37,538 research outputs found
Linear, Deterministic, and Order-Invariant Initialization Methods for the K-Means Clustering Algorithm
Over the past five decades, k-means has become the clustering algorithm of
choice in many application domains primarily due to its simplicity, time/space
efficiency, and invariance to the ordering of the data points. Unfortunately,
the algorithm's sensitivity to the initial selection of the cluster centers
remains to be its most serious drawback. Numerous initialization methods have
been proposed to address this drawback. Many of these methods, however, have
time complexity superlinear in the number of data points, which makes them
impractical for large data sets. On the other hand, linear methods are often
random and/or sensitive to the ordering of the data points. These methods are
generally unreliable in that the quality of their results is unpredictable.
Therefore, it is common practice to perform multiple runs of such methods and
take the output of the run that produces the best results. Such a practice,
however, greatly increases the computational requirements of the otherwise
highly efficient k-means algorithm. In this chapter, we investigate the
empirical performance of six linear, deterministic (non-random), and
order-invariant k-means initialization methods on a large and diverse
collection of data sets from the UCI Machine Learning Repository. The results
demonstrate that two relatively unknown hierarchical initialization methods due
to Su and Dy outperform the remaining four methods with respect to two
objective effectiveness criteria. In addition, a recent method due to Erisoglu
et al. performs surprisingly poorly.Comment: 21 pages, 2 figures, 5 tables, Partitional Clustering Algorithms
(Springer, 2014). arXiv admin note: substantial text overlap with
arXiv:1304.7465, arXiv:1209.196
Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity
A general framework for solving image inverse problems is introduced in this
paper. The approach is based on Gaussian mixture models, estimated via a
computationally efficient MAP-EM algorithm. A dual mathematical interpretation
of the proposed framework with structured sparse estimation is described, which
shows that the resulting piecewise linear estimate stabilizes the estimation
when compared to traditional sparse inverse problem techniques. This
interpretation also suggests an effective dictionary motivated initialization
for the MAP-EM algorithm. We demonstrate that in a number of image inverse
problems, including inpainting, zooming, and deblurring, the same algorithm
produces either equal, often significantly better, or very small margin worse
results than the best published ones, at a lower computational cost.Comment: 30 page
A Generative Model of Natural Texture Surrogates
Natural images can be viewed as patchworks of different textures, where the
local image statistics is roughly stationary within a small neighborhood but
otherwise varies from region to region. In order to model this variability, we
first applied the parametric texture algorithm of Portilla and Simoncelli to
image patches of 64X64 pixels in a large database of natural images such that
each image patch is then described by 655 texture parameters which specify
certain statistics, such as variances and covariances of wavelet coefficients
or coefficient magnitudes within that patch.
To model the statistics of these texture parameters, we then developed
suitable nonlinear transformations of the parameters that allowed us to fit
their joint statistics with a multivariate Gaussian distribution. We find that
the first 200 principal components contain more than 99% of the variance and
are sufficient to generate textures that are perceptually extremely close to
those generated with all 655 components. We demonstrate the usefulness of the
model in several ways: (1) We sample ensembles of texture patches that can be
directly compared to samples of patches from the natural image database and can
to a high degree reproduce their perceptual appearance. (2) We further
developed an image compression algorithm which generates surprisingly accurate
images at bit rates as low as 0.14 bits/pixel. Finally, (3) We demonstrate how
our approach can be used for an efficient and objective evaluation of samples
generated with probabilistic models of natural images.Comment: 34 pages, 9 figure
Static Analysis for Extracting Permission Checks of a Large Scale Framework: The Challenges And Solutions for Analyzing Android
A common security architecture is based on the protection of certain
resources by permission checks (used e.g., in Android and Blackberry). It has
some limitations, for instance, when applications are granted more permissions
than they actually need, which facilitates all kinds of malicious usage (e.g.,
through code injection). The analysis of permission-based framework requires a
precise mapping between API methods of the framework and the permissions they
require. In this paper, we show that naive static analysis fails miserably when
applied with off-the-shelf components on the Android framework. We then present
an advanced class-hierarchy and field-sensitive set of analyses to extract this
mapping. Those static analyses are capable of analyzing the Android framework.
They use novel domain specific optimizations dedicated to Android.Comment: IEEE Transactions on Software Engineering (2014). arXiv admin note:
substantial text overlap with arXiv:1206.582
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