Towards Best Practice of Interpreting Deep Learning Models for EEG-based Brain Computer Interfaces

As deep learning has achieved state-of-the-art performance for many tasks of EEG-based BCI, many efforts have been made in recent years trying to understand what have been learned by the models. This is commonly done by generating a heatmap indicating to which extent each pixel of the input contributes to the final classification for a trained model. Despite the wide use, it is not yet understood to which extent the obtained interpretation results can be trusted and how accurate they can reflect the model decisions. In order to fill this research gap, we conduct a study to evaluate different deep interpretation techniques quantitatively on EEG datasets. The results reveal the importance of selecting a proper interpretation technique as the initial step. In addition, we also find that the quality of the interpretation results is inconsistent for individual samples despite when a method with an overall good performance is used. Many factors, including model structure and dataset types, could potentially affect the quality of the interpretation results. Based on the observations, we propose a set of procedures that allow the interpretation results to be presented in an understandable and trusted way. We illustrate the usefulness of our method for EEG-based BCI with instances selected from different scenarios

Cell Image Segmentation with Kernel-Based Dynamic Clustering and an Ellipsoidal Cell Shape Model

AbstractIn this paper, we propose a novel approach to cell image segmentation under severe noise conditions by combining kernel-based dynamic clustering and a genetic algorithm. Our method incorporates a priori knowledge about cell shape. That is, an elliptical cell contour model is introduced to describe the boundary of the cell. Our method consists of the following components: (1) obtain the gradient image; (2) use the gradient image to obtain points which possibly belong to cell boundaries; (3) adjust the parameters of the elliptical cell boundary model to match the cell contour using a genetic algorithm. The method is tested on images of noisy human thyroid and small intestine cells

Model-Free, Regularized, Fast, and Robust Analytical Orientation Distribution Function Estimation

International audienceHigh Angular Resolution Imaging (HARDI) can better explore the complex micro-structure of white matter compared to Diffusion Tensor Imaging (DTI). Orientation Distribution Function (ODF) in HARDI is used to describe the probability of the fiber direction. There are two type definitions of the ODF, which were respectively proposed in Q-Ball Imaging (QBI) and Diffusion Spectrum Imaging (DSI). Some analytical reconstructions methods have been proposed to estimate these two type of ODFs from single shell HARDI data. However they all have some assumptions and intrinsic modeling errors. In this article, we propose, almost without any assumption, a uniform analytical method to estimate these two ODFs from DWI signals in q space, which is based on Spherical Polar Fourier Expression (SPFE) of signals. The solution is analytical and is a linear transformation from the q-space signal to the ODF represented by Spherical Harmonics (SH). It can naturally combines the DWI signals in dierent Q-shells. Moreover It can avoid the intrinsic Funk-Radon Transform (FRT) blurring error in QBI and it does not need any assumption of the signals, such as the multiple tensor model and mono/multi-exponential decay. We validate our method using synthetic data, phantom data and real data. Our method works well in all experiments, especially for the data with low SNR, low anisotropy and non-exponential decay

A Riemannian Framework for Orientation Distribution Function Computing

International audienceCompared with Diffusion Tensor Imaging (DTI), High Angular Resolution Imaging (HARDI) can better explore the complex microstructure of white matter. Orientation Distribution Function (ODF) is used to describe the probability of the fiber direction. Fisher information metric has been constructed for probability density family in Information Geometry theory and it has been successfully applied for tensor computing in DTI. In this paper, we present a state of the art Riemannian framework for ODF computing based on Information Geometry and sparse representation of orthonormal bases. In this Riemannian framework, the exponential map, logarithmic map and geodesic have closed forms. And the weighted Frechet mean exists uniquely on this manifold. We also propose a novel scalar measurement, named Geometric Anisotropy (GA), which is the Riemannian geodesic distance between the ODF and the isotropic ODF. The Renyi entropy H_{1/2} of the ODF can be computed from the GA. Moreover, we present an Affine-Euclidean framework and a Log-Euclidean framework so that we can work in an Euclidean space. As an application, Lagrange interpolation on ODF field is proposed based on weighted Frechet mean. We validate our methods on synthetic and real data experiments. Compared with existing Riemannian frameworks on ODF, our framework is model-free. The estimation of the parameters, i.e. Riemannian coordinates, is robust and linear. Moreover it should be noted that our theoretical results can be used for any probability density function (PDF) under an orthonormal basis representation

Riemannian Median and Its Applications for Orientation Distribution Function Computing

International audienceThe geometric median is a classic robust estimator of centrality for data in Euclidean spaces, and it has been generalized in analytical manifold in [1]. Recently, an intrinsic Riemannian framework for Orientation Distribution Function (ODF) was proposed for the calculation in ODF field [2]. In this work, we prove the unique existence of the Riemannian median in ODF space. Then we explore its two potential applications, median filtering and atlas estimation

Diffeomorphism Invariant Riemannian Framework for Ensemble Average Propagator Computing

International audienceBackground: In Diffusion Tensor Imaging (DTI), Riemannian framework based on Information Geometry theory has been proposed for processing tensors on estimation, interpolation, smoothing, regularization, segmentation, statistical test and so on. Recently Riemannian framework has been generalized to Orientation Distribution Function (ODF) and it is applicable to any Probability Density Function (PDF) under orthonormal basis representation. Spherical Polar Fourier Imaging (SPFI) was proposed for ODF and Ensemble Average Propagator (EAP) estimation from arbitrary sampled signals without any assumption. Purpose: Tensors only can represent Gaussian EAP and ODF is the radial integration of EAP, while EAP has full information for diffusion process. To our knowledge, so far there is no work on how to process EAP data. In this paper, we present a Riemannian framework as a mathematical tool for such task. Method: We propose a state-of-the-art Riemannian framework for EAPs by representing the square root of EAP, called wavefunction based on quantum mechanics, with the Fourier dual Spherical Polar Fourier (dSPF) basis. In this framework, the exponential map, logarithmic map and geodesic have closed forms, and weighted Riemannian mean and median uniquely exist. We analyze theoretically the similarities and differences between Riemannian frameworks for EAPs and for ODFs and tensors. The Riemannian metric for EAPs is diffeomorphism invariant, which is the natural extension of the affine-invariant metric for tensors. We propose Log-Euclidean framework to fast process EAPs, and Geodesic Anisotropy (GA) to measure the anisotropy of EAPs. With this framework, many important data processing operations, such as interpolation, smoothing, atlas estimation, Principal Geodesic Analysis (PGA), can be performed on EAP data. Results and Conclusions: The proposed Riemannian framework was validated in synthetic data for interpolation, smoothing, PGA and in real data for GA and atlas estimation. Riemannian median is much robust for atlas estimation

Fast, Model-Free , Analytical ODF Reconstruction from the Q-Space Signal

International audienceThe orientation distribution function (ODF) is very important in diffusion MRI. There are two types of ODFs. One is proposed using radial projection in Q-ball imaging [7]. Another one is the marginal pdf proposed in diffusion spectrum imaging (DSI) [8]. Since the marginal pdf is much sharper and mathematically correct, it could be more useful. Recently some reconstruction methods were proposed for this kind of ODF [1, 6]. They are both based on mono-exponential model, globally or locally, which has some intrinsic modeling error [4]. Although the authors in [1] extended the mono-exponential model to multi-exponential model, this multi-exponential model needs to be estimated non-linearly for every voxel and only in some special sampling scheme it has a analytical solution. Here we give a model-free analytical reconstruction method based on the Spherical Polar Fourier expression of the signal. It can estimate the ODF fast and analytically from the signal

Esub8: A novel tool to predict protein subcellular localizations in eukaryotic organisms

BACKGROUND: Subcellular localization of a new protein sequence is very important and fruitful for understanding its function. As the number of new genomes has dramatically increased over recent years, a reliable and efficient system to predict protein subcellular location is urgently needed. RESULTS: Esub8 was developed to predict protein subcellular localizations for eukaryotic proteins based on amino acid composition. In this research, the proteins are classified into the following eight groups: chloroplast, cytoplasm, extracellular, Golgi apparatus, lysosome, mitochondria, nucleus and peroxisome. We know subcellular localization is a typical classification problem; consequently, a one-against-one (1-v-1) multi-class support vector machine was introduced to construct the classifier. Unlike previous methods, ours considers the order information of protein sequences by a different method. Our method is tested in three subcellular localization predictions for prokaryotic proteins and four subcellular localization predictions for eukaryotic proteins on Reinhardt's dataset. The results are then compared to several other methods. The total prediction accuracies of two tests are both 100% by a self-consistency test, and are 92.9% and 84.14% by the jackknife test, respectively. Esub8 also provides excellent results: the total prediction accuracies are 100% by a self-consistency test and 87% by the jackknife test. CONCLUSIONS: Our method represents a different approach for predicting protein subcellular localization and achieved a satisfactory result; furthermore, we believe Esub8 will be a useful tool for predicting protein subcellular localizations in eukaryotic organisms

Multi-Scale Expressions of One Optimal State Regulated by Dopamine in the Prefrontal Cortex

The prefrontal cortex (PFC), which plays key roles in many higher cognitive processes, is a hierarchical system consisting of multi-scale organizations. Optimizing the working state at each scale is essential for PFC's information processing. Typical optimal working states at different scales have been separately reported, including the dopamine-mediated inverted-U profile of the working memory (WM) at the system level, critical dynamics at the network level, and detailed balance of excitatory and inhibitory currents (E/I balance) at the cellular level. However, it remains unclear whether these states are scale-specific expressions of the same optimal state and, if so, what is the underlying mechanism for its regulation traversing across scales. Here, by studying a neural network model, we show that the optimal performance of WM co-occurs with the critical dynamics at the network level and the E/I balance at the level of individual neurons, suggesting the existence of a unified, multi-scale optimal state for the PFC. Importantly, such a state could be modulated by dopamine at the synaptic level through a series of U or inverted-U profiles. These results suggest that seemingly different optimal states for specific scales are multi-scale expressions of one condition regulated by dopamine. Our work suggests a cross-scale perspective to understand the PFC function and its modulation