English | MP4 | AVC 1920×1080 | AAC 44KHz 2ch | 100 Lessons (17h 34m) | 6.36 GB
Learn and apply cutting-edge data analysis techniques for “big neurodata” (theory and MATLAB/Python code)
What is this course all about?
Neuroscience (brain science) is changing — new brain-imaging technologies are allowing increasingly huge data sets, but analyzing the resulting Big Data is one of the biggest struggles in modern neuroscience (if don’t believe me, ask a neuroscientist!).
The increases in the number of simultaneously recorded data channels allows new discoveries about spatiotemporal structure in the brain, but also presents new challenges for data analyses. Because data are stored in matrices, algorithms developed in linear algebra are extremely useful.
The purpose of this course is to teach you some matrix-based data analysis methods in neural time series data, with a focus on multivariate dimensionality reduction and source-separation methods. This includes covariance matrices, principal components analysis (PCA), generalized eigendecomposition (even better than PCA!), and independent components analysis (ICA). The course is mathematically rigorous but is approachable to individuals with no formal mathematics background. The course comes with MATLAB and Python code (note that the videos show the MATLAB code and the Python code is a close match).
You should take this course if you are a…
- neuroscience researcher who is looking for ways to analyze your multivariate data.
- student who wants to be competitive for a neuroscience PhD or postdoc position.
- non-neuroscientist who is interested in learning more about the big questions in modern brain science.
- independent learner who wants to advance your linear algebra knowledge.
- mathematician, engineer, or physicist who is curious about applied matrix decompositions in neuroscience.
- person who wants to learn more about principal components analysis (PCA) and/or independent components analysis (ICA)
- intrigued by the image that starts off the Course Preview and want to know what it means! (The answers are in this course!)
Unsure if this course is right for you?
I worked hard to make this course accessible to anyone with at least minimal linear algebra and programming background. But this course is not right for everyone. Check out the preview videos and feel free to contact me if you have any questions.
What you’ll learn
- Understand advanced linear algebra methods
- Includes a 3+ hour “crash course” on linear algebra
- Apply advanced linear algebra methods in MATLAB and Python
- Simulate multivariate data for testing analysis methods
- Analyzing multivariate time series datasets
- Appreciate the challenges neuroscientists are struggling with!
- Learn about modern neuroscience data analysis
Who this course is for:
- Anyone interested in next-generation neuroscience data analyses
- Learners with interest in applied linear algebra to modern big-data challenges
- Neuroscientists dealing with “big data”
- Mathematicians, engineers, and physicists who are interested in learning about neuroscience data
Table of Contents
Introduction
1 Target audience and learning from this course
2 What is multivariate neuroscience
3 What are linear spatial filters
4 Why spatial filters are useful for neuroscience
Download all course materials
5 IMPORTANT Download all course materials
6 Download Python code
Dimensions and sources
7 The concept of dimension in measured signals
8 The concept of source in measured signals
9 Sources mixing and unmixing
10 Dimension reduction vs source separation
11 Linear vs nonlinear filtering
12 Data requirements for source separation
Linear algebra crash course
13 Introduction to this section
14 Vectors and matrices
15 Vector multiplications incl dot product
16 Matrix multiplications
17 MATLAB vectors and matrices
18 Linear independence
19 Matrix rank
20 Shifting a matrix
21 MATLAB rank and shifting
22 Matrix inverse
23 A transpose A
24 MATLAB Inverse and AtA
25 Eigenvaluesvectors and diagonalization
26 The singular value decomposition SVD
27 SVD for compression
28 MATLAB eig and svd
Creating and interpreting covariance matrices
29 Using real and simulated data
30 Correlation and covariance terms and matrices
31 Creating covariance matrices in data
32 MATLAB covariance of simulated data
33 MATLAB covariance with real data
34 Proof Covariance matrices are symmetric
35 Evaluating and improving covariance quality
36 MATLAB Single trial covariance distances
37 The quadratic form and the covariance surface
38 MATLAB visualizing the quadratic form
Dimension reduction with PCA
39 PCA Goals objective and solution
40 MATLAB PCA intuition with 2D data
41 How to perform a principal components analysis
42 Exercise PCA on nonphaselocked data
43 The geometry of PCA
44 Proof of principal component orthogonality
45 Scree plots and eigenspectra
46 MATLAB PCA of simulated EEG data
47 MATLAB PCA of real EEG data
48 Exercise Repeat PCA using pca
49 MATLAB importance of meancentering for PCA
50 Dimension reduction using SVD instead of eigendecomposition
51 MATLAB PCA via SVD and covariance
52 PCA for statespace representation
53 MATLAB statespace representation via PCA
54 MATLAB PCA on multitrial data
55 Limitations of principal components analysis
Source separation with GED
56 Tutorial paper on GED
57 Hypothesisdriven motivation for GED
58 GED Goals objective and solution
59 MATLAB GED intuition with covariance surfaces
60 GED weights and nonorthogonality
61 MATLAB GED in a simple example
62 Visualizing the spatial filter vs spatial patterns
63 Component sign uncertainty
64 MATLAB Adjusting component signs
65 MATLAB 2 components in simulated EEG data
66 Constructing the S and R matrices
67 MATLAB Taskrelevant component in EEG
68 MATLAB Spectral scanning in MEG and EEG
69 Twostage compression and source separation
70 Exercise Twostage source separation in real EEG data
71 ZCA prewhitening
72 MATLAB Simulated data with and without ZCA
73 Exercise ZCAtwostage separation on real EEG data
74 Source separation with nonstationary covariances
75 MATLAB Simulated EEG data with alternating dipoles
76 Regularization Theory math and intuition
77 MATLAB Effects of regularization in real data
78 Empirical methods for regularization amount
79 MATLAB Regularization crossvalidation
80 Complexvalued solutions
81 MATLAB GED vs factor analysis
Source separation for steadystate responses
82 The steadystate evoked potential
83 Motivations for a spatial filter for the steadystate response
84 RESS analysis pipeline
85 MATLAB example with real EEG data
Independent components analysis ICA
86 Overview of independent components analysis
87 MATLAB Data distributions and ICA
88 MATLAB ICA PCA GED on simulated data
89 MATLAB Explore IC distributions in real data
Overfitting and inferential statistics
90 What is overfitting and why is it inappropriate
91 Unbiased filter creation and application
92 Crossvalidation in vs outofsample testing
93 Permutation testing
94 MATLAB Permutation testing
Big questions in multivariate neuroscience
95 Math physiology and anatomy
96 Functional networks vs volume conduction
97 Interpreting individual differences
98 A surfeit of source separation selections and a reading list
99 Is reducing dimensionality always good
Bonus section
100 Bonus lecture
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