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# AMATH 563 Homework 1 Regression, Model Selection and DMD solved

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Download the MNIST data set (both training and test sets and labels): http://yann.lecun.com/exdb/mnist/.
The labels will tell you which digit it is: 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. Let each output be denoted by the vector yj
.
“1” =

1
0
0
.
.
.

0
0

, “2” =

0
1
0
.
.

.
0
0

, · · · , “9” =

0
0
0
.
.
.
1
0

, “0” =

0
0
0
.
.
.
0
1

(1)

Now let B be the set of output vectors
B = [y1 y2 y3 · · · yn] (2)
and let the matrix A be the corresponding reshaped (vectorized) MNIST images
A = [x1 x2 x3 · · · xn] (3)
Thus each vector xj ∈ R
n
2
is an a vector reshaped from the n × n image.

1. Using various AX = B solvers, determine a mapping from the image space to the label space.
2. By promoting sparsity, determine and rank which pixels in the MNIST set are most informative for
correctly labeling the digits. (You’ll have to come up with your own heuristics or empirical rules for