# PCA in Matlab reduce dimensionality

38 views (last 30 days)
Matlaber on 19 Feb 2019
Commented: Matlaber on 21 Feb 2019
I just want to have a simple PCA to reduce my dimensionality of let say 400 * 5000 to 400 * 4
meaning reduce from 5000 to 4.
I am not sure where can i set the value of reduction.
coeff = pca(X)
I am trying to follow:
Then:
The dataset of ingredient is 13 * 4
coeff = pca(ingredients)
Output:
coeff = 4×4
-0.0678 -0.6460 0.5673 0.5062
-0.6785 -0.0200 -0.5440 0.4933
0.0290 0.7553 0.4036 0.5156
0.7309 -0.1085 -0.4684 0.4844
I am wondering can i change it to output of 13 *2
Edited: Adam on 20 Feb 2019
Dimension reduction is 'throwing some information away'. It isn't magic, unfortunately. Unless you have perfectly correlated redundant variables then if you have 8 variables and you want to reduce down to 3 dimensions then you will obviously lose some information.
Of course, doing it without PCA you would lose a huge amount of information if you just chop off 5 variables.
Because you have used PCA though you are throwing away the dimensions that contain least information about the data.
Looking at the explained output from PCA will help you see what you are throwing away. This is a measure of how much of the data variation is captured by each dimension. You will usually see a large number (between 0 and 100, e.g. 80) for the first, then progressivley smaller numbers. Unless your data is very random you will often find that after the first few principal components the values in the explained vector are < 1 (i.e. that dimension hold less than 1% of the information so that is all you lose if you throw that dimension away).
Matlaber on 21 Feb 2019
Yes, I checked the file of the PCA output, you are correct, usually large number for the first row and progressively smaller number.
Thanks once again.
Do you have any idea how can we use Linear Discriminant Analysis (LDA) aka. Fisher Discriminant Analysis (FDA) in matlab? It seemed do not have this function.

Elysi Cochin on 20 Feb 2019
[coeff, score] = pca(ingr);
requiredResult = score(:,1:2);
or if you want to change coeff to 13 x 2 matrix, you'll have to use reshape function, but to use reshape your variable coeff must have atleast 13 x 2 elements
or you can use repmat, it will repeat copies of the array coeff
Matlaber on 20 Feb 2019
Thanks!
Do you mind explain what is the different between "coeff" and "score"?
I did read the documenation, unable to understand.
[coeff, score] = pca(ingredients);
requiredResultscore = score(:,1:3);
requiredResultcoeff = coeff(:,1:3);
Orginal "ingredients" is 13*4 matrix
coefficient is 4 * 4 matrix
score is 13 * 4 matrix
requiredResultscore is 13 * 3 matrix
requiredResultcoeff is 4 * 3 matrix
Matlaber on 20 Feb 2019
The original dataset which is 'ingredient' is 13 * 4 matrix.
>> ingredients
ingredients =
7 26 6 60
1 29 15 52
11 56 8 20
11 31 8 47
7 52 6 33
11 55 9 22
3 71 17 6
1 31 22 44
2 54 18 22
21 47 4 26
1 40 23 34
11 66 9 12
10 68 8 12
After PCA:
coeff = pca(ingredients)
The output is of coeff is 4 * 4 matrix.
>> coeff
coeff =
-0.0678 -0.6460 0.5673 0.5062
-0.6785 -0.0200 -0.5440 0.4933
0.0290 0.7553 0.4036 0.5156
0.7309 -0.1085 -0.4684 0.4844
I am wondering how can I get a 13 * 2 matrix as output.
In your question "to use reshape your variable coeff must have atleast 13 x 2 elements". How can I get at least 13 * 2 elements.
Thanks