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Spacing and shape of random peaks in non-parametric spectrum estimates.

ABSTRACT: In this paper, expressions are derived for the expected number of spurious peaks in a spectrum estimate, that is, crossings above a given significance level per frequency unit, as well as the expected width of these peaks. In numerous scientific applications, spectrum estimates are used for the purpose of identifying sinusoidal or modal components, often thinning large sets of candidate frequencies with coincidence detection. Because one always expects numerous false peaks in a spectrum estimate, knowing the expected rate of false peaks helps to decide whether the number observed is abnormal and hence determine the true nature of the process. An example using solar wind data from the Advanced Composition Explorer is given where spectra display pathological numbers of significant peaks, while temporally permuted versions of the data possess spectra with the number expected for a white, Gaussian process. The permutation test is a valuable diagnostic for processes suspected to contain many line components.

SUBMITTER: Thomson DJ

PROVIDER: S-EPMC4032558 | biostudies-literature | 2014 Jul

REPOSITORIES: biostudies-literature

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Spacing and shape of random peaks in non-parametric spectrum estimates.

Thomson D J DJ Haley C L CL

Proceedings. Mathematical, physical, and engineering sciences 20140701 2167

In this paper, expressions are derived for the expected number of spurious peaks in a spectrum estimate, that is, crossings above a given significance level per frequency unit, as well as the expected width of these peaks. In numerous scientific applications, spectrum estimates are used for the purpose of identifying sinusoidal or modal components, often thinning large sets of candidate frequencies with coincidence detection. Because one always expects numerous false peaks in a spectrum estimate ...[more]

PMID: 25002827

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Project description:BackgroundFlow cytometry (FC)-based computer-aided diagnostics is an emerging technique utilizing modern multiparametric cytometry systems.The major difficulty in using machine-learning approaches for classification of FC data arises from limited access to a wide variety of anomalous samples for training. In consequence, any learning with an abundance of normal cases and a limited set of specific anomalous cases is biased towards the types of anomalies represented in the training set. Such models do not accurately identify anomalies, whether previously known or unknown, that may exist in future samples tested. Although one-class classifiers trained using only normal cases would avoid such a bias, robust sample characterization is critical for a generalizable model. Owing to sample heterogeneity and instrumental variability, arbitrary characterization of samples usually introduces feature noise that may lead to poor predictive performance. Herein, we present a non-parametric Bayesian algorithm called ASPIRE (anomalous sample phenotype identification with random effects) that identifies phenotypic differences across a batch of samples in the presence of random effects. Our approach involves simultaneous clustering of cellular measurements in individual samples and matching of discovered clusters across all samples in order to recover global clusters using probabilistic sampling techniques in a systematic way.ResultsWe demonstrate the performance of the proposed method in identifying anomalous samples in two different FC data sets, one of which represents a set of samples including acute myeloid leukemia (AML) cases, and the other a generic 5-parameter peripheral-blood immunophenotyping. Results are evaluated in terms of the area under the receiver operating characteristics curve (AUC). ASPIRE achieved AUCs of 0.99 and 1.0 on the AML and generic blood immunophenotyping data sets, respectively.ConclusionsThese results demonstrate that anomalous samples can be identified by ASPIRE with almost perfect accuracy without a priori access to samples of anomalous subtypes in the training set. The ASPIRE approach is unique in its ability to form generalizations regarding normal and anomalous states given only very weak assumptions regarding sample characteristics and origin. Thus, ASPIRE could become highly instrumental in providing unique insights about observed biological phenomena in the absence of full information about the investigated samples.

Dataset Information

Spacing and shape of random peaks in non-parametric spectrum estimates.

Publications

Spacing and shape of random peaks in non-parametric spectrum estimates.

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