12,136 research outputs found
Visual and interactive exploration of point data
Point data, such as Unit Postcodes (UPC), can provide very detailed information at fine
scales of resolution. For instance, socio-economic attributes are commonly assigned to
UPC. Hence, they can be represented as points and observable at the postcode level.
Using UPC as a common field allows the concatenation of variables from disparate data
sources that can potentially support sophisticated spatial analysis. However, visualising
UPC in urban areas has at least three limitations. First, at small scales UPC occurrences
can be very dense making their visualisation as points difficult. On the other hand,
patterns in the associated attribute values are often hardly recognisable at large scales.
Secondly, UPC can be used as a common field to allow the concatenation of highly
multivariate data sets with an associated postcode. Finally, socio-economic variables
assigned to UPC (such as the ones used here) can be non-Normal in their distributions
as a result of a large presence of zero values and high variances which constrain their
analysis using traditional statistics.
This paper discusses a Point Visualisation Tool (PVT), a proof-of-concept system
developed to visually explore point data. Various well-known visualisation techniques
were implemented to enable their interactive and dynamic interrogation. PVT provides
multiple representations of point data to facilitate the understanding of the relations
between attributes or variables as well as their spatial characteristics. Brushing between
alternative views is used to link several representations of a single attribute, as well as
to simultaneously explore more than one variable. PVT’s functionality shows how the
use of visual techniques embedded in an interactive environment enable the exploration
of large amounts of multivariate point data
Mapping Topographic Structure in White Matter Pathways with Level Set Trees
Fiber tractography on diffusion imaging data offers rich potential for
describing white matter pathways in the human brain, but characterizing the
spatial organization in these large and complex data sets remains a challenge.
We show that level set trees---which provide a concise representation of the
hierarchical mode structure of probability density functions---offer a
statistically-principled framework for visualizing and analyzing topography in
fiber streamlines. Using diffusion spectrum imaging data collected on
neurologically healthy controls (N=30), we mapped white matter pathways from
the cortex into the striatum using a deterministic tractography algorithm that
estimates fiber bundles as dimensionless streamlines. Level set trees were used
for interactive exploration of patterns in the endpoint distributions of the
mapped fiber tracks and an efficient segmentation of the tracks that has
empirical accuracy comparable to standard nonparametric clustering methods. We
show that level set trees can also be generalized to model pseudo-density
functions in order to analyze a broader array of data types, including entire
fiber streamlines. Finally, resampling methods show the reliability of the
level set tree as a descriptive measure of topographic structure, illustrating
its potential as a statistical descriptor in brain imaging analysis. These
results highlight the broad applicability of level set trees for visualizing
and analyzing high-dimensional data like fiber tractography output
Uncertainty-Aware Principal Component Analysis
We present a technique to perform dimensionality reduction on data that is
subject to uncertainty. Our method is a generalization of traditional principal
component analysis (PCA) to multivariate probability distributions. In
comparison to non-linear methods, linear dimensionality reduction techniques
have the advantage that the characteristics of such probability distributions
remain intact after projection. We derive a representation of the PCA sample
covariance matrix that respects potential uncertainty in each of the inputs,
building the mathematical foundation of our new method: uncertainty-aware PCA.
In addition to the accuracy and performance gained by our approach over
sampling-based strategies, our formulation allows us to perform sensitivity
analysis with regard to the uncertainty in the data. For this, we propose
factor traces as a novel visualization that enables to better understand the
influence of uncertainty on the chosen principal components. We provide
multiple examples of our technique using real-world datasets. As a special
case, we show how to propagate multivariate normal distributions through PCA in
closed form. Furthermore, we discuss extensions and limitations of our
approach
- …