# Correlation Pattern Recognition by B. V. K. Vijaya Kumar

By B. V. K. Vijaya Kumar

Correlation is a sturdy and basic method for trend acceptance and is utilized in many functions, equivalent to automated aim attractiveness, biometric acceptance and optical personality acceptance. The layout, research and use of correlation development reputation algorithms calls for history details, together with linear platforms concept, random variables and techniques, matrix/vector tools, detection and estimation concept, electronic sign processing and optical processing. This booklet offers a wanted evaluate of this various heritage fabric and develops the sign processing thought, the trend attractiveness metrics, and the sensible software knowledge from easy premises. It exhibits either electronic and optical implementations. It additionally includes know-how provided through the workforce that built it and comprises case stories of vital curiosity, resembling face and fingerprint popularity. appropriate for graduate scholars taking classes in development attractiveness idea, when attaining technical degrees of curiosity to the pro practitioner.

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Xn} are Pn said to be linearly independent if the only solution to k¼1 k xk ¼ 0 is 1 ¼ 2 ¼ . . n ¼ 0. If at least one k is non-zero, then the n vectors are linearly dependent. The rank of a matrix is the number of linearly independent rows (or equivalently, the number of linearly independent columns). 2 Basic matrix–vector operations 19 matrix and its transpose have the same rank. If A and B are square matrices of size n Â n with ranks rA and rB respectively, then the rank of their product AB can be bounded as follows: minðrA ; rB Þ !

A random variable (RV) X is defined as a mapping from the events in the random experiment to the real line. For example, we can define an RV X as taking on the real value k in our six-sided die experiment where k is the outcome. This RV takes on only discrete values (namely 1, 2, 3, 4, 5, and 6) and is thus called a discrete RV. We will use continuous RVs to model outcomes such as noise where we can have a continuum of values. Continuous RVs take on real values in an interval or in sets of intervals.

Beforehand) which of the six faces will show up. All we can say is that it is equally likely that any of the six sides will show up. Probability theory is an attempt to quantify such randomness. In this section, we will provide a brief review of probability theory concepts and results that we will find useful in correlation pattern recognition. 1 Basics of probability theory Let us go back to the example of the six-sided die. This experiment has a random outcome in that the output can be any one of the six numbers.