36,524 research outputs found
Clustering by compression
We present a new method for clustering based on compression. The method
doesn't use subject-specific features or background knowledge, and works as
follows: First, we determine a universal similarity distance, the normalized
compression distance or NCD, computed from the lengths of compressed data files
(singly and in pairwise concatenation). Second, we apply a hierarchical
clustering method. The NCD is universal in that it is not restricted to a
specific application area, and works across application area boundaries. A
theoretical precursor, the normalized information distance, co-developed by one
of the authors, is provably optimal but uses the non-computable notion of
Kolmogorov complexity. We propose precise notions of similarity metric, normal
compressor, and show that the NCD based on a normal compressor is a similarity
metric that approximates universality. To extract a hierarchy of clusters from
the distance matrix, we determine a dendrogram (binary tree) by a new quartet
method and a fast heuristic to implement it. The method is implemented and
available as public software, and is robust under choice of different
compressors. To substantiate our claims of universality and robustness, we
report evidence of successful application in areas as diverse as genomics,
virology, languages, literature, music, handwritten digits, astronomy, and
combinations of objects from completely different domains, using statistical,
dictionary, and block sorting compressors. In genomics we presented new
evidence for major questions in Mammalian evolution, based on
whole-mitochondrial genomic analysis: the Eutherian orders and the Marsupionta
hypothesis against the Theria hypothesis.Comment: LaTeX, 27 pages, 20 figure
Fronthaul-Constrained Cloud Radio Access Networks: Insights and Challenges
As a promising paradigm for fifth generation (5G) wireless communication
systems, cloud radio access networks (C-RANs) have been shown to reduce both
capital and operating expenditures, as well as to provide high spectral
efficiency (SE) and energy efficiency (EE). The fronthaul in such networks,
defined as the transmission link between a baseband unit (BBU) and a remote
radio head (RRH), requires high capacity, but is often constrained. This
article comprehensively surveys recent advances in fronthaul-constrained
C-RANs, including system architectures and key techniques. In particular, key
techniques for alleviating the impact of constrained fronthaul on SE/EE and
quality of service for users, including compression and quantization,
large-scale coordinated processing and clustering, and resource allocation
optimization, are discussed. Open issues in terms of software-defined
networking, network function virtualization, and partial centralization are
also identified.Comment: 5 Figures, accepted by IEEE Wireless Communications. arXiv admin
note: text overlap with arXiv:1407.3855 by other author
3D oil reservoir visualisation using octree compression techniques utilising logical grid co-ordinates
Octree compression techniques have been used for several years for compressing large three dimensional
data sets into homogeneous regions. This compression technique is ideally suited to datasets
which have similar values in clusters. Oil engineers represent reservoirs as a three dimensional grid
where hydrocarbons occur naturally in clusters. This research looks at the efficiency of storing these
grids using octree compression techniques where grid cells are broken into active and inactive regions.
Initial experiments yielded high compression ratios as only active leaf nodes and their ancestor, header
nodes are stored as a bitstream to file on disk. Savings in computational time and memory were possible
at decompression, as only active leaf nodes are sent to the graphics card eliminating the need of
reconstructing the original matrix. This results in a more compact vertex table, which can be loaded
into the graphics card quicker and generating shorter refresh delay times
Preconditioned Data Sparsification for Big Data with Applications to PCA and K-means
We analyze a compression scheme for large data sets that randomly keeps a
small percentage of the components of each data sample. The benefit is that the
output is a sparse matrix and therefore subsequent processing, such as PCA or
K-means, is significantly faster, especially in a distributed-data setting.
Furthermore, the sampling is single-pass and applicable to streaming data. The
sampling mechanism is a variant of previous methods proposed in the literature
combined with a randomized preconditioning to smooth the data. We provide
guarantees for PCA in terms of the covariance matrix, and guarantees for
K-means in terms of the error in the center estimators at a given step. We
present numerical evidence to show both that our bounds are nearly tight and
that our algorithms provide a real benefit when applied to standard test data
sets, as well as providing certain benefits over related sampling approaches.Comment: 28 pages, 10 figure
Compressive Mining: Fast and Optimal Data Mining in the Compressed Domain
Real-world data typically contain repeated and periodic patterns. This
suggests that they can be effectively represented and compressed using only a
few coefficients of an appropriate basis (e.g., Fourier, Wavelets, etc.).
However, distance estimation when the data are represented using different sets
of coefficients is still a largely unexplored area. This work studies the
optimization problems related to obtaining the \emph{tightest} lower/upper
bound on Euclidean distances when each data object is potentially compressed
using a different set of orthonormal coefficients. Our technique leads to
tighter distance estimates, which translates into more accurate search,
learning and mining operations \textit{directly} in the compressed domain.
We formulate the problem of estimating lower/upper distance bounds as an
optimization problem. We establish the properties of optimal solutions, and
leverage the theoretical analysis to develop a fast algorithm to obtain an
\emph{exact} solution to the problem. The suggested solution provides the
tightest estimation of the -norm or the correlation. We show that typical
data-analysis operations, such as k-NN search or k-Means clustering, can
operate more accurately using the proposed compression and distance
reconstruction technique. We compare it with many other prevalent compression
and reconstruction techniques, including random projections and PCA-based
techniques. We highlight a surprising result, namely that when the data are
highly sparse in some basis, our technique may even outperform PCA-based
compression.
The contributions of this work are generic as our methodology is applicable
to any sequential or high-dimensional data as well as to any orthogonal data
transformation used for the underlying data compression scheme.Comment: 25 pages, 20 figures, accepted in VLD
Normalized Web Distance and Word Similarity
There is a great deal of work in cognitive psychology, linguistics, and
computer science, about using word (or phrase) frequencies in context in text
corpora to develop measures for word similarity or word association, going back
to at least the 1960s. The goal of this chapter is to introduce the
normalizedis a general way to tap the amorphous low-grade knowledge available
for free on the Internet, typed in by local users aiming at personal
gratification of diverse objectives, and yet globally achieving what is
effectively the largest semantic electronic database in the world. Moreover,
this database is available for all by using any search engine that can return
aggregate page-count estimates for a large range of search-queries. In the
paper introducing the NWD it was called `normalized Google distance (NGD),' but
since Google doesn't allow computer searches anymore, we opt for the more
neutral and descriptive NWD. web distance (NWD) method to determine similarity
between words and phrases. ItComment: Latex, 20 pages, 7 figures, to appear in: Handbook of Natural
Language Processing, Second Edition, Nitin Indurkhya and Fred J. Damerau
Eds., CRC Press, Taylor and Francis Group, Boca Raton, FL, 2010, ISBN
978-142008592
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