Narrow Results

The determination of principal curves relies on the arc-length as a global index to describe the middle of the data distribution. With a non-constant data distribution, however, curves that are constructed by the approach introduced in reference¹³ may not reflect the middle of data distribution, as demonstrated in this article. This is particularly so for curve segments that have a large curvature and a high data density. To overcome this problem, the paper revisits the projection of the samples onto the curve by incorporating Riemannian distances. This analysis suggests estimating the density value of each sample relative to its neighbors and utilize this value to compute the projection index for the curve. The use of density values, in turn, allows penalizing distances between samples along with the arc-length. In a similar fashion to conventional principal curves algorithms, for example proposed by Hastie and Stuetzle¹⁴ and Tibshirani,²⁹ the incorporation of Riemannian distances gives rise to an iterative algorithm that includes a projection and a self-consistent step. Application studies to simulated and experimental data sets shows that the proposed modification has the potential to outperform existing algorithms in areas of high curvature under an non-constant data distribution.

In this article we propose a polygonal principal curve based nonlinear feature extraction method, which achieves statistical redundancy elimination without loss of information and provides more robust nonlinear pattern identification for high-dimensional data. Recognizing the limitations of linear statistical methods, this article integrates local principal component analysis (PCA) with a polygonal line algorithm to approximate the complicated nonlinear data structure. Experimental results demonstrate that the proposed algorithm can be implemented to reduce the computation complexity for nonlinear feature extraction in multivariate cases.

It is difficult but crucial for minutiae extraction and pseudo minutiae deletion of low quality fingerprint images in auto fingerprint identification systems. Traditional methods based on thinning images or gray-level images are, however, susceptible to noise. Reference 14 indicated that principal curves based fingerprint minutiae extraction was feasible to overcome the drawback, but the extended polygonal line (EPL) principal curves algorithm used in the paper extracted the principal curves ineffectively. As the fingerprint data sets are usually large, the original EPL principal curves algorithm is time-consuming. Meanwhile, scattered fingerprint data lead to the deviation of fingerprint skeleton. In this paper, the algorithm is modified, and a fingerprint minutiae extraction and pseudo minutiae detection method based on principal curves is proposed. Experimental results show that the modified EPL principal curves algorithm outperforms the original EPL algorithm both in efficiency and quality, and the proposed minutiae extraction method outperforms the methods proposed by Miao under noise conditions.