5,791 research outputs found
Recent advances in directional statistics
Mainstream statistical methodology is generally applicable to data observed
in Euclidean space. There are, however, numerous contexts of considerable
scientific interest in which the natural supports for the data under
consideration are Riemannian manifolds like the unit circle, torus, sphere and
their extensions. Typically, such data can be represented using one or more
directions, and directional statistics is the branch of statistics that deals
with their analysis. In this paper we provide a review of the many recent
developments in the field since the publication of Mardia and Jupp (1999),
still the most comprehensive text on directional statistics. Many of those
developments have been stimulated by interesting applications in fields as
diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics,
image analysis, text mining, environmetrics, and machine learning. We begin by
considering developments for the exploratory analysis of directional data
before progressing to distributional models, general approaches to inference,
hypothesis testing, regression, nonparametric curve estimation, methods for
dimension reduction, classification and clustering, and the modelling of time
series, spatial and spatio-temporal data. An overview of currently available
software for analysing directional data is also provided, and potential future
developments discussed.Comment: 61 page
Hierarchical Feature Learning
The success of many tasks depends on good feature representation which is often domain-specific and hand-crafted requiring substantial human effort. Such feature representation is not general, i.e. unsuitable for even the same task across multiple domains, let alone different tasks.To address these issues, a multilayered convergent neural architecture is presented for learning from repeating spatially and temporally coincident patterns in data at multiple levels of abstraction. The bottom-up weights in each layer are learned to encode a hierarchy of overcomplete and sparse feature dictionaries from space- and time-varying sensory data. Two algorithms are investigated: recursive layer-by-layer spherical clustering and sparse coding to learn feature hierarchies. The model scales to full-sized high-dimensional input data and to an arbitrary number of layers thereby having the capability to capture features at any level of abstraction. The model learns features that correspond to objects in higher layers and object-parts in lower layers.Learning features invariant to arbitrary transformations in the data is a requirement for any effective and efficient representation system, biological or artificial. Each layer in the proposed network is composed of simple and complex sublayers motivated by the layered organization of the primary visual cortex. When exposed to natural videos, the model develops simple and complex cell-like receptive field properties. The model can predict by learning lateral connections among the simple sublayer neurons. A topographic map to their spatial features emerges by minimizing the wiring length simultaneously with feature learning.The model is general-purpose, unsupervised and online. Operations in each layer of the model can be implemented in parallelized hardware, making it very efficient for real world applications
Zero-bias autoencoders and the benefits of co-adapting features
Regularized training of an autoencoder typically results in hidden unit
biases that take on large negative values. We show that negative biases are a
natural result of using a hidden layer whose responsibility is to both
represent the input data and act as a selection mechanism that ensures sparsity
of the representation. We then show that negative biases impede the learning of
data distributions whose intrinsic dimensionality is high. We also propose a
new activation function that decouples the two roles of the hidden layer and
that allows us to learn representations on data with very high intrinsic
dimensionality, where standard autoencoders typically fail. Since the decoupled
activation function acts like an implicit regularizer, the model can be trained
by minimizing the reconstruction error of training data, without requiring any
additional regularization
Rotationally Invariant Image Representation for Viewing Direction Classification in Cryo-EM
We introduce a new rotationally invariant viewing angle classification method
for identifying, among a large number of Cryo-EM projection images, similar
views without prior knowledge of the molecule. Our rotationally invariant
features are based on the bispectrum. Each image is denoised and compressed
using steerable principal component analysis (PCA) such that rotating an image
is equivalent to phase shifting the expansion coefficients. Thus we are able to
extend the theory of bispectrum of 1D periodic signals to 2D images. The
randomized PCA algorithm is then used to efficiently reduce the dimensionality
of the bispectrum coefficients, enabling fast computation of the similarity
between any pair of images. The nearest neighbors provide an initial
classification of similar viewing angles. In this way, rotational alignment is
only performed for images with their nearest neighbors. The initial nearest
neighbor classification and alignment are further improved by a new
classification method called vector diffusion maps. Our pipeline for viewing
angle classification and alignment is experimentally shown to be faster and
more accurate than reference-free alignment with rotationally invariant K-means
clustering, MSA/MRA 2D classification, and their modern approximations
Log-Euclidean Bag of Words for Human Action Recognition
Representing videos by densely extracted local space-time features has
recently become a popular approach for analysing actions. In this paper, we
tackle the problem of categorising human actions by devising Bag of Words (BoW)
models based on covariance matrices of spatio-temporal features, with the
features formed from histograms of optical flow. Since covariance matrices form
a special type of Riemannian manifold, the space of Symmetric Positive Definite
(SPD) matrices, non-Euclidean geometry should be taken into account while
discriminating between covariance matrices. To this end, we propose to embed
SPD manifolds to Euclidean spaces via a diffeomorphism and extend the BoW
approach to its Riemannian version. The proposed BoW approach takes into
account the manifold geometry of SPD matrices during the generation of the
codebook and histograms. Experiments on challenging human action datasets show
that the proposed method obtains notable improvements in discrimination
accuracy, in comparison to several state-of-the-art methods
Characterising population variability in brain structure through models of whole-brain structural connectivity
Models of whole-brain connectivity are valuable for understanding neurological function. This thesis
seeks to develop an optimal framework for extracting models of whole-brain connectivity from clinically
acquired diffusion data. We propose new approaches for studying these models. The aim is to
develop techniques which can take models of brain connectivity and use them to identify biomarkers
or phenotypes of disease.
The models of connectivity are extracted using a standard probabilistic tractography algorithm, modified
to assess the structural integrity of tracts, through estimates of white matter anisotropy. Connections
are traced between 77 regions of interest, automatically extracted by label propagation from
multiple brain atlases followed by classifier fusion. The estimates of tissue integrity for each tract
are input as indices in 77x77 ”connectivity” matrices, extracted for large populations of clinical data.
These are compared in subsequent studies.
To date, most whole-brain connectivity studies have characterised population differences using graph
theory techniques. However these can be limited in their ability to pinpoint the locations of differences
in the underlying neural anatomy. Therefore, this thesis proposes new techniques. These include
a spectral clustering approach for comparing population differences in the clustering properties of
weighted brain networks. In addition, machine learning approaches are suggested for the first time.
These are particularly advantageous as they allow classification of subjects and extraction of features
which best represent the differences between groups.
One limitation of the proposed approach is that errors propagate from segmentation and registration
steps prior to tractography. This can cumulate in the assignment of false positive connections, where
the contribution of these factors may vary across populations, causing the appearance of population
differences where there are none. The final contribution of this thesis is therefore to develop a common
co-ordinate space approach. This combines probabilistic models of voxel-wise diffusion for each subject
into a single probabilistic model of diffusion for the population. This allows tractography to be
performed only once, ensuring that there is one model of connectivity. Cross-subject differences can
then be identified by mapping individual subjects’ anisotropy data to this model. The approach is
used to compare populations separated by age and gender
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