Reducing high-dimensional data by principal component analysis vs. random projection for nearest neighbor classification

The computational cost of using nearest neighbor classification often prevents the method from being applied in practice when dealing with high-dimensional data, such as images and micro arrays. One possible solution to this problem is to reduce the dimensionality of the data, ideally without loosing predictive performance. Two different dimensionality reduction methods, principle component analysis (PCA) and random projection (RP), are investigated for this purpose and compared w.r.t. the performance of the resulting nearest neighbor classifier on five image data sets and five micro array data sets. The experiment results demonstrate that PCA outperforms RP for all data sets used in this study. However the experiments also show that PCA is more sensitive to the choice of the number of reduced dimensions. After reaching a peak, the accuracy degrades with the number of dimensions for PCA, while the accuracy for RP increases with the number of dimensions. The experiments also show that the use of PCA and RP may even outperform using the non-reduced feature set (in 9 respectively 6 cases out of 10), hence not only resulting in more efficient, but also more effective, nearest neighbor classification.