Ryota Tomioka

Optimizing Spatial filters for Robust EEG Single-Trial Analysis

Due to the volume conduction multichannel electroencephalogram (EEG) recordings give a rather blurred image of brain activity. Therefore spatial filters are extremely useful in single-trial analysis in order to improve the signal-to-noise ratio. There are powerful methods from machine learning and signal processing that permit the optimization of spatio-temporal filters for each subject in a data dependent fashion beyond the fixed filters based on the sensor geometry, e.g., Laplacians. Here we elucidate the theoretical background of the common spatial pattern (CSP) algorithm, a popular method in brain-computer interface (BCD research. Apart from reviewing several variants of the basic algorithm, we reveal tricks of the trade for achieving a powerful CSP performance, briefly elaborate on theoretical aspects of CSP, and demonstrate the application of CSP-type preprocessing in our studies of the Berlin BCI (BBCI) project.

A regularized discriminative framework for EEG analysis with application to brain-computer interface.

We propose a framework for signal analysis of electroencephalography (EEG) that unifies tasks such as feature extraction, feature selection, feature combination, and classification, which are often independently tackled conventionally, under a regularized empirical risk minimization problem. The features are automatically learned, selected and combined through a convex optimization problem. Moreover we propose regularizers that induce novel types of sparsity providing a new technique for visualizing EEG of subjects during tasks from a discriminative point of view. The proposed framework is applied to two typical BCI problems, namely the P300 speller system and the prediction of self-paced finger tapping. In both datasets the proposed approach shows competitive performance against conventional methods, while at the same time the results are easier accessible to neurophysiological interpretation. Note that our novel approach is not only applicable to Brain imaging beyond EEG but also to general discriminative modeling of experimental paradigms beyond BCI.

Modeling Sparse Connectivity Between Underlying Brain Sources for EEG/MEG

We propose a novel technique to assess functional brain connectivity in electroencephalographic (EEG)/magnetoencephalographic (MEG) signals. Our method, called sparsely connected sources analysis (SCSA), can overcome the problem of volume conduction by modeling neural data innovatively with the following ingredients: 1) the EEG/MEG is assumed to be a linear mixture of correlated sources following a multivariate autoregressive (MVAR) model; 2) the demixing is estimated jointly with the source MVAR parameters; and 3) overfitting is avoided by using the group lasso penalty. This approach allows us to extract the appropriate level of crosstalk between the extracted sources and, in this manner, we obtain a sparse data-driven model of functional connectivity. We demonstrate the usefulness of SCSA with simulated data and compare it to a number of existing algorithms with excellent results.

Large-scale EEG/MEG source localization with spatial flexibility.

We propose a novel approach to solving the electro-/magnetoencephalographic (EEG/MEG) inverse problem which is based upon a decomposition of the current density into a small number of spatial basis fields. It is designed to recover multiple sources of possibly different extent and depth, while being invariant with respect to phase angles and rotations of the coordinate system. We demonstrate the methods ability to reconstruct simulated sources of random shape and show that the accuracy of the recovered sources can be increased, when interrelated field patterns are co-localized. Technically, this leads to large-scale mathematical problems, which are solved using recent advances in convex optimization. We apply our method for localizing brain areas involved in different types of motor imagery using real data from Brain-Computer Interface (BCI) sessions. Our approach based on single-trial localization of complex Fourier coefficients yields class-specific focal sources in the sensorimotor cortices.

Classifying matrices with a spectral regularization

We propose a method for the classification of matrices. We use a linear classifier with a novel regularization scheme based on the spectral l1-norm of its coefficient matrix. The spectral regularization not only provides a principled way of complexity control but also enables automatic determination of the rank of the coefficient matrix. Using the Linear Matrix Inequality technique, we formulate the inference task as a single convex optimization problem. We apply our method to the motor-imagery EEG classification problem. The method not only improves upon conventional methods in the classification performance but also determines a subspace in the signal that concentrates discriminative information without any additional feature extraction step. The method can be easily generalized to regression problems by changing the loss function. Connections to other methods are also discussed.

Tensor factorization using auxiliary information

Most of the existing analysis methods for tensors (or multi-way arrays) only assume that tensors to be completed are of low rank. However, for example, when they are applied to tensor completion problems, their prediction accuracy tends to be significantly worse when only a limited number of entries are observed. In this paper, we propose to use relationships among data as auxiliary information in addition to the low-rank assumption to improve the quality of tensor decomposition. We introduce two regularization approaches using graph Laplacians induced from the relationships, one for moderately sparse cases and the other for extremely sparse cases. We also give present two kinds of iterative algorithms for approximate solutions: one based on an EM-like algorithms which is stable but not so scalable, and the other based on gradient-based optimization which is applicable to large scale datasets. Numerical experiments on tensor completion using synthetic and benchmark datasets show that the use of auxiliary information improves completion accuracy over the existing methods based only on the low-rank assumption, especially when observations are sparse.

Dual-Augmented Lagrangian Method for Efficient Sparse Reconstruction

We propose an efficient algorithm for sparse signal reconstruction problems. The proposed algorithm is an augmented Lagrangian method based on the dual problem. It is efficient when the number of unknown variables is much larger than the number of observations because of the dual formulation. Moreover, the primal variable is explicitly updated and the sparsity in the solution is exploited. Numerical comparison with the state-of-the-art algorithms shows that the proposed algorithm is favorable when the design matrix is poorly conditioned or dense and very large.

Discovering Emerging Topics in Social Streams via Link-Anomaly Detection

Detection of emerging topics is now receiving renewed interest motivated by the rapid growth of social networks. Conventional-term-frequency-based approaches may not be appropriate in this context, because the information exchanged in social-network posts include not only text but also images, URLs, and videos. We focus on emergence of topics signaled by social aspects of theses networks. Specifically, we focus on mentions of users--links between users that are generated dynamically (intentionally or unintentionally) through replies, mentions, and retweets. We propose a probability model of the mentioning behavior of a social network user, and propose to detect the emergence of a new topic from the anomalies measured through the model. Aggregating anomaly scores from hundreds of users, we show that we can detect emerging topics only based on the reply/mention relationships in social-network posts. We demonstrate our technique in several real data sets we gathered from Twitter. The experiments show that the proposed mention-anomaly-based approaches can detect new topics at least as early as text-anomaly-based approaches, and in some cases much earlier when the topic is poorly identified by the textual contents in posts.

The algebraic combinatorial approach for low-rank matrix completion

We present a novel algebraic combinatorial view on low-rank matrix completion based on studying relations between a few entries with tools from algebraic geometry and matroid theory. The intrinsic locality of the approach allows for the treatment of single entries in a closed theoretical and practical framework. More specifically, apart from introducing an algebraic combinatorial theory of low-rank matrix completion, we present probability-one algorithms to decide whether a particular entry of the matrix can be completed. We also describe methods to complete that entry from a few others, and to estimate the error which is incurred by any method completing that entry. Furthermore, we show how known results on matrix completion and their sampling assumptions can be related to our new perspective and interpreted in terms of a completability phase transition.

SpicyMKL: a fast algorithm for Multiple Kernel Learning with thousands of kernels

We propose a new optimization algorithm for Multiple Kernel Learning (MKL) called SpicyMKL, which is applicable to general convex loss functions and general types of regularization. The proposed SpicyMKL iteratively solves smooth minimization problems. Thus, there is no need of solving SVM, LP, or QP internally. SpicyMKL can be viewed as a proximal minimization method and converges super-linearly. The cost of inner minimization is roughly proportional to the number of active kernels. Therefore, when we aim for a sparse kernel combination, our algorithm scales well against increasing number of kernels. Moreover, we give a general block-norm formulation of MKL that includes non-sparse regularizations, such as elastic-net and ℓp-norm regularizations. Extending SpicyMKL, we propose an efficient optimization method for the general regularization framework. Experimental results show that our algorithm is faster than existing methods especially when the number of kernels is large (>1000).