Heterogeneous multiple kernel learning for breast cancer outcome evaluation

Breast cancer is one of the common kinds of cancer among women, and it ranks second among all cancers in terms of incidence, after lung cancer. Therefore, it is of great necessity to study the detection methods of breast cancer. Recent research has focused on using gene expression data to predict outcomes, and kernel methods have received a lot of attention regarding the cancer outcome evaluation. However, selecting the appropriate kernels and their parameters still needs further investigation.

We utilized heterogeneous kernels from a specific kernel set including the Hadamard, RBF and linear kernels. The mixed coefficients of the heterogeneous kernel were computed by solving the standard convex quadratic programming problem of the quadratic constraints. The algorithm is named the heterogeneous multiple kernel learning (HMKL). Using the particle swarm optimization (PSO) in HMKL, we selected the kernel parameters, then we employed HMKL to perform the breast cancer outcome evaluation. By testing real-world microarray datasets, the HMKL method outperforms the methods of the random forest, decision tree, GA with Rotation Forest, BFA + RF, SVM and MKL.

On one hand, HMKL is effective for the breast cancer evaluation and can be utilized by physicians to better understand the patient's condition. On the other hand, HMKL can choose the function and parameters of the kernel. At the same time, this study proves that the Hadamard kernel is effective in HMKL. We hope that HMKL could be applied as a new method to more actual problems.