643 research outputs found
Identifiability of the Simplex Volume Minimization Criterion for Blind Hyperspectral Unmixing: The No Pure-Pixel Case
In blind hyperspectral unmixing (HU), the pure-pixel assumption is well-known
to be powerful in enabling simple and effective blind HU solutions. However,
the pure-pixel assumption is not always satisfied in an exact sense, especially
for scenarios where pixels are heavily mixed. In the no pure-pixel case, a good
blind HU approach to consider is the minimum volume enclosing simplex (MVES).
Empirical experience has suggested that MVES algorithms can perform well
without pure pixels, although it was not totally clear why this is true from a
theoretical viewpoint. This paper aims to address the latter issue. We develop
an analysis framework wherein the perfect endmember identifiability of MVES is
studied under the noiseless case. We prove that MVES is indeed robust against
lack of pure pixels, as long as the pixels do not get too heavily mixed and too
asymmetrically spread. The theoretical results are verified by numerical
simulations
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Recursive least squares semi-blind beamforming for MIMO using decision directed adaptation and constant modulus criterion
A new semi-blind adaptive beamforming scheme is proposed for multi-input multi-output (MIMO) induced and space-
division multiple-access based wireless systems that employ high order phase shift keying signaling. A minimum number of training
symbols, very close to the number of receiver antenna elements, are used to provide a rough initial least squares estimate of the
beamformer0s weight vector. A novel cost function combining the constant modulus criterion with decision-directed adaptation is
adopted to adapt the beamformer weight vector. This cost function can be approximated as a quadratic form with a closed-form
solution, based on which we then derive the recursive least squares (RLS) semi-blind adaptive beamforming algorithm. This semi-blind
adaptive beamforming scheme is capable of converging fast to the minimum mean-square-error beamforming solution, as demonstrated
in our simulation study. Our proposed semi-blind RLS beamforming algorithm therefore provides an e±cient detection scheme for the
future generation of MIMO aided mobile communication systems
Variation-based Cause Effect Identification
Mining genuine mechanisms underlying the complex data generation process in
real-world systems is a fundamental step in promoting interpretability of, and
thus trust in, data-driven models. Therefore, we propose a variation-based
cause effect identification (VCEI) framework for causal discovery in bivariate
systems from a single observational setting. Our framework relies on the
principle of independence of cause and mechanism (ICM) under the assumption of
an existing acyclic causal link, and offers a practical realization of this
principle. Principally, we artificially construct two settings in which the
marginal distributions of one covariate, claimed to be the cause, are
guaranteed to have non-negligible variations. This is achieved by re-weighting
samples of the marginal so that the resultant distribution is notably distinct
from this marginal according to some discrepancy measure. In the causal
direction, such variations are expected to have no impact on the effect
generation mechanism. Therefore, quantifying the impact of these variations on
the conditionals reveals the genuine causal direction. Moreover, we formulate
our approach in the kernel-based maximum mean discrepancy, lifting all
constraints on the data types of cause-and-effect covariates, and rendering
such artificial interventions a convex optimization problem. We provide a
series of experiments on real and synthetic data showing that VCEI is, in
principle, competitive to other cause effect identification frameworks
Nonnegative Matrix Factorization for Signal and Data Analytics: Identifiability, Algorithms, and Applications
Nonnegative matrix factorization (NMF) has become a workhorse for signal and
data analytics, triggered by its model parsimony and interpretability. Perhaps
a bit surprisingly, the understanding to its model identifiability---the major
reason behind the interpretability in many applications such as topic mining
and hyperspectral imaging---had been rather limited until recent years.
Beginning from the 2010s, the identifiability research of NMF has progressed
considerably: Many interesting and important results have been discovered by
the signal processing (SP) and machine learning (ML) communities. NMF
identifiability has a great impact on many aspects in practice, such as
ill-posed formulation avoidance and performance-guaranteed algorithm design. On
the other hand, there is no tutorial paper that introduces NMF from an
identifiability viewpoint. In this paper, we aim at filling this gap by
offering a comprehensive and deep tutorial on model identifiability of NMF as
well as the connections to algorithms and applications. This tutorial will help
researchers and graduate students grasp the essence and insights of NMF,
thereby avoiding typical `pitfalls' that are often times due to unidentifiable
NMF formulations. This paper will also help practitioners pick/design suitable
factorization tools for their own problems.Comment: accepted version, IEEE Signal Processing Magazine; supplementary
materials added. Some minor revisions implemente
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