81,608 research outputs found
Designing labeled graph classifiers by exploiting the R\'enyi entropy of the dissimilarity representation
Representing patterns as labeled graphs is becoming increasingly common in
the broad field of computational intelligence. Accordingly, a wide repertoire
of pattern recognition tools, such as classifiers and knowledge discovery
procedures, are nowadays available and tested for various datasets of labeled
graphs. However, the design of effective learning procedures operating in the
space of labeled graphs is still a challenging problem, especially from the
computational complexity viewpoint. In this paper, we present a major
improvement of a general-purpose classifier for graphs, which is conceived on
an interplay between dissimilarity representation, clustering,
information-theoretic techniques, and evolutionary optimization algorithms. The
improvement focuses on a specific key subroutine devised to compress the input
data. We prove different theorems which are fundamental to the setting of the
parameters controlling such a compression operation. We demonstrate the
effectiveness of the resulting classifier by benchmarking the developed
variants on well-known datasets of labeled graphs, considering as distinct
performance indicators the classification accuracy, computing time, and
parsimony in terms of structural complexity of the synthesized classification
models. The results show state-of-the-art standards in terms of test set
accuracy and a considerable speed-up for what concerns the computing time.Comment: Revised versio
Combining local regularity estimation and total variation optimization for scale-free texture segmentation
Texture segmentation constitutes a standard image processing task, crucial to
many applications. The present contribution focuses on the particular subset of
scale-free textures and its originality resides in the combination of three key
ingredients: First, texture characterization relies on the concept of local
regularity ; Second, estimation of local regularity is based on new multiscale
quantities referred to as wavelet leaders ; Third, segmentation from local
regularity faces a fundamental bias variance trade-off: In nature, local
regularity estimation shows high variability that impairs the detection of
changes, while a posteriori smoothing of regularity estimates precludes from
locating correctly changes. Instead, the present contribution proposes several
variational problem formulations based on total variation and proximal
resolutions that effectively circumvent this trade-off. Estimation and
segmentation performance for the proposed procedures are quantified and
compared on synthetic as well as on real-world textures
Eigenvalue Estimation of Differential Operators
We demonstrate how linear differential operators could be emulated by a
quantum processor, should one ever be built, using the Abrams-Lloyd algorithm.
Given a linear differential operator of order 2S, acting on functions
psi(x_1,x_2,...,x_D) with D arguments, the computational cost required to
estimate a low order eigenvalue to accuracy Theta(1/N^2) is
Theta((2(S+1)(1+1/nu)+D)log N) qubits and O(N^{2(S+1)(1+1/nu)} (D log N)^c)
gate operations, where N is the number of points to which each argument is
discretized, nu and c are implementation dependent constants of O(1). Optimal
classical methods require Theta(N^D) bits and Omega(N^D) gate operations to
perform the same eigenvalue estimation. The Abrams-Lloyd algorithm thereby
leads to exponential reduction in memory and polynomial reduction in gate
operations, provided the domain has sufficiently large dimension D >
2(S+1)(1+1/nu). In the case of Schrodinger's equation, ground state energy
estimation of two or more particles can in principle be performed with fewer
quantum mechanical gates than classical gates.Comment: significant content revisions: more algorithm details and brief
analysis of convergenc
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