Weighted kernel Fisher discriminant analysis for integrating heterogeneous data

Data integration is becoming an essential tool to cope with and make sense of the ever increasing amount of biological data. Genomic data arises in various shapes and forms including vectors, graphs or sequences, therefore, it is essential to carefully consider strategies that best capture the most information contained in each data type. The need for integration of heterogeneous data measured on the same individuals arises in a wide range of clinical applications as well. We propose weighted kernel Fisher discriminant (wKFD) analysis for integrating heterogeneous data sets. We use weights that measure relative importance of each of the data sets to be integrated. Simulation studies are conducted to assess performance of our proposed method. The results show that our method performs very well including in the presence of noisy data. We also illustrate our method using gene expression and clinical data from breast cancer patients. Weighted integration of heterogeneous data leads to improved predictive accuracy. The amount of improvement, however, depends on the quality and informativity of each of the data sets being integrated. If a data set is of poor quality and/or non-informative, one should not expect a significant improvement by adding this particular data set to other informative data sets. Likewise, important improvement might not be obtained if data do not contain independent information, that is, if there is redundancy in the data.