Deep Learning III: PCA in 2d_exercise (Stanford University UFLDL in depth learning tutorial)

Preface

This section is mainly to practice the use of PCA,PCA whitening and Zca whitening on 2D data, 2D data set is 45 data points, each data point is 2 dimensions.

Some MATLAB functions

Color Scatter point graph function: Scatter (x,y,c,s) x, y is two vectors for locating data points, S is the size of the plot point, C is the color used for the drawing, S and C can be given as vectors or expressions, s and C are marked as vectors of the same length as x or Y. Inch and color will change according to the linear law. You can also add the fifth parameter ' filled ' after the first 4 parameters of the scatter function, which means filling the drawing point. The biggest difference between scatter and plot is that scatter can draw a point graph with variable size and color.
Example: Given data t=0:pi/10:2*pi, Y=sin (t), observe the drawing results of the function at different input parameters.
T=0:pi/10:2*pi; Y=sin (t)
Subplot (3,2,1); Scatter (t,y)
Subplot (3,2,2); Scatter (t,y, ' V ')
Subplot (3,2,3); Scatter (T,y, (ABS (y) +2). ^4, ' filled ')
Subplot (3,2,4); Scatter (t,y,30,[0:2: +], ' V ', ' filled ')
Subplot (3,2,5); Scatter (T,y, (t+1). ^3,y, ' filled ')

diag function : extracting and creating diagonal matrices of diagonal elements

Set the following x as the square and V as the vector

1, X = Diag (v,k) when V is a vector containing n elements, the return of a n+abs (k) square matrix X, vector v in Matrix X on the K-Diagonal, k=0 represents the main diagonal, k>0 is represented above the main diagonal,k< 0 means below the main diagonal. Example 1:

V=[1 2 3];
Diag (V, 3)

Ans =

0 0 0 1 0 0
0 0 0 0 2 0
0 0 0 0 0 3
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0

Note: Data is generated diagonally from the third position above the main diagonal matrix.

Example 2:

V=[1 2 3];
Diag (V,-1)
Ans =
0 0 0 0
1 0 0 0
0 2 0 0
0 0 3 0

Note: Data is generated diagonally from the first position below the main diagonal matrix.

2, X = Diag (v)

The vector v is on the main diagonal of the square X, similar to the Diag (v,k), k=0 case.

Example 3:

V=[1 2 3];
Diag (v)

Ans =

1 0 0
0 2 0
0 0 3

Note: Written in the form of a diagonal matrix

3. v = diag (x,k)

Returns the column vector v,v formed by the elements on the K-diagonal of the matrix X

Example 4:

V=[1 0 3;2 3 1;4 5 3];
Diag (v,1)

Ans =

0
1

Note: The first data above the main diagonal is taken as the starting data, and is sorted in diagonal order as a column vector form

4, V = diag (x) returns the element on the main diagonal of matrix X, similar to Diag (X,K), Case 5 of K=0:

V=[1 0 0;0 3 0;0 0 3];
Diag (v)

Ans =

1
3
3

or instead:

V=[1 0 3;2 3 1;4 5 3];
Diag (v)

Ans =

1
3
3

Note: The data of the main diagonal is taken out as a column vector form

5,diag (diag (X))

Take the diagonal element of the X-matrix and construct a diagonal matrix with the diagonal of the X-diagonal element.
Example 6:

X=[1 2;3 4]
Diag (Diag (X))

X =

1 2
3 4

Ans =

1 0
0 4

Deep Learning III: PCA in 2d_exercise (Stanford University UFLDL in depth learning tutorial)