10,484 research outputs found
Wavelet feature extraction and genetic algorithm for biomarker detection in colorectal cancer data
Biomarkers which predict patient’s survival can play an important role in medical diagnosis and
treatment. How to select the significant biomarkers from hundreds of protein markers is a key step in
survival analysis. In this paper a novel method is proposed to detect the prognostic biomarkers ofsurvival in colorectal cancer patients using wavelet analysis, genetic algorithm, and Bayes classifier. One dimensional discrete wavelet transform (DWT) is normally used to reduce the dimensionality of biomedical data. In this study one dimensional continuous wavelet transform (CWT) was proposed to extract the features of colorectal cancer data. One dimensional CWT has no ability to reduce
dimensionality of data, but captures the missing features of DWT, and is complementary part of DWT. Genetic algorithm was performed on extracted wavelet coefficients to select the optimized features, using Bayes classifier to build its fitness function. The corresponding protein markers were
located based on the position of optimized features. Kaplan-Meier curve and Cox regression model 2 were used to evaluate the performance of selected biomarkers. Experiments were conducted on colorectal cancer dataset and several significant biomarkers were detected. A new protein biomarker CD46 was found to significantly associate with survival time
On the Analytic Wavelet Transform
An exact and general expression for the analytic wavelet transform of a
real-valued signal is constructed, resolving the time-dependent effects of
non-negligible amplitude and frequency modulation. The analytic signal is first
locally represented as a modulated oscillation, demodulated by its own
instantaneous frequency, and then Taylor-expanded at each point in time. The
terms in this expansion, called the instantaneous modulation functions, are
time-varying functions which quantify, at increasingly higher orders, the local
departures of the signal from a uniform sinusoidal oscillation. Closed-form
expressions for these functions are found in terms of Bell polynomials and
derivatives of the signal's instantaneous frequency and bandwidth. The analytic
wavelet transform is shown to depend upon the interaction between the signal's
instantaneous modulation functions and frequency-domain derivatives of the
wavelet, inducing a hierarchy of departures of the transform away from a
perfect representation of the signal. The form of these deviation terms
suggests a set of conditions for matching the wavelet properties to suit the
variability of the signal, in which case our expressions simplify considerably.
One may then quantify the time-varying bias associated with signal estimation
via wavelet ridge analysis, and choose wavelets to minimize this bias
The Application of Continuous Wavelet Transform Based Foreground Subtraction Method in 21 cm Sky Surveys
We propose a continuous wavelet transform based non-parametric foreground
subtraction method for the detection of redshifted 21 cm signal from the epoch
of reionization. This method works based on the assumption that the foreground
spectra are smooth in frequency domain, while the 21 cm signal spectrum is full
of saw-tooth-like structures, thus their characteristic scales are
significantly different. We can distinguish them in the wavelet coefficient
space easily and perform the foreground subtraction. Compared with the
traditional spectral fitting based method, our method is more tolerant to
complex foregrounds. Furthermore, we also find that when the instrument has
uncorrected response error, our method can also work significantly better than
the spectral fitting based method. Our method can obtain similar results with
the Wp smoothing method, which is also a non-parametric method, but our method
consumes much less computing time.Comment: Accepted by Ap
Approximate Message Passing in Coded Aperture Snapshot Spectral Imaging
We consider a compressive hyperspectral imaging reconstruction problem, where
three-dimensional spatio-spectral information about a scene is sensed by a
coded aperture snapshot spectral imager (CASSI). The approximate message
passing (AMP) framework is utilized to reconstruct hyperspectral images from
CASSI measurements, and an adaptive Wiener filter is employed as a
three-dimensional image denoiser within AMP. We call our algorithm
"AMP-3D-Wiener." The simulation results show that AMP-3D-Wiener outperforms
existing widely-used algorithms such as gradient projection for sparse
reconstruction (GPSR) and two-step iterative shrinkage/thresholding (TwIST)
given the same amount of runtime. Moreover, in contrast to GPSR and TwIST,
AMP-3D-Wiener need not tune any parameters, which simplifies the reconstruction
process.Comment: to appear in Globalsip 201
Review of modern numerical methods for a simple vanilla option pricing problem
Option pricing is a very attractive issue of financial engineering and optimization. The problem of determining the fair price of an option arises from the assumptions made under a given financial market model. The increasing complexity of these market assumptions contributes to the popularity of the numerical treatment of option valuation. Therefore, the pricing and hedging of plain vanilla options under the Black–Scholes model usually serve as a bench-mark for the development of new numerical pricing approaches and methods designed for advanced option pricing models. The objective of the paper is to present and compare the methodological concepts for the valuation of simple vanilla options using the relatively modern numerical techniques in this issue which arise from the discontinuous Galerkin method, the wavelet approach and the fuzzy transform technique. A theoretical comparison is accompanied by an empirical study based on the numerical verification of simple vanilla option prices. The resulting numerical schemes represent a particularly effective option pricing tool that enables some features of options that are depend-ent on the discretization of the computational domain as well as the order of the polynomial approximation to be captured better
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