8,084 research outputs found
Entropy Encoding, Hilbert Space and Karhunen-Loeve Transforms
By introducing Hilbert space and operators, we show how probabilities,
approximations and entropy encoding from signal and image processing allow
precise formulas and quantitative estimates. Our main results yield orthogonal
bases which optimize distinct measures of data encoding.Comment: 25 pages, 1 figur
Data Mining Feature Subset Weighting and Selection Using Genetic Algorithms
We present a simple genetic algorithm (sGA), which is developed under Genetic Rule and Classifier Construction Environment (GRaCCE) to solve feature subset selection and weighting problem to have better classification accuracy on k-nearest neighborhood (KNN) algorithm. Our hypotheses are that weighting the features will affect the performance of the KNN algorithm and will cause better classification accuracy rate than that of binary classification. The weighted-sGA algorithm uses real-value chromosomes to find the weights for features and binary-sGA uses integer-value chromosomes to select the subset of features from original feature set. A Repair algorithm is developed for weighted-sGA algorithm to guarantee the feasibility of chromosomes. By feasibility we mean that the sum of values of each gene in a chromosome must be equal to 1. To calculate the fitness values for each chromosome in the population, we use K Nearest Neighbor Algorithm (KNN) as our fitness function. The Euclidean distance from one individual to other individuals is calculated on the d-dimensional feature space to classify an unknown instance. GRaCCE searches for good feature subsets and their associated weights. These feature weights are then multiplied with normalized feature values and these new values are used to calculate the distance between features
Bayesian Inverse Quantum Theory
A Bayesian approach is developed to determine quantum mechanical potentials
from empirical data. Bayesian methods, combining empirical measurements and "a
priori" information, provide flexible tools for such empirical learning
problems. The paper presents the basic theory, concentrating in particular on
measurements of particle coordinates in quantum mechanical systems at finite
temperature. The computational feasibility of the approach is demonstrated by
numerical case studies. Finally, it is shown how the approach can be
generalized to such many-body and few-body systems for which a mean field
description is appropriate. This is done by means of a Bayesian inverse
Hartree-Fock approximation.Comment: LaTex, 32 pages, 19 figure
Verification of Many-Qubit States
Verification is a task to check whether a given quantum state is close to an
ideal state or not. In this paper, we show that a variety of many-qubit quantum
states can be verified with only sequential single-qubit measurements of Pauli
operators. First, we introduce a protocol for verifying ground states of
Hamiltonians. We next explain how to verify quantum states generated by a
certain class of quantum circuits. We finally propose an adaptive test of
stabilizers that enables the verification of all polynomial-time-generated
hypergraph states, which include output states of the
Bremner-Montanaro-Shepherd-type instantaneous quantum polynomial time (IQP)
circuits. Importantly, we do not make any assumption that the identically and
independently distributed copies of the same states are given: Our protocols
work even if some highly complicated entanglement is created among copies in
any artificial way. As applications, we consider the verification of the
quantum computational supremacy demonstration with IQP models, and verifiable
blind quantum computing.Comment: 15 pages, 3 figures, published versio
One-dimensional many-body entangled open quantum systems with tensor network methods
We present a collection of methods to simulate entangled dynamics of open
quantum systems governed by the Lindblad equation with tensor network methods.
Tensor network methods using matrix product states have been proven very useful
to simulate many-body quantum systems and have driven many innovations in
research. Since the matrix product state design is tailored for closed
one-dimensional systems governed by the Schr\"odinger equation, the next step
for many-body quantum dynamics is the simulation of open quantum systems. We
review the three dominant approaches to the simulation of open quantum systems
via the Lindblad master equation: quantum trajectories, matrix product density
operators, and locally purified tensor networks. Selected examples guide
possible applications of the methods and serve moreover as a benchmark between
the techniques. These examples include the finite temperature states of the
transverse quantum Ising model, the dynamics of an exciton traveling under the
influence of spontaneous emission and dephasing, and a double-well potential
simulated with the Bose-Hubbard model including dephasing. We analyze which
approach is favorable leading to the conclusion that a complete set of all
three methods is most beneficial, push- ing the limits of different scenarios.
The convergence studies using analytical results for macroscopic variables and
exact diagonalization methods as comparison, show, for example, that matrix
product density operators are favorable for the exciton problem in our study.
All three methods access the same library, i.e., the software package Open
Source Matrix Product States, allowing us to have a meaningful comparison
between the approaches based on the selected examples. For example, tensor
operations are accessed from the same subroutines and with the same
optimization eliminating one possible bias in a comparison of such numerical
methods.Comment: 24 pages, 8 figures. Small extension of time evolution section and
moving quantum simulators to introduction in comparison to v
Enhancing multi-class classification in FARC-HD fuzzy classifier: on the synergy between n-dimensional overlap functions and decomposition strategies
There are many real-world classification problems involving multiple classes, e.g., in bioinformatics, computer vision or medicine. These problems are generally more difficult than their binary counterparts. In this scenario, decomposition strategies usually improve the performance of classifiers. Hence, in this paper we aim to improve the behaviour of FARC-HD fuzzy classifier in multi-class classification problems using decomposition strategies, and more specifically One-vs-One (OVO) and One-vs-All (OVA) strategies. However, when these strategies are applied on FARC-HD a problem emerges due to the low confidence values provided by the fuzzy reasoning method. This undesirable condition comes from the application of the product t-norm when computing the matching and association degrees, obtaining low values, which are also dependent on the number of antecedents of the fuzzy rules. As a result, robust aggregation strategies in OVO such as the weighted voting obtain poor results with this fuzzy classifier. In order to solve these problems, we propose to adapt the inference system of FARC-HD replacing the product t-norm with overlap functions. To do so, we define n-dimensional overlap functions. The usage of these new functions allows one to obtain more adequate outputs from the base classifiers for the subsequent aggregation in OVO and OVA schemes. Furthermore, we propose a new aggregation strategy for OVO to deal with the problem of the weighted voting derived from the inappropriate confidences provided by FARC-HD for this aggregation method. The quality of our new approach is analyzed using twenty datasets and the conclusions are supported by a proper statistical analysis. In order to check the usefulness of our proposal, we carry out a comparison against some of the state-of-the-art fuzzy classifiers. Experimental results show the competitiveness of our method.This work was supported in part by the Spanish Ministry of Science and
Technology under projects TIN2011-28488, TIN-2012-33856 and TIN-2013-
40765-P and the Andalusian Research Plan P10-TIC-6858 and P11-TIC-7765
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