A group model for stable multi-subject ICA on fMRI datasets

Spatial Independent Component Analysis (ICA) is an increasingly used data-driven method to analyze functional Magnetic Resonance Imaging (fMRI) data. To date, it has been used to extract sets of mutually correlated brain regions without prior information on the time course of these regions. Some of these sets of regions, interpreted as functional networks, have recently been used to provide markers of brain diseases and open the road to paradigm-free population comparisons. Such group studies raise the question of modeling subject variability within ICA: how can the patterns representative of a group be modeled and estimated via ICA for reliable inter-group comparisons? In this paper, we propose a hierarchical model for patterns in multi-subject fMRI datasets, akin to mixed-effect group models used in linear-model-based analysis. We introduce an estimation procedure, CanICA (Canonical ICA), based on i) probabilistic dimension reduction of the individual data, ii) canonical correlation analysis to identify a data subspace common to the group iii) ICA-based pattern extraction. In addition, we introduce a procedure based on cross-validation to quantify the stability of ICA patterns at the level of the group. We compare our method with state-of-the-art multi-subject fMRI ICA methods and show that the features extracted using our procedure are more reproducible at the group level on two datasets of 12 healthy controls: a resting-state and a functional localizer study

A physics-based approach to flow control using system identification

Control of amplifier flows poses a great challenge, since the influence of environmental noise sources and measurement contamination is a crucial component in the design of models and the subsequent performance of the controller. A modelbased approach that makes a priori assumptions on the noise characteristics often yields unsatisfactory results when the true noise environment is different from the assumed one. An alternative approach is proposed that consists of a data-based systemidentification technique for modelling the flow; it avoids the model-based shortcomings by directly incorporating noise influences into an auto-regressive (ARMAX) design. This technique is applied to flow over a backward-facing step, a typical example of a noise-amplifier flow. Physical insight into the specifics of the flow is used to interpret and tailor the various terms of the auto-regressive model. The designed compensator shows an impressive performance as well as a remarkable robustness to increased noise levels and to off-design operating conditions. Owing to its reliance on only timesequences of observable data, the proposed technique should be attractive in the design of control strategies directly from experimental data and should result in effective compensators that maintain performance in a realistic disturbance environment

Parsimonious Mahalanobis Kernel for the Classification of High Dimensional Data

The classification of high dimensional data with kernel methods is considered in this article. Exploit- ing the emptiness property of high dimensional spaces, a kernel based on the Mahalanobis distance is proposed. The computation of the Mahalanobis distance requires the inversion of a covariance matrix. In high dimensional spaces, the estimated covariance matrix is ill-conditioned and its inversion is unstable or impossible. Using a parsimonious statistical model, namely the High Dimensional Discriminant Analysis model, the specific signal and noise subspaces are estimated for each considered class making the inverse of the class specific covariance matrix explicit and stable, leading to the definition of a parsimonious Mahalanobis kernel. A SVM based framework is used for selecting the hyperparameters of the parsimonious Mahalanobis kernel by optimizing the so-called radius-margin bound. Experimental results on three high dimensional data sets show that the proposed kernel is suitable for classifying high dimensional data, providing better classification accuracies than the conventional Gaussian kernel

Nearness to Local Subspace Algorithm for Subspace and Motion Segmentation

There is a growing interest in computer science, engineering, and mathematics for modeling signals in terms of union of subspaces and manifolds. Subspace segmentation and clustering of high dimensional data drawn from a union of subspaces are especially important with many practical applications in computer vision, image and signal processing, communications, and information theory. This paper presents a clustering algorithm for high dimensional data that comes from a union of lower dimensional subspaces of equal and known dimensions. Such cases occur in many data clustering problems, such as motion segmentation and face recognition. The algorithm is reliable in the presence of noise, and applied to the Hopkins 155 Dataset, it generates the best results to date for motion segmentation. The two motion, three motion, and overall segmentation rates for the video sequences are 99.43%, 98.69%, and 99.24%, respectively

Low-Rank Matrices on Graphs: Generalized Recovery & Applications

Many real world datasets subsume a linear or non-linear low-rank structure in a very low-dimensional space. Unfortunately, one often has very little or no information about the geometry of the space, resulting in a highly under-determined recovery problem. Under certain circumstances, state-of-the-art algorithms provide an exact recovery for linear low-rank structures but at the expense of highly inscalable algorithms which use nuclear norm. However, the case of non-linear structures remains unresolved. We revisit the problem of low-rank recovery from a totally different perspective, involving graphs which encode pairwise similarity between the data samples and features. Surprisingly, our analysis confirms that it is possible to recover many approximate linear and non-linear low-rank structures with recovery guarantees with a set of highly scalable and efficient algorithms. We call such data matrices as \textit{Low-Rank matrices on graphs} and show that many real world datasets satisfy this assumption approximately due to underlying stationarity. Our detailed theoretical and experimental analysis unveils the power of the simple, yet very novel recovery framework \textit{Fast Robust PCA on Graphs

Spatial Filtering Pipeline Evaluation of Cortically Coupled Computer Vision System for Rapid Serial Visual Presentation

Rapid Serial Visual Presentation (RSVP) is a paradigm that supports the application of cortically coupled computer vision to rapid image search. In RSVP, images are presented to participants in a rapid serial sequence which can evoke Event-related Potentials (ERPs) detectable in their Electroencephalogram (EEG). The contemporary approach to this problem involves supervised spatial filtering techniques which are applied for the purposes of enhancing the discriminative information in the EEG data. In this paper we make two primary contributions to that field: 1) We propose a novel spatial filtering method which we call the Multiple Time Window LDA Beamformer (MTWLB) method; 2) we provide a comprehensive comparison of nine spatial filtering pipelines using three spatial filtering schemes namely, MTWLB, xDAWN, Common Spatial Pattern (CSP) and three linear classification methods Linear Discriminant Analysis (LDA), Bayesian Linear Regression (BLR) and Logistic Regression (LR). Three pipelines without spatial filtering are used as baseline comparison. The Area Under Curve (AUC) is used as an evaluation metric in this paper. The results reveal that MTWLB and xDAWN spatial filtering techniques enhance the classification performance of the pipeline but CSP does not. The results also support the conclusion that LR can be effective for RSVP based BCI if discriminative features are available

Optimal phase space projection for noise reduction

In this communication we will re-examine the widely studied technique of phase space projection. By imposing a time domain constraint (TDC) on the residual noise, we deduce a more general version of the optimal projector, which includes those appearing in previous literature as subcases but does not assume the independence between the clean signal and the noise. As an application, we will apply this technique for noise reduction. Numerical results show that our algorithm has succeeded in augmenting the signal-to-noise ratio (SNR) for simulated data from the R\"ossler system and experimental speech record.Comment: Accepted version for PR