There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Data Mining - Concepts and Techniques.

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Convex Analysisの二,三の進展について

Deep learning with convolutional neural networks (deep ConvNets) has revolutionized computer vision through end-to-end learning, that is, learning from the raw data. There is increasing interest in using deep ConvNets for end-to-end EEG analysis, but a better understanding of how to design and train ConvNets for end-to-end EEG decoding and how to visualize the informative EEG features the ConvNets learn is still needed. Here, we studied deep ConvNets with a range of different architectures, designed for decoding imagined or executed tasks from raw EEG. Our results show that recent advances from the machine learning field, including batch normalization and exponential linear units, together with a cropped training strategy, boosted the deep ConvNets decoding performance, reaching at least as good performance as the widely used filter bank common spatial patterns (FBCSP) algorithm (mean decoding accuracies 82.1% FBCSP, 84.0% deep ConvNets). While FBCSP is designed to use spectral power modulations, the features used by ConvNets are not fixed a priori. Our novel methods for visualizing the learned features demonstrated that ConvNets indeed learned to use spectral power modulations in the alpha, beta, and high gamma frequencies, and proved useful for spatially mapping the learned features by revealing the topography of the causal contributions of features in different frequency bands to the decoding decision. Our study thus shows how to design and train ConvNets to decode task-related information from the raw EEG without handcrafted features and highlights the potential of deep ConvNets combined with advanced visualization techniques for EEG-based brain mapping. Hum Brain Mapp 38:5391-5420, 2017. © 2017 Wiley Periodicals, Inc.

Deep learning with convolutional neural networks for EEG decoding and visualization.

Electroencephalograms (EEGs) are becoming increasingly important measurements of brain activity and they have great potential for the diagnosis and treatment of mental and brain diseases and abnormalities. With appropriate interpretation methods they are emerging as a key methodology to satisfy the increasing global demand for more affordable and effective clinical and healthcare services. Developing and understanding advanced signal processing techniques for the analysis of EEG signals is crucial in the area of biomedical research. This book focuses on these techniques, providing expansive coverage of algorithms and tools from the field of digital signal processing. It discusses their applications to medical data, using graphs and topographic images to show simulation results that assess the efficacy of the methods. Additionally, expect to find: explanations of the significance of EEG signal analysis and processing (with examples) and a useful theoretical and mathematical background for the analysis and processing of EEG signals; an exploration of normal and abnormal EEGs, neurological symptoms and diagnostic information, and representations of the EEGs; reviews of theoretical approaches in EEG modelling, such as restoration, enhancement, segmentation, and the removal of different internal and external artefacts from the EEG and ERP (event-related potential) signals; coverage of major abnormalities such as seizure, and mental illnesses such as dementia, schizophrenia, and Alzheimer's disease, together with their mathematical interpretations from the EEG and ERP signals and sleep phenomenon; descriptions of nonlinear and adaptive digital signal processing techniques for abnormality detection, source localization and brain-computer interfacing using multi-channel EEG data with emphasis on non-invasive techniques, together with future topics for research in the area of EEG signal processing. © 2007 by John Wiley & Sons Ltd,. All Rights Reserved.

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EEG Signal Processing

A gradient-based alternating minimization approach for optimization of the measurement matrix in compressive sensing

Artifacts such as eye blinks and heart rhythm (ECG) cause the main interfering signals within electroencephalogram (EEG) measurements. Therefore, we propose a method for artifact removal based on exploitation of certain carefully chosen statistical features of independent components extracted from the EEGs, by fusing support vector machines (SVMs) and blind source separation (BSS). We use the second-order blind identification (SOBI) algorithm to separate the EEG into statistically independent sources and SVMs to identify the artifact components and thereby to remove such signals. The remaining independent components are remixed to reproduce the artifact-free EEGs. Objective and subjective assessment of the simulation results shows that the algorithm is successful in mitigating the interference within EEGs.

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Artifact removal from electroencephalograms using a hybrid BSS-SVM algorithm

Gait analysis continues to be an important technique for many clinical applications to diagnose and monitor certain diseases. Many mental and physical abnormalities cause measurable differences in a person's gait. Gait analysis has applications in sport, computer games, physical rehabilitation, clinical assessment, surveillance, human recognition, modeling, and many other fields. There are established methods using various sensors for gait analysis, of which accelerometers are one of the most often employed. Accelerometer sensors are generally more user friendly and less invasive. In this paper, we review research regarding accelerometer sensors used for gait analysis with particular focus on clinical applications. We provide a brief introduction to accelerometer theory followed by other popular sensing technologies. Commonly used gait phases and parameters are enumerated. The details of selecting the papers for review are provided. We also review several gait analysis software. Then we provide an extensive report of accelerometry-based gait analysis systems and applications, with additional emphasis on trunk accelerometry. We conclude this review with future research directions.

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A Review on Accelerometry-Based Gait Analysis and Emerging Clinical Applications

In this paper the problem of Compressive Sensing (CS) is addressed. The focus is on estimating a proper measurement matrix for compressive sampling of signals. The fact that a small mutual coherence between the measurement matrix and the representing matrix is a requirement for achieving a successful CS is now well known. Therefore, designing measurement matrices with smaller coherence is desired. In this paper a gradient descent method is proposed to optimize the measurement matrix. The proposed algorithm is designed to minimize the mutual coherence which is described as absolute off-diagonal elements of the corresponding Gram matrix. The optimization is mainly applied to random Gaussian matrices which is common in CS. An extended approach is also presented for sparse signals with respect to redundant dictionaries. Our experiments yield promising results and show higher reconstruction quality of the proposed method compared to those of both unoptimized case and previous methods.

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Saeid Sanei

Papers

EEG Signal Processing

A gradient-based alternating minimization approach for optimization of the measurement matrix in compressive sensing

Artifact removal from electroencephalograms using a hybrid BSS-SVM algorithm

A Review on Accelerometry-Based Gait Analysis and Emerging Clinical Applications

On optimization of the measurement matrix for compressive sensing