MATLAB for Brain and Cognitive Scientists

Transcription

1 MATLAB for Brain and Cognitive Scientists Mike X Cohen The MIT Press Cambridge, Massachusetts London, England 10947_000.indd 3

2 2017 Massachusetts Institute of Technology All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher. This book was set in Stone Sans and Stone Serif by Toppan Best-set Premedia Limited. Printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Names: Cohen, Mike X., author. Title: MATLAB for brain and cognitive scientists / Mike X. Cohen. Description: Cambridge, MA : MIT Press, [2017] Includes bibliographical references and index. Identifiers: LCCN ISBN (h : alk. paper) Subjects: LCSH: MATLAB. Neurosciences--Data processing. Cognitive science--data processing. Classification: LCC QP357.5.C DDC dc23 LC record available at _000.indd 4

3 Preface xv Part I: Introductions 1 1 What Is MATLAB and Why Use It? I Want to Be a Scientist; Do I Also Need to Be a Good Programmer? Octave Python, Julia, C, R, SPSS, HTML, and So Forth How Long Does It Take to Become a Good Programmer? How to Learn How to Program The Three Steps of Programming How Best to Learn from This Book Exercises and Their Solutions Written Interviews Where Is All the Code? Can I Use the Code in This Book for Real Data Analyses? Is This Book Right for You? Are You Excited? 12 2 The Philosophy of Data Analysis Keep It Simple Stay Close to the Data Understand Your Analyses Use Simulations, but Trust Real Data Beware the Paralysis of Analysis Be Careful of Overfitting Noise in Neuroscience Data Avoid Circular Inference Get Free Data _000.indd 5

4 vi 3 Do Replicable Research Avoid Mistakes in Data Analysis Have a Large Enough N Maximize Level 1 Data Count Try Different Analysis Parameters, and Trust Analytic Convergence Don t Be Afraid to Report Small or Null Effects, but Be Honest About Them Do Split-Half Replication Independent Replications Write a Clear Methods Section Make Your Analysis Code or Data Available 30 4 The MATLAB Program The MATLAB Program Graphical User Interface Layouts and Visual Preferences Color-Coordinating MATLAB Where Does the Code Go? MATLAB Files and Formats Changing Directories Inside MATLAB The MATLAB Path Comments Cells Keyboard Shortcuts Help Box and Reporting Variable Content The Code Analyzer Back Up Your Scripts, and Use Only One Version MATLAB Etiquette 46 5 Variables Creating and Destroying Variables Whos Are My Variables? Variable Naming Conventions and Tips Variables for Numbers Variables for Truth Variables for Strings Variables for Cells Variables for Structures The Colon Operator Accessing Parts of Variables via Indexing Initializing Variables Soft-coding versus Hard-coding _000.indd 6

5 vii 5.13 Keep It Simple Exercises 62 6 Functions Introduction to Functions Outputs as Inputs Multiple Inputs, Multiple Outputs Help Functions Are Files Writing Your Own Function Functions in Functions Arguments In Think Global, Act Local Stepping into Functions When to Use Your Own Functions When to Modify Existing Functions Timing Functions Using the Profiler Exercises 80 7 Control Statements The Anatomy of a Control Statement If-then For-loop Skipping Forward While-loop Try-catch Switch-case Pause Exercises 99 8 Input-Output Copy-Paste Loading.mat Files Saving.mat Files Importing Text Files Exporting Text Files Importing and Exporting Microsoft Excel Files Importing and Exporting Hardware-Specific Data Files Interacting with Your Operating System via MATLAB Exercises Plotting What You Need to Know Before You Know Anything Else Plotting Lines _000.indd 7

6 viii 9.3 Bars Scatter Plots Histograms Subplots Patch Images Get, Set, and Handle Text in Plots Interacting with MATLAB Plots Creating a Color Axis Saving Figures as Picture Files Exercises 141 Part II: Foundations Matrix Algebra Vectors Vector Addition and Multiplication Matrices Finding Your Way around a Matrix Matrix Multiplication When to Use.* and./ versus * and /? Linear Independence and Rank The Matrix Inverse Solving Ax = b Making Symmetric Squares from Rectangles Full and Sparse Matrices Exercises The Fourier Transform Sine Waves The Imaginary Operator and Complex Numbers The Complex Dot Product Time Domain and Frequency Domain The Slow Fourier Transform Frequencies from the Fourier Transform The Fast Fourier Transform Fourier Coefficients as Complex Numbers DC Offsets in the Fourier Transform Zero-Padding the Fourier Transform The Inverse Fourier Transform _000.indd 8

7 ix The 2D Fourier Transform Exercises Convolution Time-Domain Convolution The Convolution Theorem Convolution Implemented in the Frequency Domain Convolution in Two Dimensions Exercises Interpolation and Extrapolation The MATLAB Functions griddedinterpolant and scatteredinterpolant Interpolation in Two Dimensions Using scatteredinterpolant Using interp* Functions Zero-Padding Theorem and Zero-Padding Down-sampling Exercises Signal Detection Theory The Four Categories of Correspondence Discrimination Isosensitivity Curves (a.k.a. ROC Curves) Response Bias Conditional Accuracy Functions Exercises Nonparametric Statistics The Idea of Permutation-Based Statistics Creating an Empirical Null Hypothesis Test Creating a Null Hypothesis Distribution Evaluating Significance Example with Real Data Extreme Value Based Correction for Multiple Comparisons Meta-permutation Tests Exercises Covariance and Correlation Simulating and Measuring Bivariate Covariance Multivariate Covariance From Covariance to Correlation Pearson and Spearman Correlations Statistical Significance of Correlation Coefficients Geometric Interpretation of Correlation Exercises _000.indd 9

8 x 17 Principal Components Analysis Eigendecomposition Simple Example with 2D Random Data PCA and Coordinate Transformation Eigenfaces Independent Components Analysis Exercises 280 Part III: Analyses of Time Series Frequency Analyses Blitz Review of the Fourier Transform Frequency Resolution Edge Artifacts and Data Tapering Many FFTs for Many Trials Defining and Extracting Frequency Ranges Effects of Nonstationarities Spectral Coherence Steady-State Evoked Potentials Exercises Time-Frequency Analysis Complex Morlet Wavelets Morlet Wavelet Convolution From Line to Plane From Single Trial to Super-trial Edge Artifacts STFFT Baseline Normalization Time-Frequency Analysis in Real EEG Data Exercises Time Series Filtering Running-Mean Filter Running-Median Filter Edges in the Frequency Domain Gaussian Narrow-Band Filtering Finite Impulse Response Filter The Hilbert Transform Exercises Fluctuation Analyses Root Mean Square to Measure Fluctuations _000.indd 10

9 xi 21.2 Fluctuations in Time Series Multichannel RMS Detrended Fluctuation Analysis Demeaned Fluctuation Analysis Local and Global Minima and Maxima Exercises 367 Part IV: Analyses of Action Potentials Spikes in Full and Sparse Matrices Spike Times as Full Matrices and as Sparse Vectors Mean Spike Count in Spikes per Second Peri-event Time Spike Histogram Exercises Spike Timing Spike Rhythmicity Spike Rhythmicity via the Frequency Domain Cross-Neuron Spike-Time Correlations Spike-Field Coherence Frequency-Specific Spike-Field Coherence Exercises Spike Sorting Spike Amplitude and Width Spike Features via Principal Components Analysis Spike Features via Independent Components Analysis Clustering Spikes into Discrete Groups Exercises 403 Part V: Analyses of Images Magnetic Resonance Images Importing and Plotting MRI Data fmri Data as a Four-Dimensional Volume fmri Statistics and Thresholding Exercises Image Segmentation Threshold-Based Segmentation Intensity-Based Segmentation Once More, with Calcium Defining Grids in Images _000.indd 11

10 xii 26.5 Fractals and Boxes Exercises Image Smoothing and Sharpening Two-Dimensional Mean Filtering Two-Dimensional Median Filter Gaussian Kernel Smoothing Image Filtering in the Frequency Domain Exercises 447 Part VI: Modeling and Model Fitting Linear Methods to Fit Models to Data Least-Squares Fitting Evaluating Model Fits Polynomial Fitting Using polyfit and polyval Example: Reaction Time and EEG Activity Data Transformations Adjust Distributions Exercises Nonlinear Methods to Fit Models to Data Nonlinear Model Fitting with fminsearch Nonlinear Model Fitting: Piece-wise Regression Nonlinear Model Fitting: Gaussian Function Nonlinear Model Fitting: Caught in Local Minima Discretizing and Binning Data Exercises Neural and Cognitive Simulations Integrate-and-Fire Neurons From Neuron to Networks Izhikevich Neurons Rescorla-Wagner Exercises Classification and Clustering Neural Networks with Backpropagation Learning K-means Clustering Support Vector Machines Exercises 515 Part VII: User Interfaces and Movies Graphical User Interfaces Basic GUIs _000.indd 12

11 xiii 32.2 Getting to Know GUIDE Writing Code in GUI Functions Exercises Movies Waving Lines Moving Gabor Patches Spinning Heads Exercises 543 References 545 Index 549 List of Interviews Chapter 13: Robert Oostenveld 215 Chapter 16: Hualou Liang 258 Chapter 17: Pascal Wallisch 276 Chapter 19: Arnaud Delorme 321 Chapter 21: Simon-Shlomo Poil 364 Chapter 24: Rodrigo Quian Quiroga 399 Chapter 26: Dylan Richard Muir 429 Chapter 30: Eugene M. Izhikevich 496 Chapter 32: Vladimir Litvak _000.indd 13