Pattern Recognition Problems

Fingerprint scanners are the most widely used form of personal biometric today, due largely to their small size and ease of use. A person simply places his finger on the reader, and he is either granted or denied access. In this section, we will examine the operation of the fingerprint scanner at the device and analysis levels so that technology selection and implementation decisions can be made with better awareness of possible limitations.

At the very beginning, the reader needs to be cautioned that the degree to which a person's fingerprint templates (the recorded characteristics of the finger) are protected while being stored by the operating system may create an easier attack point than trying to break the system by creating a fake fingerprint. These biometric fingerprint scanners should be used with careful attention paid to encryption and protection of the user fingerprint templates. Failure to do so will directly affect the strength of protection offered by the system.

In comparison with rich literature in feature extraction-oriented LDA for SSS problems, studies on pattern classification aspect of LDA for SSS problems are quite few. To the best of our knowledge, except for large margin linear projection (LMLP), minimum norm minimum squared-error (MNMSE), and maximum scatter difference (MSD) there is almost no endeavor in this direction.

Since FDC, MSE, FLD, and FSD all involve the computation of the inverse of one or several scatter matrices of sample data, it is a precondition that these matrices should be nonsingular. In the small sample size (SSS) pattern recognition problems such as appearance-based face recognition, the ratio of dimensionality of input space to the number of samples is so large that the matrices involved are all singular. As a result, standard LDA methods cannot directly be applied to these SSS problems. Due to the prospective applications to biometric identification and computer vision, LDA for solving the SSS problems becomes one of the hottest research topics in pattern recognition.