3,225 research outputs found
Masking Strategies for Image Manifolds
We consider the problem of selecting an optimal mask for an image manifold,
i.e., choosing a subset of the pixels of the image that preserves the
manifold's geometric structure present in the original data. Such masking
implements a form of compressive sensing through emerging imaging sensor
platforms for which the power expense grows with the number of pixels acquired.
Our goal is for the manifold learned from masked images to resemble its full
image counterpart as closely as possible. More precisely, we show that one can
indeed accurately learn an image manifold without having to consider a large
majority of the image pixels. In doing so, we consider two masking methods that
preserve the local and global geometric structure of the manifold,
respectively. In each case, the process of finding the optimal masking pattern
can be cast as a binary integer program, which is computationally expensive but
can be approximated by a fast greedy algorithm. Numerical experiments show that
the relevant manifold structure is preserved through the data-dependent masking
process, even for modest mask sizes
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
Visual Cluster Separation Using High-Dimensional Sharpened Dimensionality Reduction
Applying dimensionality reduction (DR) to large, high-dimensional data sets
can be challenging when distinguishing the underlying high-dimensional data
clusters in a 2D projection for exploratory analysis. We address this problem
by first sharpening the clusters in the original high-dimensional data prior to
the DR step using Local Gradient Clustering (LGC). We then project the
sharpened data from the high-dimensional space to 2D by a user-selected DR
method. The sharpening step aids this method to preserve cluster separation in
the resulting 2D projection. With our method, end-users can label each distinct
cluster to further analyze an otherwise unlabeled data set. Our
`High-Dimensional Sharpened DR' (HD-SDR) method, tested on both synthetic and
real-world data sets, is favorable to DR methods with poor cluster separation
and yields a better visual cluster separation than these DR methods with no
sharpening. Our method achieves good quality (measured by quality metrics) and
scales computationally well with large high-dimensional data. To illustrate its
concrete applications, we further apply HD-SDR on a recent astronomical
catalog.Comment: This paper has been accepted for Information Visualization. Copyright
may be transferred without notice, after which this version may no longer be
accessibl
A Distributed and Approximated Nearest Neighbors Algorithm for an Efficient Large Scale Mean Shift Clustering
In this paper we target the class of modal clustering methods where clusters
are defined in terms of the local modes of the probability density function
which generates the data. The most well-known modal clustering method is the
k-means clustering. Mean Shift clustering is a generalization of the k-means
clustering which computes arbitrarily shaped clusters as defined as the basins
of attraction to the local modes created by the density gradient ascent paths.
Despite its potential, the Mean Shift approach is a computationally expensive
method for unsupervised learning. Thus, we introduce two contributions aiming
to provide clustering algorithms with a linear time complexity, as opposed to
the quadratic time complexity for the exact Mean Shift clustering. Firstly we
propose a scalable procedure to approximate the density gradient ascent.
Second, our proposed scalable cluster labeling technique is presented. Both
propositions are based on Locality Sensitive Hashing (LSH) to approximate
nearest neighbors. These two techniques may be used for moderate sized
datasets. Furthermore, we show that using our proposed approximations of the
density gradient ascent as a pre-processing step in other clustering methods
can also improve dedicated classification metrics. For the latter, a
distributed implementation, written for the Spark/Scala ecosystem is proposed.
For all these considered clustering methods, we present experimental results
illustrating their labeling accuracy and their potential to solve concrete
problems.Comment: Algorithms are available at
https://github.com/Clustering4Ever/Clustering4Eve
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