How to perform Principal component analysis

Question

Mekala balaji 2016-7-30

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链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/297760-how-to-perform-principal-component-analysis

评论： the cyclist 2016-7-31

Hi,

I have 10 variables, and the correlation between each single variable is very poor, so I want to perform the PCA such as to see the correlation by grouping the variable based on their similar behaviour (similar Rsquare or similar correlation coefficient). Please someone help.

My input data(Each column represent a variable, column1-->Variable1, Column2--> Varaible2,...Column10-->Variable10, for each variable I have 25 observations)

74   0.83   0.85   0.63   0.15   0.62   0.56   0.18   0.46   0.53 
39   0.77   0.56   0.66   0.19   0.57   0.85   0.21   0.10   0.73 
68   0.17   0.93   0.73   0.04   0.05   0.35   0.91   1.00   0.71 
70   0.86   0.70   0.89   0.64   0.93   0.45   0.68   0.33   0.78 
44   0.99   0.58   0.98   0.28   0.73   0.05   0.47   0.30   0.29 
02   0.51   0.82   0.77   0.54   0.74   0.18   0.91   0.06   0.69 
33   0.88   0.88   0.58   0.70   0.06   0.66   0.10   0.30   0.56 
42   0.59   0.99   0.93   0.50   0.86   0.33   0.75   0.05   0.40 
27   0.15   0.00   0.58   0.54   0.93   0.90   0.74   0.51   0.06 
20   0.20   0.87   0.02   0.45   0.98   0.12   0.56   0.76   0.78 
82   0.41   0.61   0.12   0.12   0.86   0.99   0.18   0.63   0.34 
43   0.75   0.99   0.86   0.49   0.79   0.54   0.60   0.09   0.61 
89   0.83   0.53   0.48   0.85   0.51   0.71   0.30   0.08   0.74 
39   0.79   0.48   0.84   0.87   0.18   1.00   0.13   0.78   0.10 
77   0.32   0.80   0.21   0.27   0.40   0.29   0.21   0.91   0.13 
40   0.53   0.23   0.55   0.21   0.13   0.41   0.89   0.53   0.55 
81   0.09   0.50   0.63   0.56   0.03   0.46   0.07   0.11   0.49 
76   0.11   0.90   0.03   0.64   0.94   0.76   0.24   0.83   0.89 
38   0.14   0.57   0.61   0.42   0.30   0.82   0.05   0.34   0.80 
22   0.68   0.85   0.36   0.21   0.30   0.10   0.44   0.29   0.73 
79   0.50   0.74   0.05   0.95   0.33   0.18   0.01   0.75   0.05 
95   0.19   0.59   0.49   0.08   0.47   0.36   0.90   0.01   0.07 
33   0.50   0.25   0.19   0.11   0.65   0.06   0.20   0.05   0.09 
67   0.15   0.67   0.12   0.14   0.03   0.52   0.09   0.67   0.80 
44   0.05   0.08   0.21   0.17   0.84   0.34   0.31   0.60   0.94

Many thanks in advance.

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Answer 1

the cyclist 2016-7-30

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https://ww2.mathworks.cn/matlabcentral/answers/297760-how-to-perform-principal-component-analysis#answer_230276

If you have the Statistics and Machine Learning Toolbox, you can used the pca function.

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Answer 2

Image Analyst 2016-7-30

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/297760-how-to-perform-principal-component-analysis#answer_230280

编辑：Image Analyst 2016-7-30

在 MATLAB Online 中打开

See plotmatrix() in the Statistics and Machine Learning Toolbox.

To "see the correlation":

plotmatrix(yourMatrix);

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Image Analyst 2016-7-30

在 MATLAB Online 中打开

You can do

m = [...
74   0.83   0.85   0.63   0.15   0.62   0.56   0.18   0.46   0.53 
39   0.77   0.56   0.66   0.19   0.57   0.85   0.21   0.10   0.73 
68   0.17   0.93   0.73   0.04   0.05   0.35   0.91   1.00   0.71 
70   0.86   0.70   0.89   0.64   0.93   0.45   0.68   0.33   0.78 
44   0.99   0.58   0.98   0.28   0.73   0.05   0.47   0.30   0.29 
02   0.51   0.82   0.77   0.54   0.74   0.18   0.91   0.06   0.69 
33   0.88   0.88   0.58   0.70   0.06   0.66   0.10   0.30   0.56 
42   0.59   0.99   0.93   0.50   0.86   0.33   0.75   0.05   0.40 
27   0.15   0.00   0.58   0.54   0.93   0.90   0.74   0.51   0.06 
20   0.20   0.87   0.02   0.45   0.98   0.12   0.56   0.76   0.78 
82   0.41   0.61   0.12   0.12   0.86   0.99   0.18   0.63   0.34 
43   0.75   0.99   0.86   0.49   0.79   0.54   0.60   0.09   0.61 
89   0.83   0.53   0.48   0.85   0.51   0.71   0.30   0.08   0.74 
39   0.79   0.48   0.84   0.87   0.18   1.00   0.13   0.78   0.10 
77   0.32   0.80   0.21   0.27   0.40   0.29   0.21   0.91   0.13 
40   0.53   0.23   0.55   0.21   0.13   0.41   0.89   0.53   0.55 
81   0.09   0.50   0.63   0.56   0.03   0.46   0.07   0.11   0.49 
76   0.11   0.90   0.03   0.64   0.94   0.76   0.24   0.83   0.89 
38   0.14   0.57   0.61   0.42   0.30   0.82   0.05   0.34   0.80 
22   0.68   0.85   0.36   0.21   0.30   0.10   0.44   0.29   0.73 
79   0.50   0.74   0.05   0.95   0.33   0.18   0.01   0.75   0.05 
95   0.19   0.59   0.49   0.08   0.47   0.36   0.90   0.01   0.07 
33   0.50   0.25   0.19   0.11   0.65   0.06   0.20   0.05   0.09 
67   0.15   0.67   0.12   0.14   0.03   0.52   0.09   0.67   0.80 
44   0.05   0.08   0.21   0.17   0.84   0.34   0.31   0.60   0.94 ]
% plotmatrix(m)
[coeff,score,latent,tsquared,explained,mu] = pca(m)

I didn't group columns together. You can concatenate columns to do your groupings.

Image Analyst 2016-7-31

I don't know what that means. There is no question mark, so is that a question? What do you mean by automatically as opposed to manually in this situation?

But how can you group different number of observations (columns) together. If so, then how can you compare a new columns with 3 columns grouped together with another one that has only 2 columns grouped together?

the cyclist 2016-7-31

Mekala, PCA is a specific technique that has a specific use. It seems like you need a deeper understand of the technique. It is difficult to teach you all of PCA in this forum.

What PCA "automatically" does is calculate the combination of variables that explains the most variation of another variable. There is no "manual" grouping in the function.

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