Kernel Statistics toolbox is still in development. Two algorithms are now available. One is kernel principal component analysis (KPCA). The other is kernel sliced inverse regression (KSIR).

• Construct principal components in the input space and feature space.
• Provide a preprocess for preventing ill-posed problem encountered in KSIR.
• Support linear, polynomial and radial basis kernels.
• Can handle large scale problems by using reduced kernel.

• Matlab implementation

Kernel Statistics toolbox is implemented in Matlab. Use a data format which can be loaded into Matlab. The instances are represented by a matrix (rows for instances and columns for variables) and the labels (1,2,...,k) or responses are represented by a column vector. Note that you also can represent the labels of binary classification by 1 or -1.

For classification

For regression

KStat toolbox contains two main functions: KDR for constructing PCs and UseKDR for using the results of KDR. Besides, users also can directly use the two core programs, KPCA and KSIR, for a specific kernel matrix.

Description for codes:

[Info] = KDR(label, inst, 'options')

• Construct ten PCs via KPCA by using Gaussian kernel
  [Info_one] = KDR([], inst, '-s 0 -t 2 -g 0.1 -p 10');
• Construct five PCs via reduced KPCA (10%) by using Gaussian kernel
  [Info_two] = KDR([], inst, '-s 0 -t 2 -p 5 -g 0.2 -r 0.1');
• Construct PCs of 90% eigenvalue via KPCA by using reduced polynomial kernel
  [Info_three] = KDR([], inst, '-s 0 -t 1 -p 0.9 -r 0.1 -d 2 -m 3 -b 2');
• Construct one PCs via KSIR by using Gaussian kernel for 2-class problems
  [Info_four] = KDR(label, inst, '-s 1 -t 2 -p 1 -z 0 -g 0.3');
• Construct 5 PCs via KSIR (30 slices) by using Gaussian kernel for regression problemsl
  [Info_five] = KDR(label, inst, '-s 1 -t 2 -p 1 -z 30 -g 0.2');

[ProjInst] = UseKDR(inst, Info)

• Get the projected inst form Info_one
  [ProjInst_one] = UseKDR(inst, Info_one);
• Get the projected inst form Info_four
  [ProjInst_four] = UseKDR(inst, Info_four);

[EigenVectors, EigenValues, ratio] = KPCA(K, NumOfPC);

• Construct ten PCs via KPCA by using a specific kernel matrix
  [EigenVectors, EigenValues, ratio] = KPCA(K, 10);
• Construct PCs whose ratio to the total sum is 95%
  [EigenVectors, EigenValues, ratio] = KPCA(K, 0.95);

[EigenVectors, EigenValues, ratio] = KSIR(K, y, NumOfSlice, NumOfPC)

• Construct PCs via KSIR for classification by using a specific kernel matrix
  [EigenVectors, EigenValues, ratio] = KSIR(K, y, 'CLASS');
• Construct two PCs via KSIR for 3-class problem
  [EigenVectors, EigenValues, ratio] = KSIR(K, y, 'CLASS', 2);
• Construct PCs via KSIR for regression (20 slices)
  [EigenVectors, EigenValues, ratio] = KSIR(K, y, 20);
• Construct five PCs via KSIR for regression
  [EigenVectors, EigenValues, ratio] = KSIR(K, y, 20, 5);
• Construct PCs whose ratio to the total sum is 95% via KSIR for regression
  [EigenVectors, EigenValues, ratio] = KSIR(K, y, 20, 0.95);

1. Change your current directory to KStat toolbox folder
2. Load dataset Ionosphere_dataset.mat (can be found in Kernel Statistics toolbox)

load Ionosphere_dataset.mat

3. Construct PCs via KPCA

[Info] = KDR([], inst, '-s 0 -t 2 -g 0.1 -p 10');

4. Read the contents of Info (PCs, eigenvalues, parameters, ...etc)

 Info
 Info.PC

5. Get the projected inst form the PCs

[ProjInst] = UseKDR(inst, Info);

1. Change your current directory to KStat toolbox folder
2. Load dataset Ionosphere_dataset.mat (can be found in Kernel Statistics toolbox)

load Ionosphere_dataset.mat

3. Construct PCs via KSIR (note that we extracts m-1 PCs for m-class problems)

[Info] = KDR(label, inst, '-s 1 -t 2 -g 0.165 -z 0 -p 1');

4. Read the contents of Info (PCs, eigenvalues, parameters, ...etc)

Info
Info.PC

5. Get the projected inst form the PCs

[ProjInst] = UseKDR(inst, Info);

1. Change your current directory to Kernel Statistics toolbox folder
2. Load dataset Housing_dataset.txt (can be found in Kernel Statistics toolbox)

load Housing_dataset.txt

3. Split the Housing data into inst and label

inst =Housing_dataset(:,1:13);
label = Housing_dataset(:,14);

4. Construct PCs via KSIR (note that we usually use 1030 slices and extracts 35 PCs for regression problems)

[Info] = KDR(label, inst, '-s 1 -t 2 -g 0.0037 -z 20 -p 5');

5. Read the contents of Info (PCs, eigenvalues, parameters, ...etc)

Info
Info.PC

6. Get the projected inst form the PCs

[ProjInst] = UseKDR(inst, Info);