This paper presents a novel solution to the inverse Frobenius-Perron problem of reconstructing an unknown nonlinear and ergodic map from causal sequences of probability density functions generated by the map. The original solution to this problem successfully reconstructs members of the canonical map class (i.e., a subset of the piecewise linear semi-Markov maps), provided all the map’s branches are monotonically increasing. The original solution constructs a matrix estimate of the map’s Frobenius-Perron operator, which governs the evolution of density functions under iteration of the map, from the density sequences. The one-dimensional map is reconstructed from this matrix. In contrast, the proposed solution constructs a higher-order matrix estimate of the Frobenius-Perron operator. A member of the newly proposed class of generalized hat maps, a superset of the canonical maps, is constructed from this matrix estimate. The proposed solution successfully distinguishes between increasing and decreasing map branches and enlarges the class of maps that can be successfully reconstructed to canonical maps with any subset of decreasing branches. When used to reconstruct any piecewise linear semi-Markov map, the proposed solution generates a map with consistent invariant density and power spectrum mode characteristics, regardless of the unknown map’s canonicity or branch monotonicity. Numerical examples that illustrate the proposed solution’s characteristics are presented.

A new approach to solving a more general formulation of the inverse Frobenius-Perron problem, which requires the construction of a one-dimensional ergodic map with prescribed invariant probability density function and power spectral density, is presented. The proposed approach relies on a novel technique for generating distinct maps with the same invariant density, and which facilitates selection of the structural characteristics of each map in advance. We consider a new class of maps constructed with this technique, the piecewise monotonic hat maps, and present an algorithm for selecting the map parameters to achieve simultaneous and independent prescription of the invariant density and multimodal power spectrum characteristics. This approach to solving the generalized inverse Frobenius-Perron problem is demonstrated by constructing several ergodic maps with the beta invariant density as well as unimodal and bimodal power spectra with distinct mode center frequencies and bandwidths. We conclude that the proposed approach provides a means for generating more realistic models of systems and processes as compared to existing methods.

This technical note presents some new and explicit stability results for Volterra systems using two different approaches. The first approach is based on monomial domination of the Volterra system's memoryless output nonlinearity and the second on its Lipschitz-norm. The former yields more widely applicable results, but introduces nonconvexity in the signal spaces to be dealt with for certain parameter values.

Texture features derived using Haralick's Gray-Level Cooccurrence Matrix (GLCM) are by far the most popular in urban remote sensing research - but are they the best features for every application? In order to select the most appropriate texture algorithm for an automated informal settlement classification system, we performed an experiment to compare the performance of the GLCM with that of other texture features. The performance of a texture feature is measured by computing the classification accuracy achieved on a supervised set of images spread over 8 settlement classes, focusing on informal and low-cost housing. The results show that GLCMs perform very well, but that Local Binary Pattern texture features have a small advantage in this classification problem.

This paper presents a unifying review of a learning-based framework for kernel-based attributed graph matching. The framework, which includes as special cases the RKHS Interplator-Based Graph Matching (RIGM) and Interpolator-Based Kronecker Product Graph Matching (IBKPGM) algorithms, incorporates a general approach where no assumption is made about the adjacency structure of the graphs to be matched. Corresponding pairs of attributed adjacency matrices and attribute vectors of an input and reference graph are used as the input–output training set of a constrained multi-input multi-output multi-variable mapping to be learned. It is shown that a Reproducing Kernel Hilbert Space (RKHS) based interpolator can be used to infer this mapping. Partially constraining the inferred mapping by the generation of additional consistency input–output training pairs and the use of polynomial feature augmentation lead to improved performance. The proposed learning-based framework avoids the explicit calculation of compatibility values.

A novel Projections Onto Convex Sets (POCS) graph matching algorithm is presented. Two-way assignment constraints are enforced without using elaborate penalty terms, graduated nonconvexity, or sophisticated annealing mechanisms to escape from poor local minima. Results indicate that the presented algorithm is robust and compares favorably to other well-known algorithms.

We present an algorithm for performing attributed graph matching. This algorithm is derived from a generalized framework for describing functionally expanded interpolators which is based on the theory of reproducing kernel Hilbert spaces (RKHS). The algorithm incorporates a general approach to a wide class of graph matching problems based on attributed graphs, allowing the structure of the graphs to be based on multiple sets of attributes. No assumption is made about the adjacency structure of the graphs to be matched.