Domain Correction Based on Kernel Transformation for Drift Compensation in the E-Nose System

. 2018 Sep 23;18(10):3209. doi: 10.3390/s18103209

Algorithm 1 DCKT

Input: Source data

X_{S}

, target data

X_{T}

, source label

y_{S}

, regularization coefficients

μ

, and dimension m:
Procedure:
1. Construct the kernel matrix K from

{x_{S}^{i}}_{i = 1}^{N_{S}}

and

{x_{T}^{i}}_{i = 1}^{N_{T}}

via (2), matric L via (3), and centering matric H via (6);
2. Solve the eigendecomposition of

{(K L K + μ I)}^{- 1} K H K

;
3. Build P by m smallest eigenvectors via (8);
4. Compute the mapped source domain data

X_{S}^{'} = P^{T} X_{S}

;
5. Compute the mapped target domain data

X_{T}^{'} = P^{T} X_{T}

;
6. Train the SVM classifier with

{X_{S}^{'}, y_{S}}

, and predict the odor label of

X_{T}^{'}

;

Output:
The classification results of target data.