1,448 research outputs found
Dimensionality reduction with image data
A common objective in image analysis is dimensionality reduction. The most common often used data-exploratory technique with this objective is principal component analysis. We propose a new method based on the projection of the images as matrices after a Procrustes rotation and show that it leads to a better reconstruction of images
Bayesian matching of unlabelled point sets using Procrustes and configuration models
The problem of matching unlabelled point sets using Bayesian inference is
considered. Two recently proposed models for the likelihood are compared, based
on the Procrustes size-and-shape and the full configuration. Bayesian inference
is carried out for matching point sets using Markov chain Monte Carlo
simulation. An improvement to the existing Procrustes algorithm is proposed
which improves convergence rates, using occasional large jumps in the burn-in
period. The Procrustes and configuration methods are compared in a simulation
study and using real data, where it is of interest to estimate the strengths of
matches between protein binding sites. The performance of both methods is
generally quite similar, and a connection between the two models is made using
a Laplace approximation
Disentangling Orthogonal Matrices
Motivated by a certain molecular reconstruction methodology in cryo-electron
microscopy, we consider the problem of solving a linear system with two unknown
orthogonal matrices, which is a generalization of the well-known orthogonal
Procrustes problem. We propose an algorithm based on a semi-definite
programming (SDP) relaxation, and give a theoretical guarantee for its
performance. Both theoretically and empirically, the proposed algorithm
performs better than the na\"{i}ve approach of solving the linear system
directly without the orthogonal constraints. We also consider the
generalization to linear systems with more than two unknown orthogonal
matrices
Most Likely Separation of Intensity and Warping Effects in Image Registration
This paper introduces a class of mixed-effects models for joint modeling of
spatially correlated intensity variation and warping variation in 2D images.
Spatially correlated intensity variation and warp variation are modeled as
random effects, resulting in a nonlinear mixed-effects model that enables
simultaneous estimation of template and model parameters by optimization of the
likelihood function. We propose an algorithm for fitting the model which
alternates estimation of variance parameters and image registration. This
approach avoids the potential estimation bias in the template estimate that
arises when treating registration as a preprocessing step. We apply the model
to datasets of facial images and 2D brain magnetic resonance images to
illustrate the simultaneous estimation and prediction of intensity and warp
effects
Subspace procrustes analysis
Postprint (author's final draft
Crosslingual Document Embedding as Reduced-Rank Ridge Regression
There has recently been much interest in extending vector-based word
representations to multiple languages, such that words can be compared across
languages. In this paper, we shift the focus from words to documents and
introduce a method for embedding documents written in any language into a
single, language-independent vector space. For training, our approach leverages
a multilingual corpus where the same concept is covered in multiple languages
(but not necessarily via exact translations), such as Wikipedia. Our method,
Cr5 (Crosslingual reduced-rank ridge regression), starts by training a
ridge-regression-based classifier that uses language-specific bag-of-word
features in order to predict the concept that a given document is about. We
show that, when constraining the learned weight matrix to be of low rank, it
can be factored to obtain the desired mappings from language-specific
bags-of-words to language-independent embeddings. As opposed to most prior
methods, which use pretrained monolingual word vectors, postprocess them to
make them crosslingual, and finally average word vectors to obtain document
vectors, Cr5 is trained end-to-end and is thus natively crosslingual as well as
document-level. Moreover, since our algorithm uses the singular value
decomposition as its core operation, it is highly scalable. Experiments show
that our method achieves state-of-the-art performance on a crosslingual
document retrieval task. Finally, although not trained for embedding sentences
and words, it also achieves competitive performance on crosslingual sentence
and word retrieval tasks.Comment: In The Twelfth ACM International Conference on Web Search and Data
Mining (WSDM '19
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