452 research outputs found
Autoregressive Kernels For Time Series
We propose in this work a new family of kernels for variable-length time
series. Our work builds upon the vector autoregressive (VAR) model for
multivariate stochastic processes: given a multivariate time series x, we
consider the likelihood function p_{\theta}(x) of different parameters \theta
in the VAR model as features to describe x. To compare two time series x and
x', we form the product of their features p_{\theta}(x) p_{\theta}(x') which is
integrated out w.r.t \theta using a matrix normal-inverse Wishart prior. Among
other properties, this kernel can be easily computed when the dimension d of
the time series is much larger than the lengths of the considered time series x
and x'. It can also be generalized to time series taking values in arbitrary
state spaces, as long as the state space itself is endowed with a kernel
\kappa. In that case, the kernel between x and x' is a a function of the Gram
matrices produced by \kappa on observations and subsequences of observations
enumerated in x and x'. We describe a computationally efficient implementation
of this generalization that uses low-rank matrix factorization techniques.
These kernels are compared to other known kernels using a set of benchmark
classification tasks carried out with support vector machines
Group-Lasso on Splines for Spectrum Cartography
The unceasing demand for continuous situational awareness calls for
innovative and large-scale signal processing algorithms, complemented by
collaborative and adaptive sensing platforms to accomplish the objectives of
layered sensing and control. Towards this goal, the present paper develops a
spline-based approach to field estimation, which relies on a basis expansion
model of the field of interest. The model entails known bases, weighted by
generic functions estimated from the field's noisy samples. A novel field
estimator is developed based on a regularized variational least-squares (LS)
criterion that yields finitely-parameterized (function) estimates spanned by
thin-plate splines. Robustness considerations motivate well the adoption of an
overcomplete set of (possibly overlapping) basis functions, while a sparsifying
regularizer augmenting the LS cost endows the estimator with the ability to
select a few of these bases that ``better'' explain the data. This parsimonious
field representation becomes possible, because the sparsity-aware spline-based
method of this paper induces a group-Lasso estimator for the coefficients of
the thin-plate spline expansions per basis. A distributed algorithm is also
developed to obtain the group-Lasso estimator using a network of wireless
sensors, or, using multiple processors to balance the load of a single
computational unit. The novel spline-based approach is motivated by a spectrum
cartography application, in which a set of sensing cognitive radios collaborate
to estimate the distribution of RF power in space and frequency. Simulated
tests corroborate that the estimated power spectrum density atlas yields the
desired RF state awareness, since the maps reveal spatial locations where idle
frequency bands can be reused for transmission, even when fading and shadowing
effects are pronounced.Comment: Submitted to IEEE Transactions on Signal Processin
Least-squares methods for nonnegative matrix factorization over rational functions
Nonnegative Matrix Factorization (NMF) models are widely used to recover
linearly mixed nonnegative data. When the data is made of samplings of
continuous signals, the factors in NMF can be constrained to be samples of
nonnegative rational functions, which allow fairly general models; this is
referred to as NMF using rational functions (R-NMF). We first show that, under
mild assumptions, R-NMF has an essentially unique factorization unlike NMF,
which is crucial in applications where ground-truth factors need to be
recovered such as blind source separation problems. Then we present different
approaches to solve R-NMF: the R-HANLS, R-ANLS and R-NLS methods. From our
tests, no method significantly outperforms the others, and a trade-off should
be done between time and accuracy. Indeed, R-HANLS is fast and accurate for
large problems, while R-ANLS is more accurate, but also more resources
demanding, both in time and memory. R-NLS is very accurate but only for small
problems. Moreover, we show that R-NMF outperforms NMF in various tasks
including the recovery of semi-synthetic continuous signals, and a
classification problem of real hyperspectral signals.Comment: 13 page
Segmentation of Infant Brain Using Nonnegative Matrix Factorization
This study develops an atlas-based automated framework for segmenting infants\u27 brains from magnetic resonance imaging (MRI). For the accurate segmentation of different structures of an infant\u27s brain at the isointense age (6-12 months), our framework integrates features of diffusion tensor imaging (DTI) (e.g., the fractional anisotropy (FA)). A brain diffusion tensor (DT) image and its region map are considered samples of a Markov-Gibbs random field (MGRF) that jointly models visual appearance, shape, and spatial homogeneity of a goal structure. The visual appearance is modeled with an empirical distribution of the probability of the DTI features, fused by their nonnegative matrix factorization (NMF) and allocation to data clusters. Projecting an initial high-dimensional feature space onto a low-dimensional space of the significant fused features with the NMF allows for better separation of the goal structure and its background. The cluster centers in the latter space are determined at the training stage by the K-means clustering. In order to adapt to large infant brain inhomogeneities and segment the brain images more accurately, appearance descriptors of both the first-order and second-order are taken into account in the fused NMF feature space. Additionally, a second-order MGRF model is used to describe the appearance based on the voxel intensities and their pairwise spatial dependencies. An adaptive shape prior that is spatially variant is constructed from a training set of co-aligned images, forming an atlas database. Moreover, the spatial homogeneity of the shape is described with a spatially uniform 3D MGRF of the second-order for region labels. In vivo experiments on nine infant datasets showed promising results in terms of the accuracy, which was computed using three metrics: the 95-percentile modified Hausdorff distance (MHD), the Dice similarity coefficient (DSC), and the absolute volume difference (AVD). Both the quantitative and visual assessments confirm that integrating the proposed NMF-fused DTI feature and intensity MGRF models of visual appearance, the adaptive shape prior, and the shape homogeneity MGRF model is promising in segmenting the infant brain DTI
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