11,487 research outputs found
Non-linear projection to latent structures
PhD ThesisThis Thesis focuses on the study of multivariate statistical regression techniques which have
been used to produce non-linear empirical models of chemical processes, and on the
development of a novel approach to non-linear Projection to Latent Structures regression.
Empirical modelling relies on the availability of process data and sound empirical regression
techniques which can handle variable collinearities, measurement noise, unknown variable and
noise distributions and high data set dimensionality. Projection based techniques, such as
Principal Component Analysis (PCA) and Projection to Latent Structures (PLS), have been
shown to be appropriate for handling such data sets. The multivariate statistical projection based
techniques of PCA and linear PLS are described in detail, highlighting the benefits which can be
gained by using these approaches. However, many chemical processes exhibit severely nonlinear
behaviour and non-linear regression techniques are required to develop empirical models.
The derivation of an existing quadratic PLS algorithm is described in detail. The procedure for
updating the model parameters which is required by the quadratic PLS algorithms is explored
and modified. A new procedure for updating the model parameters is presented and is shown to
perform better the existing algorithm. The two procedures have been evaluated on the basis of
the performance of the corresponding quadratic PLS algorithms in modelling data generated
with a strongly non-linear mathematical function and data generated with a mechanistic model of
a benchmark pH neutralisation system. Finally a novel approach to non-linear PLS modelling is
then presented combining the general approximation properties of sigmoid neural networks and
radial basis function networks with the new weights updating procedure within the PLS
framework. These algorithms are shown to outperform existing neural network PLS algorithms
and the quadratic PLS approaches. The new neural network PLS algorithms have been evaluated
on the basis of their performance in modelling the same data used to compare the quadratic PLS
approaches.Strang Studentship
European project ESPRIT PROJECT 22281 (PROGNOSIS)
Centre for Process Analysis, Chemometrics
and Control
Multi-view Learning as a Nonparametric Nonlinear Inter-Battery Factor Analysis
Factor analysis aims to determine latent factors, or traits, which summarize
a given data set. Inter-battery factor analysis extends this notion to multiple
views of the data. In this paper we show how a nonlinear, nonparametric version
of these models can be recovered through the Gaussian process latent variable
model. This gives us a flexible formalism for multi-view learning where the
latent variables can be used both for exploratory purposes and for learning
representations that enable efficient inference for ambiguous estimation tasks.
Learning is performed in a Bayesian manner through the formulation of a
variational compression scheme which gives a rigorous lower bound on the log
likelihood. Our Bayesian framework provides strong regularization during
training, allowing the structure of the latent space to be determined
efficiently and automatically. We demonstrate this by producing the first (to
our knowledge) published results of learning from dozens of views, even when
data is scarce. We further show experimental results on several different types
of multi-view data sets and for different kinds of tasks, including exploratory
data analysis, generation, ambiguity modelling through latent priors and
classification.Comment: 49 pages including appendi
Nonlinear tube-fitting for the analysis of anatomical and functional structures
We are concerned with the estimation of the exterior surface and interior
summaries of tube-shaped anatomical structures. This interest is motivated by
two distinct scientific goals, one dealing with the distribution of HIV
microbicide in the colon and the other with measuring degradation in
white-matter tracts in the brain. Our problem is posed as the estimation of the
support of a distribution in three dimensions from a sample from that
distribution, possibly measured with error. We propose a novel tube-fitting
algorithm to construct such estimators. Further, we conduct a simulation study
to aid in the choice of a key parameter of the algorithm, and we test our
algorithm with validation study tailored to the motivating data sets. Finally,
we apply the tube-fitting algorithm to a colon image produced by single photon
emission computed tomography (SPECT) and to a white-matter tract image produced
using diffusion tensor imaging (DTI).Comment: Published in at http://dx.doi.org/10.1214/10-AOAS384 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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