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Matlaber
0

PCA in Matlab reduce dimensionality

Matlaber
さんによって質問されました 2019 年 2 月 19 日
最新アクティビティ Matlaber
さんによって コメントされました 2019 年 2 月 21 日
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:
load hald
Then:
The dataset of ingredient is 13 * 4
Capture.PNG
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

  6 件のコメント

Matlaber
2019 年 2 月 20 日
Thanks.
I did that. However, it seemed throw away those matrix I do not want, is that means missing out some information by throwing away?
For example:
load hald
[coeff, score] = pca(ingredients);
reducedDimension = score(:,1:3);
Result of Score is 13*4 matrix
Capture.PNG
Result of ReduceDimension is 13*3 matrix
ssss.PNG
It looks like the 4th row is throwing away, is that mean dimension reduction using PCA?
looks like throwing the 4th row will miss some information?
Adam
2019 年 2 月 20 日
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
2019 年 2 月 21 日
Thanks for your reply.
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.

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1 件の回答

回答者: Elysi Cochin 2019 年 2 月 20 日
 採用された回答

[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

  2 件のコメント

Matlaber
2019 年 2 月 20 日
Thanks!
Do you mind explain what is the different between "coeff" and "score"?
I did read the documenation, unable to understand.
load hald
[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
2019 年 2 月 20 日
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:
load hald
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

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