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Register a new userMixed-norm Regularization for Brain Decoding
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Added by
Remi Flamary
Publication date
2014
fields
Informatics Engineering
and research's language is
English
Authors
Remi Flamary
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This work investigates the use of mixed-norm regularization for sensor selection in Event-Related Potential (ERP) based Brain-Computer Interfaces (BCI). The classification problem is cast as a discriminative optimization framework where sensor selection is induced through the use of mixed-norms. This framework is extended to the multi-task learning situation where several similar classification tasks related to different subjects are learned simultaneously. In this case, multi-task learning helps in leveraging data scarcity issue yielding to more robust classifiers. For this purpose, we have introduced a regularizer that induces both sensor selection and classifier similarities. The different regularization approaches are compared on three ERP datasets showing the interest of mixed-norm regularization in terms of sensor selection. The multi-task approaches are evaluated when a small number of learning examples are available yielding to significant performance improvements especially for subjects performing poorly.
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Functional magnetic resonance imaging produces high dimensional data, with a less then ideal number of labelled samples for brain decoding tasks (predicting brain states). In this study, we propose a new deep temporal convolutional neural network architecture with spatial pooling for brain decoding which aims to reduce dimensionality of feature space along with improved classification performance. Temporal representations (filters) for each layer of the convolutional model are learned by leveraging unlabelled fMRI data in an unsupervised fashion with regularized autoencoders. Learned temporal representations in multiple levels capture the regularities in the temporal domain and are observed to be a rich bank of activation patterns which also exhibit similarities to the actual hemodynamic responses. Further, spatial pooling layers in the convolutional architecture reduce the dimensionality without losing excessive information. By employing the proposed temporal convolutional architecture with spatial pooling, raw input fMRI data is mapped to a non-linear, highly-expressive and low-dimensional feature space where the final classification is conducted. In addition, we propose a simple heuristic approach for hyper-parameter tuning when no validation data is available. Proposed method is tested on a ten class recognition memory experiment with nine subjects. The results support the efficiency and potential of the proposed model, compared to the baseline multi-voxel pattern analysis techniques.
We give a formal and complete characterization of the explicit regularizer induced by dropout in deep linear networks with squared loss. We show that (a) the explicit regularizer is composed of an $ell_2$-path regularizer and other terms that are also re-scaling invariant, (b) the convex envelope of the induced regularizer is the squared nuclear norm of the network map, and (c) for a sufficiently large dropout rate, we characterize the global optima of the dropout objective. We validate our theoretical findings with empirical results.
Using the $ell_1$-norm to regularize the estimation of the parameter vector of a linear model leads to an unstable estimator when covariates are highly correlated. In this paper, we introduce a new penalty function which takes into account the correlation of the design matrix to stabilize the estimation. This norm, called the trace Lasso, uses the trace norm, which is a convex surrogate of the rank, of the selected covariates as the criterion of model complexity. We analyze the properties of our norm, describe an optimization algorithm based on reweighted least-squares, and illustrate the behavior of this norm on synthetic data, showing that it is more adapted to strong correlations than competing methods such as the elastic net.
We represent the sequence of fMRI (Functional Magnetic Resonance Imaging) brain volumes recorded during a cognitive stimulus by a graph which consists of a set of local meshes. The corresponding cognitive process, encoded in the brain, is then represented by these meshes each of which is estimated assuming a linear relationship among the voxel time series in a predefined locality. First, we define the concept of locality in two neighborhood systems, namely, the spatial and functional neighborhoods. Then, we construct spatially and functionally local meshes around each voxel, called seed voxel, by connecting it either to its spatial or functional p-nearest neighbors. The mesh formed around a voxel is a directed sub-graph with a star topology, where the direction of the edges is taken towards the seed voxel at the center of the mesh. We represent the time series recorded at each seed voxel in terms of linear combination of the time series of its p-nearest neighbors in the mesh. The relationships between a seed voxel and its neighbors are represented by the edge weights of each mesh, and are estimated by solving a linear regression equation. The estimated mesh edge weights lead to a better representation of information in the brain for encoding and decoding of the cognitive tasks. We test our model on a visual object recognition and emotional memory retrieval experiments using Support Vector Machines that are trained using the mesh edge weights as features. In the experimental analysis, we observe that the edge weights of the spatial and functional meshes perform better than the state-of-the-art brain decoding models.
Brain imaging data are important in brain sciences yet expensive to obtain, with big volume (i.e., large p) but small sample size (i.e., small n). To tackle this problem, transfer learning is a promising direction that leverages source data to improve performance on related, target data. Most transfer learning methods focus on minimizing data distribution mismatch. However, a big challenge in brain imaging is the large domain discrepancies in cognitive experiment designs and subject-specific structures and functions. A recent transfer learning approach minimizes domain dependence to learn common features across domains, via the Hilbert-Schmidt Independence Criterion (HSIC). Inspired by this method, we propose a new Domain Independent Support Vector Machine (DI-SVM) for transfer learning in brain condition decoding. Specifically, DI-SVM simultaneously minimizes the SVM empirical risk and the dependence on domain information via a simplified HSIC. We use public data to construct 13 transfer learning tasks in brain decoding, including three interesting multi-source transfer tasks. Experiments show that DI-SVMs superior performance over eight competing methods on these tasks, particularly an improvement of more than 24% on multi-source transfer tasks.
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