Tensor Analysis and Fusion of Multimodal Brain Images

Current high-throughput data acquisition technologies probe dynamical systems with different imaging modalities, generating massive data sets at different spatial and temporal resolutions posing challenging problems in multimodal data fusion. A case in point is the attempt to parse out the brain structures and networks that underpin human cognitive processes by analysis of different neuroimaging modalities (functional MRI, EEG, NIRS etc.). We emphasize that the multimodal, multi-scale nature of neuroimaging data is well reflected by a multi-way (tensor) structure where the underlying processes can be summarized by a relatively small number of components or "atoms". We introduce Markov-Penrose diagrams - an integration of Bayesian DAG and tensor network notation in order to analyze these models. These diagrams not only clarify matrix and tensor EEG and fMRI time/frequency analysis and inverse problems, but also help understand multimodal fusion via Multiway Partial Least Squares and Coupled Matrix-Tensor Factorization. We show here, for the first time, that Granger causal analysis of brain networks is a tensor regression problem, thus allowing the atomic decomposition of brain networks. Analysis of EEG and fMRI recordings shows the potential of the methods and suggests their use in other scientific domains.Comment: 23 pages, 15 figures, submitted to Proceedings of the IEE

Challenges in Complex Systems Science

FuturICT foundations are social science, complex systems science, and ICT. The main concerns and challenges in the science of complex systems in the context of FuturICT are laid out in this paper with special emphasis on the Complex Systems route to Social Sciences. This include complex systems having: many heterogeneous interacting parts; multiple scales; complicated transition laws; unexpected or unpredicted emergence; sensitive dependence on initial conditions; path-dependent dynamics; networked hierarchical connectivities; interaction of autonomous agents; self-organisation; non-equilibrium dynamics; combinatorial explosion; adaptivity to changing environments; co-evolving subsystems; ill-defined boundaries; and multilevel dynamics. In this context, science is seen as the process of abstracting the dynamics of systems from data. This presents many challenges including: data gathering by large-scale experiment, participatory sensing and social computation, managing huge distributed dynamic and heterogeneous databases; moving from data to dynamical models, going beyond correlations to cause-effect relationships, understanding the relationship between simple and comprehensive models with appropriate choices of variables, ensemble modeling and data assimilation, modeling systems of systems of systems with many levels between micro and macro; and formulating new approaches to prediction, forecasting, and risk, especially in systems that can reflect on and change their behaviour in response to predictions, and systems whose apparently predictable behaviour is disrupted by apparently unpredictable rare or extreme events. These challenges are part of the FuturICT agenda

Bayesian Nonparametric Hidden Semi-Markov Models

There is much interest in the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) as a natural Bayesian nonparametric extension of the ubiquitous Hidden Markov Model for learning from sequential and time-series data. However, in many settings the HDP-HMM's strict Markovian constraints are undesirable, particularly if we wish to learn or encode non-geometric state durations. We can extend the HDP-HMM to capture such structure by drawing upon explicit-duration semi-Markovianity, which has been developed mainly in the parametric frequentist setting, to allow construction of highly interpretable models that admit natural prior information on state durations. In this paper we introduce the explicit-duration Hierarchical Dirichlet Process Hidden semi-Markov Model (HDP-HSMM) and develop sampling algorithms for efficient posterior inference. The methods we introduce also provide new methods for sampling inference in the finite Bayesian HSMM. Our modular Gibbs sampling methods can be embedded in samplers for larger hierarchical Bayesian models, adding semi-Markov chain modeling as another tool in the Bayesian inference toolbox. We demonstrate the utility of the HDP-HSMM and our inference methods on both synthetic and real experiments

Human Interaction Recognition with Audio and Visual Cues

The automated recognition of human activities from video is a fundamental problem with applications in several areas, ranging from video surveillance, and robotics, to smart healthcare, and multimedia indexing and retrieval, just to mention a few. However, the pervasive diffusion of cameras capable of recording audio also makes available to those applications a complementary modality. Despite the sizable progress made in the area of modeling and recognizing group activities, and actions performed by people in isolation from video, the availability of audio cues has rarely being leveraged. This is even more so in the area of modeling and recognizing binary interactions between humans, where also the use of video has been limited.;This thesis introduces a modeling framework for binary human interactions based on audio and visual cues. The main idea is to describe an interaction with a spatio-temporal trajectory modeling the visual motion cues, and a temporal trajectory modeling the audio cues. This poses the problem of how to fuse temporal trajectories from multiple modalities for the purpose of recognition. We propose a solution whereby trajectories are modeled as the output of kernel state space models. Then, we developed kernel-based methods for the audio-visual fusion that act at the feature level, as well as at the kernel level, by exploiting multiple kernel learning techniques. The approaches have been extensively tested and evaluated with a dataset made of videos obtained from TV shows and Hollywood movies, containing five different interactions. The results show the promise of this approach by producing a significant improvement of the recognition rate when audio cues are exploited, clearly setting the state-of-the-art in this particular application

Polyphonic Sound Event Tracking Using Linear Dynamical Systems

In this paper, a system for polyphonic sound event detection and tracking is proposed, based on spectrogram factorisation techniques and state space models. The system extends probabilistic latent component analysis (PLCA) and is modelled around a 4-dimensional spectral template dictionary of frequency, sound event class, exemplar index, and sound state. In order to jointly track multiple overlapping sound events over time, the integration of linear dynamical systems (LDS) within the PLCA inference is proposed. The system assumes that the PLCA sound event activation is the (noisy) observation in an LDS, with the latent states corresponding to the true event activations. LDS training is achieved using fully observed data, making use of ground truth-informed event activations produced by the PLCA-based model. Several LDS variants are evaluated, using polyphonic datasets of office sounds generated from an acoustic scene simulator, as well as real and synthesized monophonic datasets for comparative purposes. Results show that the integration of LDS tracking within PLCA leads to an improvement of +8.5-10.5% in terms of frame-based F-measure as compared to the use of the PLCA model alone. In addition, the proposed system outperforms several state-of-the-art methods for the task of polyphonic sound event detection