21,264 research outputs found
A Fast and Efficient algorithm for Many-To-Many Matching of Points with Demands in One Dimension
Given two point sets S and T, a many-to-many matching with demands (MMD)
problem is the problem of finding a minimum-cost many-to-many matching between
S and T such that each point of S (respectively T) is matched to at least a
given number of the points of T (respectively S). We propose the first O(n^2)
time algorithm for computing a one dimensional MMD (OMMD) of minimum cost
between S and T, where |S|+|T| = n. In an OMMD problem, the input point sets S
and T lie on the real line and the cost of matching a point to another point
equals the distance between the two points. We also study a generalized version
of the MMD problem, the many-to-many matching with demands and capacities
(MMDC) problem, that in which each point has a limited capacity in addition to
a demand. We give the first O(n^2) time algorithm for the minimum-cost one
dimensional MMDC (OMMDC) problem.Comment: 14 pages,8 figures. arXiv admin note: substantial text overlap with
arXiv:1702.0108
A Faster Algorithm for the Limited-Capacity Many-to-Many Point Matching in One Dimension
Given two point sets S and T on a line, we present the first linear time
algorithm for finding the limited capacity many-to-many matching (LCMM) between
S and T improving the previous best known quadratic time algorithm. The aim of
the LCMM is to match each point of S (T) to at least one point of T (S) such
that the matching costs is minimized and the number of the points matched to
each point is limited to a given number.Comment: 18 pages, 7 figures. arXiv admin note: text overlap with
arXiv:1702.0108
Sketching for Large-Scale Learning of Mixture Models
Learning parameters from voluminous data can be prohibitive in terms of
memory and computational requirements. We propose a "compressive learning"
framework where we estimate model parameters from a sketch of the training
data. This sketch is a collection of generalized moments of the underlying
probability distribution of the data. It can be computed in a single pass on
the training set, and is easily computable on streams or distributed datasets.
The proposed framework shares similarities with compressive sensing, which aims
at drastically reducing the dimension of high-dimensional signals while
preserving the ability to reconstruct them. To perform the estimation task, we
derive an iterative algorithm analogous to sparse reconstruction algorithms in
the context of linear inverse problems. We exemplify our framework with the
compressive estimation of a Gaussian Mixture Model (GMM), providing heuristics
on the choice of the sketching procedure and theoretical guarantees of
reconstruction. We experimentally show on synthetic data that the proposed
algorithm yields results comparable to the classical Expectation-Maximization
(EM) technique while requiring significantly less memory and fewer computations
when the number of database elements is large. We further demonstrate the
potential of the approach on real large-scale data (over 10 8 training samples)
for the task of model-based speaker verification. Finally, we draw some
connections between the proposed framework and approximate Hilbert space
embedding of probability distributions using random features. We show that the
proposed sketching operator can be seen as an innovative method to design
translation-invariant kernels adapted to the analysis of GMMs. We also use this
theoretical framework to derive information preservation guarantees, in the
spirit of infinite-dimensional compressive sensing
Channel Capacity Estimation using Free Probability Theory
In many channel measurement applications, one needs to estimate some
characteristics of the channels based on a limited set of measurements. This is
mainly due to the highly time varying characteristics of the channel. In this
contribution, it will be shown how free probability can be used for channel
capacity estimation in MIMO systems. Free probability has already been applied
in various application fields such as digital communications, nuclear physics
and mathematical finance, and has been shown to be an invaluable tool for
describing the asymptotic behaviour of many large-dimensional systems. In
particular, using the concept of free deconvolution, we provide an
asymptotically (w.r.t. the number of observations) unbiased capacity estimator
for MIMO channels impaired with noise called the free probability based
estimator. Another estimator, called the Gaussian matrix mean based estimator,
is also introduced by slightly modifying the free probability based estimator.
This estimator is shown to give unbiased estimation of the moments of the
channel matrix for any number of observations. Also, the estimator has this
property when we extend to MIMO channels with phase off-set and frequency
drift, for which no estimator has been provided so far in the literature. It is
also shown that both the free probability based and the Gaussian matrix mean
based estimator are asymptotically unbiased capacity estimators as the number
of transmit antennas go to infinity, regardless of whether phase off-set and
frequency drift are present. The limitations in the two estimators are also
explained. Simulations are run to assess the performance of the estimators for
a low number of antennas and samples to confirm the usefulness of the
asymptotic results.Comment: Submitted to IEEE Transactions on Signal Processing. 12 pages, 9
figure
Probabilistic Shaping for Finite Blocklengths: Distribution Matching and Sphere Shaping
In this paper, we provide for the first time a systematic comparison of
distribution matching (DM) and sphere shaping (SpSh) algorithms for short
blocklength probabilistic amplitude shaping. For asymptotically large
blocklengths, constant composition distribution matching (CCDM) is known to
generate the target capacity-achieving distribution. As the blocklength
decreases, however, the resulting rate loss diminishes the efficiency of CCDM.
We claim that for such short blocklengths and over the additive white Gaussian
channel (AWGN), the objective of shaping should be reformulated as obtaining
the most energy-efficient signal space for a given rate (rather than matching
distributions). In light of this interpretation, multiset-partition DM (MPDM),
enumerative sphere shaping (ESS) and shell mapping (SM), are reviewed as
energy-efficient shaping techniques. Numerical results show that MPDM and SpSh
have smaller rate losses than CCDM. SpSh--whose sole objective is to maximize
the energy efficiency--is shown to have the minimum rate loss amongst all. We
provide simulation results of the end-to-end decoding performance showing that
up to 1 dB improvement in power efficiency over uniform signaling can be
obtained with MPDM and SpSh at blocklengths around 200. Finally, we present a
discussion on the complexity of these algorithms from the perspective of
latency, storage and computations.Comment: 18 pages, 10 figure
Adaptive optical networks using photorefractive crystals
The capabilities of photorefractive crystals as media for holographic interconnections in neural networks are examined. Limitations on the density of interconnections and the number of holographic associations which can be stored in photorefractive crystals are derived. Optical architectures for implementing various neural schemes are described. Experimental results are presented for one of these architectures
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