Analysis of Medical Data Using Dimensionality Reduction Techniques

High-dimensional data can be dicult to analyze, almost impossible to visualize, and expensive to process and store. In many cases, the high-dimensional data points may all lie on or close to a much lower-dimensional surface, or manifold, implying the intrinsic dimensionality of the data is much lower. In that case, the data could be described with fewer dimensions, allowing us to mitigate the curse of dimensionality. Transforming the highdimensional representation of the data to a lower-dimensional one without losing important information is the central problem of dimensionality reduction. Many methods of dimensionality reduction have been developed, including classical techniques like Principal Component Analysis (PCA) and newer methods such as Diusion Maps (DM). Most of these methods often perform well on some types of data but poorly on others. We apply dierent dimensionality reduction methods to medical data, including breast tissue tumor data and kidney proteomics data, in order to determine which methods and parameters work best on on the dierent types of data. To evaluate the performance of the reduction method, we also classify the data in the reduced dimension using standard classication algorithms and evaluate the accuracy.