A Generalization of Principal Component Analysis
This provides a theoretical extension of PCA with potential applications in various data analysis domains, though it appears incremental.
The authors tackled the problem of generalizing principal component analysis by maximizing an arbitrary convex function of principal components instead of just second powers, presenting a gradient ascent algorithm and showing kernel solutions correspond to fixed points of a simple recurrent neural network.
Conventional principal component analysis (PCA) finds a principal vector that maximizes the sum of second powers of principal components. We consider a generalized PCA that aims at maximizing the sum of an arbitrary convex function of principal components. We present a gradient ascent algorithm to solve the problem. For the kernel version of generalized PCA, we show that the solutions can be obtained as fixed points of a simple single-layer recurrent neural network. We also evaluate our algorithms on different datasets.