Assignment GSOC 2016 project

Motivation

Since many machine learning algorithms rely on matrices it is important to master matrix manipulation. Therefore, the following assignment is proposed.

Assignment

The successful student should demonstrate a clean implementation of the NIPALS algorithm. In statistics, non-linear iterative partial least squares (NIPALS) is an algorithm for computing the first few components in a principal component or partial least squares analysis. For very-high-dimensional datasets it is usually only necessary to compute the first few principal components.

Here is the description of the algorithm: pca_nipals.

Testing data: pcadata

 

 

 

 

 

$$\begin{pmatrix}0.5376671395461 & -1.34988694015652 & 0.671497133608081 & 0.888395631757642 & -0.102242446085491\cr 1.83388501459509 & 3.03492346633185 & -1.20748692268504 & -1.14707010696915 & -0.241447041607358\cr -2.25884686100365 & 0.725404224946106 & 0.717238651328839 & -1.06887045816803 & 0.319206739165502\cr 0.862173320368121 & -0.0630548731896562 & 1.63023528916473 & -0.809498694424876 & 0.312858596637428\cr 0.318765239858981 & 0.714742903826096 & 0.488893770311789 & -2.9442841619949 & -0.864879917324457\cr -1.30768829630527 & -0.204966058299775 & 1.03469300991786 & 1.4383802928151 & -0.0300512961962686\cr -0.433592022305684 & -0.124144348216312 & 0.726885133383238 & 0.325190539456198 & -0.164879019209038\cr 0.34262446653865 & 1.48969760778547 & -0.303440924786016 & -0.754928319169703 & 0.627707287528727\cr 3.57839693972576 & 1.40903448980048 & 0.293871467096658 & 1.37029854009523 & 1.09326566903948\cr 2.76943702988488 & 1.41719241342961 & -0.787282803758638 & -1.7115164188537 & 1.1092732976144\end{pmatrix}$$

Hint: The second T component is

$$\begin{pmatrix}1.660216125606425\cr -1.051259702224144\cr -1.669934902174654\cr 0.2265172335344322\cr -2.365906683261095\cr 1.06347394301301\cr 0.4215061657724768\cr -0.6249919834179163\cr 2.693294214551594\cr -0.3529144114001289\end{pmatrix}$$

and P  is

$$\begin{pmatrix}0.4233935251355345\cr -0.2926014769271022\cr 0.1433716236799124\cr 0.8271416668709591\cr 0.1743661062899016\end{pmatrix}$$