A new sub-class linear discriminant for miniature spectrometer based food analysis

Omar Nibouche; Fayas Asharindavida; Hui Wang; Jordan Vincent; Jun Liu; Saskia van Ruth; Paul Maguire; Enayet Rahman

doi:10.1016/j.chemolab.2024.105136

A new sub-class linear discriminant for miniature spectrometer based food analysis

Omar Nibouche
, Fayas Asharindavida
, Hui Wang
, Jordan Vincent
, Jun Liu
, Saskia van Ruth
, Paul Maguire
, Enayet Rahman

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

40 Downloads (Pure)

Abstract

The well-known and extensively studied Linear Discriminant Analysis (LDA) can have its performance lowered in
scenarios where data is not homoscedastic or not Gaussian. That is, the classical assumptions when LDA models
are built are not applicable, and consequently LDA projections would not be able to extract the needed features to
explain the intrinsic structure of data and for classes to be separated. As with many real word data sets, data
obtained using miniature spectrometers can suffer from such drawbacks which would limit the deployment of
such technology needed for food analysis. The solution presented in the paper is to divide classes into subclasses
and to use means of sub classes, classes, and data in the suggested between classes scatter metric. Further,
samples belonging to the same subclass are used to build a measure of within subclass scatterness. Such a solution solves the shortcoming of the classical LDA. The obtained results when using the proposed solution on food data and on general machine learning datasets show that the work in this paper compares well to and is very
competitive with similar sub-class LDA algorithms in the literature. An extension to a Hilbert space is also
presented; and the kernel version of the presented solution can be fused with its linear counter parts to yield
improved classification rates.

Original language	English
Article number	105136
Pages (from-to)	1-13
Number of pages	13
Journal	Chemometrics and Intelligent Laboratory Systems
Volume	250
Early online date	4 May 2024
DOIs	https://doi.org/10.1016/j.chemolab.2024.105136
Publication status	Published (in print/issue) - 15 Jul 2024

Bibliographical note

Publisher Copyright:
© 2024 The Authors

Data Availability Statement

Data will be made available on request.

Funding

The sought representation \u03C1\u02C6 in (32) is sparse and is an optimisation attempt to reduce its l0 norm which simply measures the sparseness of the sought solution. That is, the sparse representation-based classification (SRC) regression computes the size of the support of the signal which is the number of its nonzero entries. Such optimisation can be formulated as an l1 minimisation subject to quadratic constraint as in (32) which is a convex minimisation problem. The annotation followed when equation (32) is used in the remainder of the paper is classifier+ l0 to indicate that the projection takes place first then is followed by the regression-based representation. Equation (34) seeks the classical solution of a Collaborative Representation based Classification (CRC) with an l2 regularisation term and an ensuing solution given as \u03C1\u02C6=(XXT+\u03BBI)\u22121XTy. The representation in (33) uses an l1 regularisation term; hence when used in conjuncture with a classifier the annotation classifier+ l1 is used. Similarly, the annotation classifier+ l2 indicates that the CRC representation is used once data is projected in the transform domain. Further, in (32), (33) and (34), the parameter \u03BB is a tuning parameter, y is the query sample, X is a matrix containing the training sample and acts as a code dictionary, and \u03B5 is an arbitrarily very small quantity which considers noise, hence the representation error and the sparsity of the representation \u03C1\u02C6. Tables 6\u20138 exhibit the results of using the kernel classifiers introduced in this paper, KCDA. The tables only show the best results from a larger analysis using the AD where among the classical kernels, exponential kernels have not exceeded the performance attained by the polynomial kernels used. The polynomial kernel of degree deg can be indicated by the annotation -ddeg in such tables which also exhibit the performance of the classifiers when combined with one of the representations in (32)\u2013(34). In most classification cases in Table 7, a better performance is obtained when a low polynomial degree kernel is used with the quadratic kernel attaining the best performance in Table 7 and where a regression based representation can only achieve competitive results. That is, in Table 7, KCDA-d2 is slightly better than CSDA and KCDA-d2+ l1 with the latter classifier attaining competitive but not better results than the linear classifier. The other point one can take from Tables 7 and is that when KCDA-d2 is combined with any of the regression-based representations, it persistently tends to do better than any of the classifiers in the table when combined with the same regression-based representation which really underlines the performance of a kernel-based sub class LDA. The matte can also be shown in Table 8 with a combination of KCDA and CRC representation edging slightly better than the linear CSDA in terms of classification performance. Taking the investigation further and looking deeper into the matter of using regression-based representations, a comparison of the results of fusion of multiple classifiers is shown in Table 9. Of the fusion techniques employed by the authors, only the results of the Weighted Majority Voting (WMV) and DST are reported. The weights associated with the WMV rule are the classification rates of the individual classifiers involved. Other fusion techniques have not yielded competitive res [55]ults when compared with DST and WMV; and that includes the simple fusion rules used in Table 6. Further, the analysis extended to include a polynomial kernel of up to degree 5 only; and as in the analysis in Tables 6 and 7, exponential kernels attained lower performance and have been omitted from Table 9.

Keywords

Dimensionality reduction
Feature extraction
Linear discriminant analysis
Subclass discriminant analysis
Classification
Food analysis
Miniature spectrometers

Access to Document

10.1016/j.chemolab.2024.105136Licence: CC BY

1-s2.0-S0169743924000765-mainFinal published version, 2.66 MBLicence: CC BY

Cite this

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title = "A new sub-class linear discriminant for miniature spectrometer based food analysis",

abstract = "The well-known and extensively studied Linear Discriminant Analysis (LDA) can have its performance lowered in scenarios where data is not homoscedastic or not Gaussian. That is, the classical assumptions when LDA models are built are not applicable, and consequently LDA projections would not be able to extract the needed features to explain the intrinsic structure of data and for classes to be separated. As with many real word data sets, data obtained using miniature spectrometers can suffer from such drawbacks which would limit the deployment of such technology needed for food analysis. The solution presented in the paper is to divide classes into subclasses and to use means of sub classes, classes, and data in the suggested between classes scatter metric. Further, samples belonging to the same subclass are used to build a measure of within subclass scatterness. Such a solution solves the shortcoming of the classical LDA. The obtained results when using the proposed solution on food data and on general machine learning datasets show that the work in this paper compares well to and is very competitive with similar sub-class LDA algorithms in the literature. An extension to a Hilbert space is also presented; and the kernel version of the presented solution can be fused with its linear counter parts to yield improved classification rates.",

keywords = "Dimensionality reduction, Feature extraction, Linear discriminant analysis, Subclass discriminant analysis, Classification, Food analysis, Miniature spectrometers",

author = "Omar Nibouche and Fayas Asharindavida and Hui Wang and Jordan Vincent and Jun Liu and Ruth, \{Saskia van\} and Paul Maguire and Enayet Rahman",

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AU - Nibouche, Omar

AU - Asharindavida, Fayas

AU - Wang, Hui

AU - Vincent, Jordan

AU - Liu, Jun

AU - Ruth, Saskia van

AU - Maguire, Paul

AU - Rahman, Enayet

PY - 2024/7/15

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N2 - The well-known and extensively studied Linear Discriminant Analysis (LDA) can have its performance lowered in scenarios where data is not homoscedastic or not Gaussian. That is, the classical assumptions when LDA models are built are not applicable, and consequently LDA projections would not be able to extract the needed features to explain the intrinsic structure of data and for classes to be separated. As with many real word data sets, data obtained using miniature spectrometers can suffer from such drawbacks which would limit the deployment of such technology needed for food analysis. The solution presented in the paper is to divide classes into subclasses and to use means of sub classes, classes, and data in the suggested between classes scatter metric. Further, samples belonging to the same subclass are used to build a measure of within subclass scatterness. Such a solution solves the shortcoming of the classical LDA. The obtained results when using the proposed solution on food data and on general machine learning datasets show that the work in this paper compares well to and is very competitive with similar sub-class LDA algorithms in the literature. An extension to a Hilbert space is also presented; and the kernel version of the presented solution can be fused with its linear counter parts to yield improved classification rates.

AB - The well-known and extensively studied Linear Discriminant Analysis (LDA) can have its performance lowered in scenarios where data is not homoscedastic or not Gaussian. That is, the classical assumptions when LDA models are built are not applicable, and consequently LDA projections would not be able to extract the needed features to explain the intrinsic structure of data and for classes to be separated. As with many real word data sets, data obtained using miniature spectrometers can suffer from such drawbacks which would limit the deployment of such technology needed for food analysis. The solution presented in the paper is to divide classes into subclasses and to use means of sub classes, classes, and data in the suggested between classes scatter metric. Further, samples belonging to the same subclass are used to build a measure of within subclass scatterness. Such a solution solves the shortcoming of the classical LDA. The obtained results when using the proposed solution on food data and on general machine learning datasets show that the work in this paper compares well to and is very competitive with similar sub-class LDA algorithms in the literature. An extension to a Hilbert space is also presented; and the kernel version of the presented solution can be fused with its linear counter parts to yield improved classification rates.

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A new sub-class linear discriminant for miniature spectrometer based food analysis

Abstract

Bibliographical note

Data Availability Statement

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Enhancing low quality spectral data analytics for food quality control

Cite this

A new sub-class linear discriminant for miniature spectrometer based food analysis

Abstract

Bibliographical note

Data Availability Statement

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Student theses

Enhancing low quality spectral data analytics for food quality control

Cite this