مرکز منطقه ای اطلاع رساني علوم و فناوري - Parameter identification using intrinsic dimensionality

Abstract :

Let $W$ be an $N$ -dimensional vector space and $V$ be a $K$ - dimensional topological hypersurface in $W$ . The intrinsic dimensionality problem can be stated as follows. Given $M$ randomly selected points $\\nu_i, \\nu_i \\in V$ , estimate $K$ , which is the dimensionality of $V$ and is called the intrinsic dimensionality of the points $\\nu_i$ . This problem has been attacked by several authors. If signals are represented by vectors in an abstract signal space $W$ , rather than as time or frequency functions, the locus of signals that are generated by a hypothetical signal generator possessing $K$ free parameters is a $K$ -dimensional hypersurface $V$ in the signal space. The purpose of this paper is to identify some of the free parameters of the signals. Let $H$ be a one-parameter group that acts on $W, HW = W$ . To say that a parameter associated with a group $H$ is a free parameter of $V$ means that $V$ is closed under $H$ , i.e., $HV = V$ . To decide whether $HV = V$ , the estimated dimensionalities of $HV$ and $V$ are compared. The method is illustrated by presenting several examples from the field of signal analysis. Finally, a slight modification is suggested so that parameters can he identified even when the vectors of interest do not represent time or frequency functions.