructures (T-NOVA), project number 619520.
[2013-2016]
National project Futuro in Ricerca (FIRB) program. Project title: Interpreting emotions: a computational tool integrating facial expressions and biosignals based shape analysis and bayesian networks, Founded by MIUR - Ministero dell'Istruzione dell'Università e della Ricerca.
[2001-2002]
National research project COFIN. Project title: Modelli di calcolo innovativi: metodi sintattici e combinatori, Founded by MIUR - Ministero dell'Istruzione dell'Università e della Ricerca.
[1998-2001]
National project with title Progetto Finalizzato Biotecnologie. Work: Studio e sviluppo di un sistema software per il controllo in tempo reale di esperimenti di misura del calcio intracellulare (Atti del Convegno del Progetto Finalizzato Biotecnologie Genova 2000).

### PhD student

current
Alessandro D'Amelio
Alessandro Petrini
past
Massimo Marchi

### Software

The LiMapS algorithm
A new regularization method for sparse recovery based on a fixed-point iteration schema which combines Lipschitzian-type mappings and orthogonal projectors
LiMaps package for MATLAB
The k-LiMapS algorithm
A new algorithm to solve the sparse approximation problem over redundant dictionaries based on LiMapS, but retaining the best k basis (or dictionary) atoms
k-LiMaps package for MATLAB
The PrunICA algorithm
PrunICA is way to speed-up the FastICA-like algorithms by a controlled random pruning of the input mixtures, both on the entire mixture or on fixed-size blocks when segmented
PrunICA package for MATLAB

### Papers

Dalab: Digital Architecture Laboratory at DI.
Rice University: compressive sensing resources.
ECCC: Electronic Colloquium on Computational Complexity.
Compendium: a list of NP-complete optimization problems.
GNU: free software project.
www.itcline.it: web design.