Recent advancements in chemometrics for smart sensors

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Multi-dimensional wavelet transforms (WTs) have been introduced for efficient data compression in order to accelerate chemometric calculations and to reduce requirements for data storage space. For hyphenated measurement techniques or hyperspectral imaging this wavelet compression becomes vital because such sensors acquire unprecedented amounts of information in short periods of time. Conventional, multi-dimensional wavelet compression uses the same wavelet for all dimensions. However, from a mathematical perspective there is no need for this restriction as the transforms in different dimensions are independent from each other. This manuscript presents multidimensional 'hybrid wavelet transforms', which utilize different wavelet types for different dimensions. Thus, hybrid wavelets optimize wavelet compression by adjusting WTs to the different types of data sets.In this manuscript we demonstrate that hybrid wavelets improve acceleration factors compared to conventional multi-dimensional wavelet compression and determine more precise models. Combinations of Haar, Daub4, Daub6, Daub8, Daub10, Daub12, Daub14, Daub16, Daub18 and Daub20 wavelets are considered in this study. Data obtained with two different experimental techniques are used for assessing hybrid wavelet compression: (i) a data cube obtained by means of mid-infrared hyperspectral imaging; (ii) data acquired by excitation-emission matrix (EEM) fluorescence spectroscopy in photo-catalytic studies. For the hyperspectral data cube hybrid wavelets were found, which are superior regarding acceleration and model quality to all 10 conventional WTs (Haar-Daub20). For the EEM example this was achieved in 9 out of 10 cases; thus in 19 out of 20 investigated cases hybrid WTs were found to be superior to conventional wavelet compression.

Section: Experimental Data-hyperspectral Imagingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Introducing multi‐dimensional ‘hybrid wavelets’ for enhanced evaluation of hyperspectral image cubes and multi‐way data sets

Vogt¹,

Cramer²,

Booksh³

2005

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“…First we adapt 3D wavelet compression [37] from hyperspectral imaging [32] to 3-way PARAFAC; this approach is then extended to 4-way data sets utilizing 4D Figure 1. Exemplary 4D hypercube acquired by EEM spectroscopy [4,5]; such a hypercube consists of a series of the 3D cubes; every 3D cube in turn belongs to one sample and contains a time series of EEM spectra.…”

Section: Wavelet Compression Of Multi-way Data Setsmentioning

confidence: 99%

“…For example, 1D WTs have been utilized prior to principal component analysis/regression (PCA/PCR) in order to accelerate calculations [29][30][31]. Although (inverse) WTs add computational expense, which is linear with respect to the amount of data [16], smaller data sets allow for decreasing PCA computation times in the second and third order [32]. Hence, the difference of increasing computation expense in linear order and decreasing the floating-point operations in higher orders enabled observed acceleration factors up to 52.…”

Section: Introductionmentioning

confidence: 99%

Accelerating the analyses of 3‐way and 4‐way PARAFAC models utilizing multi‐dimensional wavelet compression

Cramer

Kim

Vogt

et al. 2005

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Parallel factor analysis (PARAFAC) is one of the most popular methods for evaluating multi-way data sets, such as those typically acquired by hyphenated measurement techniques. One of the reasons for PARAFAC popularity is the ability to extract directly interpretable chemometric models with little a priori information and the capability to handle unknown interferents and missing values. However, PARAFAC requires long computation times that often prohibit sufficiently fast analyses for applications such as online sensing. An additional challenge faced by PARAFAC users is the handling and storage of very large, high-dimensional data sets. Accelerating computations and reducing storage requirements in multi-way analyses are the topics of this manuscript. This study introduces a data pre-processing method based on multi-dimensional wavelet transforms (WTs), which enables highly efficient data compression applied prior to data evaluation. Because multidimensional WTs are linear, the intrinsic underlying linear data construction is preserved in the wavelet domain. In almost all studied examples, computation times for analyzing the much smaller, compressed data sets could be reduced so much that the additional effort for wavelet compression was more than recompensated. For 3-way and 4-way synthetic and experimental data sets, acceleration factors up to 50 have been achieved; these data sets could be compressed down to a few per cent of the original size. Despite the high compression, accurate and interpretable models were derived, which are in good agreement with conventionally determined PARAFAC models. This study also found that the wavelet type used for compression is an important factor determining acceleration factors, data compression ratios and model quality.

Composing hybrid wavelets for optimum and near‐optimum representation and accelerated evaluation of N‐way data sets

Luttrell¹,

Gilbert²,

Vogt³

2007

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In hyphenated measurement devices, temporal, spatial, and spectral resolutions continue to increase. While this is advantageous from a chemical sensing perspective, the amount of data grows exponentially; this imposes challenges on Chemometric algorithms resulting in long computation times. In online sensing, however, time resolution is of vital importance and time delays introduced by lengthy computations become unacceptable. Further, in many applications, data need to be documented and a continuous stream of large data sets presents another technical burden regarding archiving space. This work builds on the previous wavelet studies that have already been published. It was found that there is no reason to use the same wavelet for all dimensions of a data set. 'Hybrid wavelets' were introduced which combine different wavelets; this facilitates fine-tuning of the compression. The challenge in using hybrid wavelets lies in the very large number of possible wavelet combinations. A method is presented that automatically determines the optimum and near-optimum wavelet combinations for a given data set. These wavelet combinations are found by evaluating each dimension of the data set separately. This procedure enables an optimization of computation speed, compressed data set size and accuracy of the Chemometric model.Two data cubes acquired from two different experiments are used to show the selection algorithm's capabilities. These examples demonstrate that this algorithm selects hybrid wavelets that are superior to randomly selected wavelet combinations regarding data approximation, compressed data set size, and acceleration of computations.