ysaditya - 1 month ago 9

R Question

I need to Perform kernel PCA on the colon-‐cancer dataset:

and then

I need to Plot number of principal components vs classification accuracy with PCA data.

For the first part i am using kernlab in R as follows (let number of features be 2 and then i will vary it from say 2-100)

`kpc <- kpca(~.,data=data[,-1],kernel="rbfdot",kpar=list(sigma=0.2),features=2)`

I am having tough time to understand how to use this PCA data for classification ( i can use any classifier for eg SVM)

data looks like this (cleaned data)

uncleaned original data looks like this

Answer

I will show you a small example on how to use the `kpca`

function of the `kernlab`

package here:

I checked the colon-cancer file but it needs a bit of cleaning to be able to use it so I will use a random data set to show you how:

Assume the following data set:

```
y <- rep(c(-1,1), c(50,50))
x1 <- runif(100)
x2 <- runif(100)
x3 <- runif(100)
x4 <- runif(100)
x5 <- runif(100)
df <- data.frame(y,x1,x2,x3,x4,x5)
> df
y x1 x2 x3 x4 x5
1 -1 0.125841208 0.040543611 0.317198114 0.40923767 0.635434021
2 -1 0.113818719 0.308030825 0.708251147 0.69739496 0.839856000
3 -1 0.744765204 0.221210582 0.002220568 0.62921565 0.907277935
4 -1 0.649595597 0.866739474 0.609516644 0.40818013 0.395951297
5 -1 0.967379006 0.926688915 0.847379556 0.77867315 0.250867680
6 -1 0.895060293 0.813189446 0.329970821 0.01106764 0.123018797
7 -1 0.192447416 0.043720717 0.170960540 0.03058768 0.173198036
8 -1 0.085086619 0.645383728 0.706830885 0.51856286 0.134086770
9 -1 0.561070374 0.134457795 0.181368729 0.04557505 0.938145228
```

In order to run the `pca`

you need to do:

```
kpc <- kpca(~.,data=data[,-1],kernel="rbfdot",kpar=list(sigma=0.2),features=4)
```

which is the same way as you use it. However, I need to point out that the features argument is the number of **principal components** and not the number of classes in your `y`

variable. Maybe you knew this already but having 2000 variables and producing only 2 principal components might not be what you are looking for. You need to choose this number carefully by checking the eigen values. In your case I would probably pick 100 principal components and chose the first n number of principal components according to the highest eigen values. Let's see this in my random example after running the previous code:

In order to see the eigen values:

```
> kpc@eig
Comp.1 Comp.2 Comp.3 Comp.4
0.03756975 0.02706410 0.02609828 0.02284068
```

In my case all of the components have extremely low eigen values because my data is random. In your case I assume you will get better ones. You need to choose the n number of components that have the highest values. A value of zero shows that the component does not explain any of the variance. (Just for the sake of the demonstration I will use all of them in the svm below).

In order to access the principal components i.e. the PCA output you do this:

```
> kpc@pcv
[,1] [,2] [,3] [,4]
[1,] -0.1220123051 1.01290883 -0.935265092 0.37279158
[2,] 0.0420830469 0.77483019 -0.009222970 1.14304032
[3,] -0.7060568260 0.31153129 -0.555538694 -0.71496666
[4,] 0.3583160509 -0.82113573 0.237544936 -0.15526000
[5,] 0.1158956953 -0.92673486 1.352983423 -0.27695507
[6,] 0.2109994978 -1.21905573 -0.453469345 -0.94749503
[7,] 0.0833758766 0.63951377 -1.348618472 -0.26070127
[8,] 0.8197838629 0.34794455 0.215414610 0.32763442
[9,] -0.5611750477 -0.03961808 -1.490553198 0.14986663
...
...
```

This returns a matrix of 4 columns i.e. the number of the features argument which is the PCA output i.e. the principal components. `kerlab`

uses the S4 Method Dispatch System and that is why you use `@`

at `kpc@pcv`

.

You then need to use the above matrix to feed in an svm in the following way:

```
svmmatrix <- kpc@pcv
library(e1071)
svm(svmmatrix, as.factor(y))
Call:
svm.default(x = svmmatrix, y = as.factor(y))
Parameters:
SVM-Type: C-classification
SVM-Kernel: radial
cost: 1
gamma: 0.25
Number of Support Vectors: 95
```

And that's it! A very good explanation I found on the internet about pca can be found here in case you or anyone else reading this wants to find out more.