1,612 research outputs found
Vector-Quantization by density matching in the minimum Kullback-Leibler divergence sense
Abstract- Representation of a large set of bigh-dimensional data is a fundamental problem in many applications such as communications and biomedical systems. The problem has been tackled by encoding the data with a compact set of code-vectors called processing elements. In this study, we propose a vector quantization technique that encodes the information in the data using concepts derived from information theoretic learning. The algorithm minimizes a cost function based on the Kullback-Liebler divergence to match the distribution of the processing elements with the distribution of the data. The performance of this algorithm is demonstrated on synthetic data as well as on an edge-image of a face. Comparisons are provided with some of the existing algorithms such as LEG and SOM. I
Quantum State Tomography of a Single Qubit: Comparison of Methods
The tomographic reconstruction of the state of a quantum-mechanical system is
an essential component in the development of quantum technologies. We present
an overview of different tomographic methods for determining the
quantum-mechanical density matrix of a single qubit: (scaled) direct inversion,
maximum likelihood estimation (MLE), minimum Fisher information distance, and
Bayesian mean estimation (BME). We discuss the different prior densities in the
space of density matrices, on which both MLE and BME depend, as well as ways of
including experimental errors and of estimating tomography errors. As a measure
of the accuracy of these methods we average the trace distance between a given
density matrix and the tomographic density matrices it can give rise to through
experimental measurements. We find that the BME provides the most accurate
estimate of the density matrix, and suggest using either the pure-state prior,
if the system is known to be in a rather pure state, or the Bures prior if any
state is possible. The MLE is found to be slightly less accurate. We comment on
the extrapolation of these results to larger systems.Comment: 15 pages, 4 figures, 2 tables; replaced previous figure 5 by new
table I. in Journal of Modern Optics, 201
Reduction of Markov Chains using a Value-of-Information-Based Approach
In this paper, we propose an approach to obtain reduced-order models of
Markov chains. Our approach is composed of two information-theoretic processes.
The first is a means of comparing pairs of stationary chains on different state
spaces, which is done via the negative Kullback-Leibler divergence defined on a
model joint space. Model reduction is achieved by solving a
value-of-information criterion with respect to this divergence. Optimizing the
criterion leads to a probabilistic partitioning of the states in the high-order
Markov chain. A single free parameter that emerges through the optimization
process dictates both the partition uncertainty and the number of state groups.
We provide a data-driven means of choosing the `optimal' value of this free
parameter, which sidesteps needing to a priori know the number of state groups
in an arbitrary chain.Comment: Submitted to Entrop
Stochastic Attraction-Repulsion Embedding for Large Scale Image Localization
This paper tackles the problem of large-scale image-based localization (IBL)
where the spatial location of a query image is determined by finding out the
most similar reference images in a large database. For solving this problem, a
critical task is to learn discriminative image representation that captures
informative information relevant for localization. We propose a novel
representation learning method having higher location-discriminating power. It
provides the following contributions: 1) we represent a place (location) as a
set of exemplar images depicting the same landmarks and aim to maximize
similarities among intra-place images while minimizing similarities among
inter-place images; 2) we model a similarity measure as a probability
distribution on L_2-metric distances between intra-place and inter-place image
representations; 3) we propose a new Stochastic Attraction and Repulsion
Embedding (SARE) loss function minimizing the KL divergence between the learned
and the actual probability distributions; 4) we give theoretical comparisons
between SARE, triplet ranking and contrastive losses. It provides insights into
why SARE is better by analyzing gradients. Our SARE loss is easy to implement
and pluggable to any CNN. Experiments show that our proposed method improves
the localization performance on standard benchmarks by a large margin.
Demonstrating the broad applicability of our method, we obtained the third
place out of 209 teams in the 2018 Google Landmark Retrieval Challenge. Our
code and model are available at https://github.com/Liumouliu/deepIBL.Comment: ICC
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