### Translated by

このページのコンテンツは英語から自動翻訳されています。自動翻訳をオフにする場合は「<a class="turn_off_mt" href="#">ここ</a>」をクリックしてください。

## PCA in Matlab reduce dimensionality

Matlaber

### Matlaber (view profile)

さんによって質問されました 2019 年 2 月 19 日

### Matlaber (view profile)

さんによって コメントされました 2019 年 2 月 21 日
Elysi Cochin

### Elysi Cochin (view profile)

さんの 回答が採用されました
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

Matlaber

### Matlaber (view profile)

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:
[coeff, score] = pca(ingredients);
reducedDimension = score(:,1:3);
Result of Score is 13*4 matrix
Result of ReduceDimension is 13*3 matrix
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?

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

### Matlaber (view profile)

2019 年 2 月 21 日
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.

サインイン to comment.

## 1 件の回答

### Elysi Cochin (view profile)

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

Matlaber

### Matlaber (view profile)

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.
[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

### Matlaber (view profile)

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:
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

サインイン to comment.

Translated by