Decompositions using maximum signal factors

Gallagher, Neal B.; Shaver, Jeremy M.; Bishop, Randall; Roginski, Robert T.; Wise, Barry M.

doi:10.1002/cem.2634

Cited by 8 publications

(8 citation statements)

References 15 publications

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“…It has been shown that combining target and anomaly detection approaches (e.g., PCA can be considered an anomaly detection approach) allows for empirically enabling target detection to be more sensitive and more relevant to image specific scenarios. 62 Thus, "targeted anomaly detection" synergistically employs laboratory measured spectra with empirical detection methods to provide an approach optimized for individual scenarios and will be investigated in future studies.…”

Section: Discussionmentioning

confidence: 99%

Hyperspectral imaging of minerals in the longwave infrared: the use of laboratory directional-hemispherical reference measurements for field exploration data

Myers

Johnson

Gallagher

et al. 2019

J. Appl. Rem. Sens.

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Hyperspectral imaging (HSI) continues to grow as a method for remote detection of vegetation, materials, minerals, and pure chemicals. We have used a longwave infrared (7.7 to 11.8 μm) imaging spectrometer in a static outdoor experiment to collect HSI data from 24 minerals and background materials to determine the efficacy with which HSI can remotely detect and distinguish both pure minerals and mineral mixtures at a 45-deg tilt angle relative to ground using two different backgrounds. Measurements were obtained separately for the minerals and materials mounted directly on both a bare plywood board and a board coated with aluminum foil: 19 powders (3 mixtures and 16 pure mineral powders) held in polyethylene bottle lids as well as five samples in rock form were taped directly to the boards. The primary goal of the experiment was to demonstrate that a longwave infrared library of solids and minerals collected as directional-hemispherical reflectance spectra in the laboratory could be used directly for HSI field identification along with simple algorithms for a rapid survey of the target materials. Prior to the experiment, all 24 mineral/inorganic samples were measured in the laboratory using a Fourier transform infrared spectrometer equipped with a gold-coated integrating sphere; the spectra were assimilated as part of a larger reference library of 21 pure minerals, 3 mixtures, and the polyethylene lid. Principal component analysis with mean-centering was used in an exploratory analysis of the HSI images and showed that, for the aluminum-coated board, the first principal component captured the difference between the signal that resembled a blackbody and the highly reflective aluminum background. In contrast, the second, third, and fourth principal components were able to discriminate the materials including phosphates, silicates, carbonates, and the mixtures. Results from generalized least squares target detection clearly showed that laboratory reference spectra of minerals could be utilized as targets with high fidelity for field detection.

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Section: Discussionmentioning

confidence: 99%

Hyperspectral imaging of minerals in the longwave infrared: the use of laboratory directional-hemispherical reference measurements for field exploration data

Myers

Johnson

Gallagher

et al. 2019

J. Appl. Rem. Sens.

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“…There has been a surge interest in the theoretical properties and practicality of MAF (Gallagher et al, 2014). In fisheries, Erzini (2005) investigated fishery catches using multiple time series of environmental parameters and compared MAF with dynamic factor analysis.…”

Section: Functional Principal Component Analysis (Fpca)mentioning

confidence: 99%

Maximal autocorrelation factors for function-valued spatial/temporal data

Hooker

Roberts

Shang

2015

Weber, T., McPhee, M.J. And Anderssen, R.S. (Eds) MODSIM2015, 21st International Congress on Modelling and Simulation

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Dimension reduction techniques play a key role in analyzing functional data that possess temporal or spatial dependence. Of these dimension reduction techniques functional principal components analysis (FPCA) remains a popular approach. Functional principal components extract a set of latent components by maximizing variance in a set of dependent functional data. However, this technique may fail to adequately capture temporal or spatial autocorrelation. Functional maximum autocorrelation factors (FMAF) are proposed as an alternative for modeling and forecasting temporally or spatially dependent functional data. FMAF find linear combinations of the original functional data that have maximum autocorrelation and that are decreasingly predictable functions of time. We show that FMAF can be obtained by searching for the rotated components that have the smallest integrated first derivatives. Through a basis function expansion, a set of scores are obtained by multiplying the extracted FMAF with the original functional data. Autocorrelation in the original functional time series is manifested in the autocorrelation of these scores derived. Through a set of Monte Carlo simulation results, we study the finite-sample properties of the proposed FMAF. Wherever possible, we compare the performance between FMAF and FPCA. In an enhanced vegetation index data from Harvard Forest we apply FMAF to capture temporal or spatial dependency.

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“…Some applications of MAF to multiple time series analysis are given in Switzer and Green [1984], Shapiro and Switzer [1989], Gallagher et al [2014]. Our interest in MAF derives from applications to the analysis of multiple time series of climate proxy data from tree ring measurements, described in Section 6.…”

Section: Maf -Maximum Autocorrelation Factorsmentioning

confidence: 99%

Extracting Common Time Trends from Concurrent Time Series: Maximum Autocorrelation Factors with Application to Tree Ring Time Series Data

Haugen,

Rajaratnam,

Switzer

2015

Preprint

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Concurrent time series commonly arise in various applications, including when monitoring the environment such as in air quality measurement networks, weather stations, oceanographic buoys, or in paleo form such as lake sediments, tree rings, ice cores, or coral isotopes, with each monitoring or sampling site providing one of the time series. The goal in such applications is to extract a common time trend or signal in the observed data. Other examples where the goal is to extract a common time trend for multiple time series are in stock price time series, neurological time series, and quality control time series. For this purpose we develop properties of MAF [Maximum Autocorrelation Factors] that linearly combines time series in order to maximize the resulting SNR [signal-to-noise-ratio] where there are multiple smooth signals present in the data. Equivalence is established in a regression setting between MAF and CCA [Canonical Correlation Analysis] even though MAF does not require specific signal knowledge as opposed to CCA. We proceed to derive the theoretical properties of MAF and quantify the SNR advantages of MAF in comparison with PCA [Principal Components Analysis], a commonly used method for linearly combining time series, and compare their statistical sample properties. MAF and PCA are then applied to real and simulated data sets to illustrate MAFs efficacy.

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Decompositions using maximum signal factors

Cited by 8 publications

References 15 publications

Hyperspectral imaging of minerals in the longwave infrared: the use of laboratory directional-hemispherical reference measurements for field exploration data

Hyperspectral imaging of minerals in the longwave infrared: the use of laboratory directional-hemispherical reference measurements for field exploration data

Maximal autocorrelation factors for function-valued spatial/temporal data

Extracting Common Time Trends from Concurrent Time Series: Maximum Autocorrelation Factors with Application to Tree Ring Time Series Data

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