Intrinsic dimension estimation of data by principal component analysis

Understand

Estimating intrinsic dimensionality of data is a classic problem in pattern recognition and statistics.

• Principal Component Analysis (PCA) is a powerful tool in discovering dimensionality of data sets with a linear structure; it, however, becomes ineffective when data have a nonlinear structure.
• In this paper, we propose a new PCA-based method to estimate intrinsic dimension of data with nonlinear structures.
• Our method works by first finding a minimal cover of the data set, then performing PCA locally on each subset in the cover and finally giving the estimation result by checking up the data variance on all small neighborhood regions.