In this paper, a novel method is proposed to extract a stable feature set representative of image content. Each image is represented by a linear combination of fractal orthonormal basis vectors. The mapping coefficients of an image projected onto each orthonormal basis constitute a feature vector. The distance remains consistent, i.e., isometric embedded, between any image pairs before and afte...

An orthonormal basis adaptation method for function approximation was developed and applied to reinforcement learning with multi-dimensional continuous state space. First, a basis used for linear function approximation of a control function is set to an orthonormal basis. Next, basis elements with small activities are replaced with other candidate elements as learning progresses. As this replac...

Semi-nonparametric (SNP) models are models where only a part of the model is parametrized, and the non-specified part is an unknown function which is represented by an infinite series expansion. Therefore, SNP models are in essence models with infinitely many parameters. The theoretical foundation of series expansions of functions is Hilbert space theory, in particular the properties of Hilbert...

where each θj is supported only on Ω ⊂ {1, 2, . . . , N}, with |Ω| = K. The matrix Ψ is orthonormal, with dimension N × N (we consider only signals sparse in an orthonormal basis). We denote by Φj the measurement matrix for signal j, where Φj is of dimension M ×N , where M < N . We let yj = Φjxj = ΦjΨθj be the observations of signal j. We assume that the measurement matrix Φj is random with i.i...