98,671 research outputs found
A Multiscale Approach for Statistical Characterization of Functional Images
Increasingly, scientific studies yield functional image data, in which the observed data consist of sets of curves recorded on the pixels of the image. Examples include temporal brain response intensities measured by fMRI and NMR frequency spectra measured at each pixel. This article presents a new methodology for improving the characterization of pixels in functional imaging, formulated as a spatial curve clustering problem. Our method operates on curves as a unit. It is nonparametric and involves multiple stages: (i) wavelet thresholding, aggregation, and Neyman truncation to effectively reduce dimensionality; (ii) clustering based on an extended EM algorithm; and (iii) multiscale penalized dyadic partitioning to create a spatial segmentation. We motivate the different stages with theoretical considerations and arguments, and illustrate the overall procedure on simulated and real datasets. Our method appears to offer substantial improvements over monoscale pixel-wise methods. An Appendix which gives some theoretical justifications of the methodology, computer code, documentation and dataset are available in the online supplements
High-Dimensional Regression with Gaussian Mixtures and Partially-Latent Response Variables
In this work we address the problem of approximating high-dimensional data
with a low-dimensional representation. We make the following contributions. We
propose an inverse regression method which exchanges the roles of input and
response, such that the low-dimensional variable becomes the regressor, and
which is tractable. We introduce a mixture of locally-linear probabilistic
mapping model that starts with estimating the parameters of inverse regression,
and follows with inferring closed-form solutions for the forward parameters of
the high-dimensional regression problem of interest. Moreover, we introduce a
partially-latent paradigm, such that the vector-valued response variable is
composed of both observed and latent entries, thus being able to deal with data
contaminated by experimental artifacts that cannot be explained with noise
models. The proposed probabilistic formulation could be viewed as a
latent-variable augmentation of regression. We devise expectation-maximization
(EM) procedures based on a data augmentation strategy which facilitates the
maximum-likelihood search over the model parameters. We propose two
augmentation schemes and we describe in detail the associated EM inference
procedures that may well be viewed as generalizations of a number of EM
regression, dimension reduction, and factor analysis algorithms. The proposed
framework is validated with both synthetic and real data. We provide
experimental evidence that our method outperforms several existing regression
techniques
Robust Head-Pose Estimation Based on Partially-Latent Mixture of Linear Regressions
Head-pose estimation has many applications, such as social event analysis,
human-robot and human-computer interaction, driving assistance, and so forth.
Head-pose estimation is challenging because it must cope with changing
illumination conditions, variabilities in face orientation and in appearance,
partial occlusions of facial landmarks, as well as bounding-box-to-face
alignment errors. We propose tu use a mixture of linear regressions with
partially-latent output. This regression method learns to map high-dimensional
feature vectors (extracted from bounding boxes of faces) onto the joint space
of head-pose angles and bounding-box shifts, such that they are robustly
predicted in the presence of unobservable phenomena. We describe in detail the
mapping method that combines the merits of unsupervised manifold learning
techniques and of mixtures of regressions. We validate our method with three
publicly available datasets and we thoroughly benchmark four variants of the
proposed algorithm with several state-of-the-art head-pose estimation methods.Comment: 12 pages, 5 figures, 3 table
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