Geometric Approach to High Dimensional Engineering Problems

Contents

• Electronic Study Book for this Part (pdf)
• Some data files
• Tutorials
• Errata for Study Book 2003

Some data files

1. gallery.mat: low resolution (24x16) gray scale images of a gallery of 30 faces for analysis (formed into a 30x384 array "b")
2. lena128.bmp: a 128x128 gray scale bitmap image for compression and reconstruction
3. soirain.m: matlab script giving the data for the SOI and rainfall for 383 seasons in the past
4. soiav.m: matlab script giving the 20 season running averages of the seasonal SOI.

Tutorials

1. Tutorial 1. Download the above files containing images and learn how to display them. Click here to download or to view the file with the sample MATLAB code.
2. Tutorial 2. Read all comments carefully while you are executing the following codes.
• Least square and covariance matrix approaches for finding the best fit straight lines through the scattered data. Download and run this matlab file .
• Image decomposition and reconstruction using SVD. Download and run this matlab file .
• Image compression using SVD. Download and run this matlab file .
3. Tutorial 3.
• The Gibbs phenomenon in the Fourier series of discontinuous functions. Download this matlab file and read all comments carefully while you are executing the code. Be aware that decomposing a discontinuous function using any set of continuous functions always leads to a finite magnitude overshoot in the vicinity of the discontinuity no matter how many terms you use in your decomposition. The width of this overshoot decreases when the number of terms in the series increases.
• Fourier transform of the time series. Download this matlab file and read all comments carefully while you are executing the code. This example confirms the four season periodicity as determined in Ex. 22.32 of the study guide through the analysis of the power spectrum of the rainfall data. Run the code for m=1 and see if you can recover the results obtained using the SVD of SOI data as discussed in Example 22.19. Try to explain the difference noting that in contrast to the Fourier exponents the singular vectors depicted in Figure 22.13 in the study guide are not perfectly periodic.

Errata for Study Book for 2003

• None found yet