8,976 research outputs found
Low dimension hierarchical subspace modelling of high dimensional data
Building models of high-dimensional data in a low dimensional space has become extremely popular in recent years. Motion tracking, facial animation, stock market tracking, digital libraries and many other different models have been built and tuned to specific application domains. However, when the underlying structure of the original data is unknown, the modelling of such data is still an open question. The problem is of interest as capturing and storing large amounts of high dimensional data has become trivial, yet the capability to process, interpret, and use this data is limited. In this thesis, we introduce novel algorithms for modelling high dimensional data with an unknown structure, which allows us to represent the data with good accuracy and in a compact manner. This work presents a novel fully automated dynamic hierarchical algorithm, together with a novel automatic data partitioning method to work alongside existing specific models (talking head, human motion). Our algorithm is applicable to hierarchical data visualisation and classification, meaningful pattern extraction and recognition, and new data sequence generation. Also during our work we investigated problems related to low dimensional data representation: automatic optimal input parameter estimation, and robustness against noise and outliers. We show the potential of our modelling with many data domains: talking head, motion, audio, etc. and we believe that it has good potential in adapting to other domains
Exploiting Low-dimensional Structures to Enhance DNN Based Acoustic Modeling in Speech Recognition
We propose to model the acoustic space of deep neural network (DNN)
class-conditional posterior probabilities as a union of low-dimensional
subspaces. To that end, the training posteriors are used for dictionary
learning and sparse coding. Sparse representation of the test posteriors using
this dictionary enables projection to the space of training data. Relying on
the fact that the intrinsic dimensions of the posterior subspaces are indeed
very small and the matrix of all posteriors belonging to a class has a very low
rank, we demonstrate how low-dimensional structures enable further enhancement
of the posteriors and rectify the spurious errors due to mismatch conditions.
The enhanced acoustic modeling method leads to improvements in continuous
speech recognition task using hybrid DNN-HMM (hidden Markov model) framework in
both clean and noisy conditions, where upto 15.4% relative reduction in word
error rate (WER) is achieved
Scalable iterative methods for sampling from massive Gaussian random vectors
Sampling from Gaussian Markov random fields (GMRFs), that is multivariate
Gaussian ran- dom vectors that are parameterised by the inverse of their
covariance matrix, is a fundamental problem in computational statistics. In
this paper, we show how we can exploit arbitrarily accu- rate approximations to
a GMRF to speed up Krylov subspace sampling methods. We also show that these
methods can be used when computing the normalising constant of a large
multivariate Gaussian distribution, which is needed for both any
likelihood-based inference method. The method we derive is also applicable to
other structured Gaussian random vectors and, in particu- lar, we show that
when the precision matrix is a perturbation of a (block) circulant matrix, it
is still possible to derive O(n log n) sampling schemes.Comment: 17 Pages, 4 Figure
A geometric framework for modelling similarity search
The aim of this paper is to propose a geometric framework for modelling
similarity search in large and multidimensional data spaces of general nature,
which seems to be flexible enough to address such issues as analysis of
complexity, indexability, and the `curse of dimensionality.' Such a framework
is provided by the concept of the so-called similarity workload, which is a
probability metric space (query domain) with a distinguished finite
subspace (dataset), together with an assembly of concepts, techniques, and
results from metric geometry. They include such notions as metric transform,
\e-entropy, and the phenomenon of concentration of measure on
high-dimensional structures. In particular, we discuss the relevance of the
latter to understanding the curse of dimensionality. As some of those concepts
and techniques are being currently reinvented by the database community, it
seems desirable to try and bridge the gap between database research and the
relevant work already done in geometry and analysis.Comment: 11 pages, LaTeX 2.
Mixture of Bilateral-Projection Two-dimensional Probabilistic Principal Component Analysis
The probabilistic principal component analysis (PPCA) is built upon a global
linear mapping, with which it is insufficient to model complex data variation.
This paper proposes a mixture of bilateral-projection probabilistic principal
component analysis model (mixB2DPPCA) on 2D data. With multi-components in the
mixture, this model can be seen as a soft cluster algorithm and has capability
of modeling data with complex structures. A Bayesian inference scheme has been
proposed based on the variational EM (Expectation-Maximization) approach for
learning model parameters. Experiments on some publicly available databases
show that the performance of mixB2DPPCA has been largely improved, resulting in
more accurate reconstruction errors and recognition rates than the existing
PCA-based algorithms
Manifold Relevance Determination
In this paper we present a fully Bayesian latent variable model which
exploits conditional nonlinear(in)-dependence structures to learn an efficient
latent representation. The latent space is factorized to represent shared and
private information from multiple views of the data. In contrast to previous
approaches, we introduce a relaxation to the discrete segmentation and allow
for a "softly" shared latent space. Further, Bayesian techniques allow us to
automatically estimate the dimensionality of the latent spaces. The model is
capable of capturing structure underlying extremely high dimensional spaces.
This is illustrated by modelling unprocessed images with tenths of thousands of
pixels. This also allows us to directly generate novel images from the trained
model by sampling from the discovered latent spaces. We also demonstrate the
model by prediction of human pose in an ambiguous setting. Our Bayesian
framework allows us to perform disambiguation in a principled manner by
including latent space priors which incorporate the dynamic nature of the data.Comment: ICML201
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