23,963 research outputs found
A Stochastic Majorize-Minimize Subspace Algorithm for Online Penalized Least Squares Estimation
Stochastic approximation techniques play an important role in solving many
problems encountered in machine learning or adaptive signal processing. In
these contexts, the statistics of the data are often unknown a priori or their
direct computation is too intensive, and they have thus to be estimated online
from the observed signals. For batch optimization of an objective function
being the sum of a data fidelity term and a penalization (e.g. a sparsity
promoting function), Majorize-Minimize (MM) methods have recently attracted
much interest since they are fast, highly flexible, and effective in ensuring
convergence. The goal of this paper is to show how these methods can be
successfully extended to the case when the data fidelity term corresponds to a
least squares criterion and the cost function is replaced by a sequence of
stochastic approximations of it. In this context, we propose an online version
of an MM subspace algorithm and we study its convergence by using suitable
probabilistic tools. Simulation results illustrate the good practical
performance of the proposed algorithm associated with a memory gradient
subspace, when applied to both non-adaptive and adaptive filter identification
problems
A Statistical Toolbox For Mining And Modeling Spatial Data
Most data mining projects in spatial economics start with an evaluation of a set of attribute variables on a sample of spatial entities, looking for the existence and strength of spatial autocorrelation, based on the Moran’s and the Geary’s coefficients, the adequacy of which is rarely challenged, despite the fact that when reporting on their properties, many users seem likely to make mistakes and to foster confusion. My paper begins by a critical appraisal of the classical definition and rational of these indices. I argue that while intuitively founded, they are plagued by an inconsistency in their conception. Then, I propose a principled small change leading to corrected spatial autocorrelation coefficients, which strongly simplifies their relationship, and opens the way to an augmented toolbox of statistical methods of dimension reduction and data visualization, also useful for modeling purposes. A second section presents a formal framework, adapted from recent work in statistical learning, which gives theoretical support to our definition of corrected spatial autocorrelation coefficients. More specifically, the multivariate data mining methods presented here, are easily implementable on the existing (free) software, yield methods useful to exploit the proposed corrections in spatial data analysis practice, and, from a mathematical point of view, whose asymptotic behavior, already studied in a series of papers by Belkin & Niyogi, suggests that they own qualities of robustness and a limited sensitivity to the Modifiable Areal Unit Problem (MAUP), valuable in exploratory spatial data analysis
TVL<sub>1</sub> Planarity Regularization for 3D Shape Approximation
The modern emergence of automation in many industries has given impetus to extensive research into mobile robotics. Novel perception technologies now enable cars to drive autonomously, tractors to till a field automatically and underwater robots to construct pipelines. An essential requirement to facilitate both perception and autonomous navigation is the analysis of the 3D environment using sensors like laser scanners or stereo cameras. 3D sensors generate a very large number of 3D data points when sampling object shapes within an environment, but crucially do not provide any intrinsic information about the environment which the robots operate within.
This work focuses on the fundamental task of 3D shape reconstruction and modelling from 3D point clouds. The novelty lies in the representation of surfaces by algebraic functions having limited support, which enables the extraction of smooth consistent implicit shapes from noisy samples with a heterogeneous density. The minimization of total variation of second differential degree makes it possible to enforce planar surfaces which often occur in man-made environments. Applying the new technique means that less accurate, low-cost 3D sensors can be employed without sacrificing the 3D shape reconstruction accuracy
A Multiscale Pyramid Transform for Graph Signals
Multiscale transforms designed to process analog and discrete-time signals
and images cannot be directly applied to analyze high-dimensional data residing
on the vertices of a weighted graph, as they do not capture the intrinsic
geometric structure of the underlying graph data domain. In this paper, we
adapt the Laplacian pyramid transform for signals on Euclidean domains so that
it can be used to analyze high-dimensional data residing on the vertices of a
weighted graph. Our approach is to study existing methods and develop new
methods for the four fundamental operations of graph downsampling, graph
reduction, and filtering and interpolation of signals on graphs. Equipped with
appropriate notions of these operations, we leverage the basic multiscale
constructs and intuitions from classical signal processing to generate a
transform that yields both a multiresolution of graphs and an associated
multiresolution of a graph signal on the underlying sequence of graphs.Comment: 16 pages, 13 figure
Oriented tensor reconstruction: tracing neural pathways from diffusion tensor MRI
In this paper we develop a new technique for tracing anatomical fibers from 3D tensor fields. The technique extracts salient tensor features using a local regularization technique that allows the algorithm to cross noisy regions and bridge gaps in the data. We applied the method to human brain DT-MRI data and recovered identifiable anatomical structures that correspond to the white matter brain-fiber pathways. The images in this paper are derived from a dataset having 121x88x60 resolution. We were able to recover fibers with less than the voxel size resolution by applying the regularization technique, i.e., using a priori assumptions about fiber smoothness. The regularization procedure is done through a moving least squares filter directly incorporated in the tracing algorithm
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