Modeling sparse connectivity between underlying brain sources for EEG/MEG

We propose a novel technique to assess functional brain connectivity in EEG/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: (a) the EEG is assumed to be a linear mixture of correlated sources following a multivariate autoregressive (MVAR) model, (b) the demixing is estimated jointly with the source MVAR parameters, (c) overfitting is avoided by using the Group Lasso penalty. This approach allows to extract the appropriate level cross-talk 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 to a number of existing algorithms with excellent results.Comment: 9 pages, 6 figure

In Search of Non-Gaussian Components of a High-Dimensional Distribution

Finding non-Gaussian components of high-dimensional data is an important preprocessing step for effcient information processing. This article proposes a new linear method to identify the ``non-Gaussian subspace´´ within a very general semi-parametric framework. Our proposed method, called NGCA (Non-Gaussian Component Analysis), is essentially based on a linear operator which, to any arbitrary nonlinear (smooth) function, associates a vector which belongs to the low dimensional non-Gaussian target subspace up to an estimation error. By applying this operator to a family of different nonlinear functions, one obtains a family of different vectors lying in a vicinity of the target space. As a final step, the target space itself is estimated by applying PCA to this family of vectors. We show that this procedure is consistent in the sense that the estimaton error tends to zero at a parametric rate, uniformly over the family, Numerical examples demonstrate the usefulness of our method.non-Gaussian components, dimension reduction

How to Explain Individual Classification Decisions

After building a classifier with modern tools of machine learning we typically have a black box at hand that is able to predict well for unseen data. Thus, we get an answer to the question what is the most likely label of a given unseen data point. However, most methods will provide no answer why the model predicted the particular label for a single instance and what features were most influential for that particular instance. The only method that is currently able to provide such explanations are decision trees. This paper proposes a procedure which (based on a set of assumptions) allows to explain the decisions of any classification method.Comment: 31 pages, 14 figure

Characterizing Variability of Modular Brain Connectivity with Constrained Principal Component Analysis

Characterizing the variability of resting-state functional brain connectivity across subjects and/or over time has recently attracted much attention. Principal component analysis (PCA) serves as a fundamental statistical technique for such analyses. However, performing PCA on high-dimensional connectivity matrices yields complicated "eigenconnectivity" patterns, for which systematic interpretation is a challenging issue. Here, we overcome this issue with a novel constrained PCA method for connectivity matrices by extending the idea of the previously proposed orthogonal connectivity factorization method. Our new method, modular connectivity factorization (MCF), explicitly introduces the modularity of brain networks as a parametric constraint on eigenconnectivity matrices. In particular, MCF analyzes the variability in both intra-and inter-module connectivities, simultaneously finding network modules in a principled, data-driven manner. The parametric constraint provides a compact module based visualization scheme with which the result can be intuitively interpreted. We develop an optimization algorithm to solve the constrained PCA problem and validate our method in simulation studies and with a resting-state functional connectivity MRI dataset of 986 subjects. The results show that the proposed MCF method successfully reveals the underlying modular eigenconnectivity patterns in more general situations and is a promising alternative to existing methods.Peer reviewe

SPLICE : Fully tractable hierarchical extension of ICA with pooling

We present a novel probabilistic framework for a hierarchical extension of independent component analysis (ICA), with a particular motivation in neuroscientific data analysis and modeling. The framework incorporates a general sub-space pooling with linear ICA-like layers stacked recursively. Unlike related previous models, our generative model is fully tractable: both the likelihood and the posterior estimates of latent variables can readily be computed with analytically simple formulae. The model is particularly simple in the case of complex-valued data since the pooling can be reduced to taking the modulus of complex numbers. Experiments on elec-troencephalography (EEG) and natural images demonstrate the validity of the method. Copyright 2017 by the author(s).Peer reviewe

CityRefer: Geography-aware 3D Visual Grounding Dataset on City-scale Point Cloud Data

City-scale 3D point cloud is a promising way to express detailed and complicated outdoor structures. It encompasses both the appearance and geometry features of segmented city components, including cars, streets, and buildings, that can be utilized for attractive applications such as user-interactive navigation of autonomous vehicles and drones. However, compared to the extensive text annotations available for images and indoor scenes, the scarcity of text annotations for outdoor scenes poses a significant challenge for achieving these applications. To tackle this problem, we introduce the CityRefer dataset for city-level visual grounding. The dataset consists of 35k natural language descriptions of 3D objects appearing in SensatUrban city scenes and 5k landmarks labels synchronizing with OpenStreetMap. To ensure the quality and accuracy of the dataset, all descriptions and labels in the CityRefer dataset are manually verified. We also have developed a baseline system that can learn encoded language descriptions, 3D object instances, and geographical information about the city's landmarks to perform visual grounding on the CityRefer dataset. To the best of our knowledge, the CityRefer dataset is the largest city-level visual grounding dataset for localizing specific 3D objects.Comment: NeurIPS D&B 2023. The first two authors are equally contribute

Non-Gaussian Component Analysis using Entropy Methods

Non-Gaussian component analysis (NGCA) is a problem in multidimensional data analysis which, since its formulation in 2006, has attracted considerable attention in statistics and machine learning. In this problem, we have a random variable $X$ in $n$-dimensional Euclidean space. There is an unknown subspace $\Gamma$ of the $n$-dimensional Euclidean space such that the orthogonal projection of $X$ onto $\Gamma$ is standard multidimensional Gaussian and the orthogonal projection of $X$ onto $\Gamma^{\perp}$, the orthogonal complement of $\Gamma$, is non-Gaussian, in the sense that all its one-dimensional marginals are different from the Gaussian in a certain metric defined in terms of moments. The NGCA problem is to approximate the non-Gaussian subspace $\Gamma^{\perp}$ given samples of $X$. Vectors in $\Gamma^{\perp}$ correspond to `interesting' directions, whereas vectors in $\Gamma$ correspond to the directions where data is very noisy. The most interesting applications of the NGCA model is for the case when the magnitude of the noise is comparable to that of the true signal, a setting in which traditional noise reduction techniques such as PCA don't apply directly. NGCA is also related to dimension reduction and to other data analysis problems such as ICA. NGCA-like problems have been studied in statistics for a long time using techniques such as projection pursuit. We give an algorithm that takes polynomial time in the dimension $n$ and has an inverse polynomial dependence on the error parameter measuring the angle distance between the non-Gaussian subspace and the subspace output by the algorithm. Our algorithm is based on relative entropy as the contrast function and fits under the projection pursuit framework. The techniques we develop for analyzing our algorithm maybe of use for other related problems

Insights from Classifying Visual Concepts with Multiple Kernel Learning

Combining information from various image features has become a standard technique in concept recognition tasks. However, the optimal way of fusing the resulting kernel functions is usually unknown in practical applications. Multiple kernel learning (MKL) techniques allow to determine an optimal linear combination of such similarity matrices. Classical approaches to MKL promote sparse mixtures. Unfortunately, so-called 1-norm MKL variants are often observed to be outperformed by an unweighted sum kernel. The contribution of this paper is twofold: We apply a recently developed non-sparse MKL variant to state-of-the-art concept recognition tasks within computer vision. We provide insights on benefits and limits of non-sparse MKL and compare it against its direct competitors, the sum kernel SVM and the sparse MKL. We report empirical results for the PASCAL VOC 2009 Classification and ImageCLEF2010 Photo Annotation challenge data sets. About to be submitted to PLoS ONE.Comment: 18 pages, 8 tables, 4 figures, format deviating from plos one submission format requirements for aesthetic reason

Higher order stationary subspace analysis

Non-stationarity in data is an ubiquitous problem in signal processing. The recent stationary subspace analysis procedure (SSA) has enabled to decompose such data into a stationary subspace and a non-stationary part respectively. Algorithmically only weak non- stationarities could be tackled by SSA. The present paper takes the conceptual step generalizing from the use of first and second moments as in SSA to higher order moments, thus defining the proposed higher order stationary subspace analysis procedure (HOSSA). The paper derives the novel procedure and shows simulations. An obvious trade-off between the necessity of estimating higher moments and the accuracy and robustness with which they can be estimated is observed. In an ideal setting of plenty of data where higher moment information is dominating our novel approach can win against standard SSA. However, with limited data, even though higher moments actually dominate the underlying data, still SSA may arrive on par.BMBF, 01IB15001B, Verbundprojekt: ALICE II - Autonomes Lernen in komplexen Umgebungen 2 (Autonomous Learning in Complex Environments 2)BMBF, 01GQ1115, D-JPN Verbund: Adaptive Gehirn-Computer-Schnittstellen (BCI) in nichtstationären UmgebungenDFG, 200318152, Theoretische Konzepte für co-adaptive Mensch-Maschine-Interaktion mit Anwendungen auf BC

Interpretable brain age prediction using linear latent variable models of functional connectivity

Neuroimaging-driven prediction of brain age, defined as the predicted biological age of a subject using only brain imaging data, is an exciting avenue of research. In this work we seek to build models of brain age based on functional connectivity while prioritizing model interpretability and understanding. This way, the models serve to both provide accurate estimates of brain age as well as allow us to investigate changes in functional connectivity which occur during the ageing process. The methods proposed in this work consist of a two-step procedure: first, linear latent variable models, such as PCA and its extensions, are employed to learn reproducible functional connectivity networks present across a cohort of subjects. The activity within each network is subsequently employed as a feature in a linear regression model to predict brain age. The proposed framework is employed on the data from the CamCAN repository and the inferred brain age models are further demonstrated to generalize using data from two open-access repositories: the Human Connectome Project and the ATR Wide-Age-Range.Peer reviewe