ISO 18115-1:2023 表面化学分析 — 用語集 — Part 1: 一般用語と分光法で使用される用語 | ページ 25

22.1

classification

procedure in which an algorithm is used to assign objects into defined groups

Note 1 to entry: The objects are typically samples or locations in a chemical map (8.58) .

Note 2 to entry: The algorithm is established using a set of training data from defined groups of objects and then applied to data from unspecified objects to assign them into the defined object groups.

22.2

cluster analysis

clustering

procedure in which objects are grouped in such a way that objects within the same group are more similar to each other than to those in other groups

Note 1 to entry: The objects are typically samples or locations in a chemical map (8.58) .

Note 2 to entry: The criteria for assessing similarity and the boundaries between cluster groups depends upon the specific cluster analysis method.

22.3

multivariate analysis

MVA

analysis involving a simultaneous statistical procedure for two or more dependent variables (22.7)

Note 1 to entry: An essential aspect of multivariate analysis is the dependence between different variables, which can involve their covariance. Multivariate analysis simplifies the interpretation of complex data sets involving a large number of dependent variables by summarizing the data using a smaller number of statistical variables.

Note 2 to entry: Multivariate analysis methods fall into two broad categories: unsupervised (or exploratory) methods and supervised methods. Unsupervised methods are used to identify trends in a data set, key differences between samples (22.6) , and key covariances between spectral features. These methods include factor analysis (22.5) , PCA (22.14) , MAF analysis (22.16) , and MCR (22.17) . Supervised methods are used for prediction, modelling, calibration, and classification (22.1) . These methods include PCR, PLS (22.18) , and DFA (22.15) .

22.4

dimensionality reduction

procedure in which the number of variables in a high dimensionality data matrix (22.8) is reduced

Note 1 to entry: Dimensionality reduction methods can be classified as either feature selection (22.24) or feature extraction (22.23) .

22.5

factor analysis

matrix decomposition of the data matrix (22.8) ( X ) into the product of the scores (22.11) matrix ( T ) and the transpose of the loadings (22.12) matrix ( P′ ), together with a residual matrix (22.13) ( E ), with the aims of describing the underlying structure of the data set using factors (22.10) in order to reduce the dimensionality of the data

Note 1 to entry: Hence, X = TP′ + E .

Note 2 to entry: Factor analysis methods include PCA (22.14) , MCR (22.17) , PLS (22.18) , and MAF analysis (22.16) as well as many others.

Note 3 to entry: The number of factors selected in factor analysis is smaller than the rank of the data matrix.

Note 4 to entry: Factor analysis is equivalent to a rotation in data space where the factors form the new axes. This is not necessarily a rotation that maintains orthogonality except in the case of PCA.

Note 5 to entry: The residual matrix contains data that are not described by the factor analysis model, and is usually assumed to contain noise (3.19) .

22.6

samples

<multivariate analysis> series of individual measurements made on one or more experimental systems

Note 1 to entry: See variables (22.7) .

Note 2 to entry: Data from each sample occupy a row in the data matrix (22.8) .

Note 3 to entry: The term sample in multivariate analysis (22.3) is not to be confused with the conventional use of the word in practical analysis, meaning a physical entity that is under measurement. In multivariate analysis, each “sample” simply denotes an independent measurement. This can be repeat measurements on the same physical sample, measurements on different physical samples, or a combination of both.

22.7

variables

<multivariate analysis> series of channels or parameters over which experimental measurements are made on the samples (22.6)

Note 1 to entry: See samples (22.6) .

Note 2 to entry: Data from each variable occupy a column in the data matrix (22.8) .

Note 3 to entry: In SIMS (19.1) , the variables refer to the mass or time of flight (20.49) of secondary ions (20.28) , and in XPS (11.6) , the variables refer to the binding energies of the photoelectrons detected.

22.8

data matrix

table of numbers, with I rows and K columns, containing experimental data obtained for I samples (22.6) over K values of one or more variables (22.7) ここで,I and K are integers

Note 1 to entry: The term samples denotes any individual measurements made on a system and the term variables denotes the channels over which the measurements are made. For example, in SIMS (19.1) , the variables refer to the mass or time of flight (20.49) of secondary ions (20.28) and, in XPS (11.6) , the variables refer to the binding energies of photoelectrons detected.

Note 2 to entry: For a multivariate map (8.57) with dimensions of I pixels × J pixels × K variables, the data are often matricized prior to multivariate analysis (22.3) to form a data matrix with dimensions IJ × K. On completion of the analysis, the results can be restored to the original map dimensions.

22.9

reproduced data matrix

<factor analysis> product of the scores (22.11) matrix and the transpose of the loadings (22.12) matrix in a factor analysis (22.5) model

Note 1 to entry: The reproduced data matrix is the difference between the data matrix (22.8) and the residual matrix (22.13) for a given factor analysis model.

Note 2 to entry: The reproduced data matrix is often considered to be the noise-filtered approximation of the data matrix. This is true if the residual matrix is assumed to contain noise (3.19) only.

22.10

factor

<factor analysis> axis in the data space of a factor analysis (22.5) model, representing an underlying dimension that contributes to summarizing or accounting for the original data set

Note 1 to entry: In PCA (22.14) , each factor is called a “principal component”. The first PCA factor is called “PC1”. This is deprecated where PCA is used along with other factor analysis techniques such as MCR (22.17) , when it becomes clearer to refer to “PCA factor 1” and “MCR factor 1”.

Note 2 to entry: In MCR, each factor is called a “pure component”. The terms component and pure component are deprecated, however, as they can be confused with real chemical components of the system.

Note 3 to entry: Each factor is associated with a set of loadings (22.12) and scores (22.11) , which occupies a column in the loadings and scores matrices, respectively.

22.11

scores

<factor analysis> projection of the samples (22.6) onto a factor (22.10)

Note 1 to entry: See loadings (22.12) .

Note 2 to entry: In PCA (22.14) , the factors are orthogonal and the scores are an orthogonal projection of the samples onto a factor.

Note 3 to entry: In MAF analysis (22.16) and MCR (22.17) , the factors are generally not orthogonal. The scores on a factor are then an oblique projection of the samples onto that factor. The direction of the projection is defined by the directions of the other factors.

Note 4 to entry: The scores on a factor reflect the relationships between samples for that factor.

Note 5 to entry: The term scores (plural) refers to a whole column in the scores matrix that relates to a particular factor. The term score (singular) is the projection of a particular sample onto the factor.

Note 6 to entry: In MCR, the term pure-component concentration is interchangeable with the term MCR score and is therefore deprecated. In spectroscopy, the term can be confused with the concentration of a pure material.

Note 7 to entry: When analysing multivariate spectral data such as those obtained from SIMS (19.1) or XPS (11.6) , the scores for a factor can be interpreted as a “pseudo-contribution” for the chemical or physical phenomena associated with that factor. There is not necessarily a simple linear relationship between the scores and real physical and chemical properties such as concentration. Calibration standards are essential in attempting to use the scores quantitatively, and any patterns observed in the scores shall be tested for statistical significance by the proper use of replicates, cross-validation, and other statistical tests.

22.12

loadings

<factor analysis> projection of a factor (22.10) onto the variables (22.7)

Note 1 to entry: See scores (22.11) .

Note 2 to entry: The term loadings (plural) refers to a whole column in the loadings matrix that relates to a particular factor. The term loading (singular) is the particular contribution of a variable in the original space to the factor.

Note 3 to entry: The loadings on a factor reflect the relationships between the variables for that factor.

Note 4 to entry: In PCA (22.14) , the loadings are also the cosine angles between the variables and a particular factor.

Note 5 to entry: In MCR (22.17) , the term pure-component spectrum is interchangeable with the term loading and is therefore deprecated. In spectroscopy, the term can be confused with the spectrum for a pure material.

Note 6 to entry: When analysing multivariate spectral data such as those obtained from SIMS (19.1) or XPS (11.6) , the loadings for a factor can be interpreted as “pseudo-spectra” and can be used to develop a chemical or physical interpretation for that factor. Since misinterpretation of these pseudo-spectra is a common caveat, it is important to verify any interpretation with the original data.

22.13

residual matrix

<factor analysis> difference between the data matrix (22.8) and the reproduced data matrix (22.9) for a given factor analysis (22.5) model

Note 1 to entry: The residual matrix contains data that are not described by the factor analysis model, and is usually assumed to contain noise (3.19) .

22.14

principal-component analysis

PCA

factor analysis (22.5) involving the extraction of orthogonal factors (22.10) that successively capture the largest amount of variance in the data set

Note 1 to entry: See MAF analysis (22.16) .

Note 2 to entry: PCA factors are eigenvectors of the matrix Z ここで, Z is the matrix transpose of the data matrix (22.8) multiplied by the data matrix itself. The data in the data matrix may, or may not, have undergone data preprocessing (22.22) . PCA factors are sorted by their associated eigenvalues in descending order. Eigenvalues are the amount of variance described by their associated factor. PCA factors are orthogonal.

Note 3 to entry: PCA has found extensive use in exploring differences in a series of SIMS (19.1) spectra. It is useful, for example, in identifying trends and clusters, discriminating between similar materials and detecting small variations in them, identifying spectral components associated with selected chemical functional groups, and the analysis of spectral changes within a depth profile (3.32) .

Note 4 to entry: PCA is useful for analysis of individual SIMS maps (8.57) and can aid in identifying and enhancing contrast between chemically different regions in a two- or three-dimensional map, and in identifying the spectral components associated with map features.

22.15

discriminant analysis

da

discriminant function analysis

DFA

supervised multivariate technique for classifying samples (22.6) into predefined groups using discriminant functions

Note 1 to entry: Discriminant functions are factors (22.10) that maximize the variance between different groups while minimizing the variance within each group. Loadings (22.12) on DFA factors can be used to provide information on the combination of variables (22.7) which is best for predicting group membership.

Note 2 to entry: DFA is often applied after PCA (22.14) to a multivariate data set. This removes collinearity from the multivariate data and ensures that the new predictor variables, which are PCA scores (22.11) , are distributed normally. This method is referred to as principal-component discriminant function analysis (PC-DFA).

Note 3 to entry: DFA can be used for calibration and prediction, provided that an independent validation data set is used to assess the accuracy of the prediction and guard against the over-fitting of the model to the calibration data. In the absence of an independent validation set, cross-validation can be useful. However, any predictions made on independent samples shall then be treated with caution.

22.16

maximum autocorrelation factor analysis

MAF analysis

factor analysis (22.5) of multivariate maps (8.57) , which involves the extraction of factors (22.10) that successively capture the largest amount of variance across the entire map while minimizing the variation between neighbouring pixels

Note 1 to entry: See PCA (22.14) .

Note 2 to entry: MAFs are the eigenvectors of matrix B ここで, B is the matrix transpose of the variables (22.7) multiplied by the data matrix (22.8) itself, all pre-multiplied by the inverse of the covariance matrix of the shift maps. The shift maps are obtained by subtracting the data matrix from a copy of itself that has been shifted by 1 pixel.

Note 3 to entry: MAF analysis is useful for analysis of individual SIMS (19.1) ion images (20.63) and can aid in identifying and enhancing contrast between chemically different regions in an ion image, as well as in identifying the spectral components associated with ion image features.

Note 4 to entry: Loadings (22.12) obtained from MAF are independent of data scaling (22.30) .

Note 5 to entry: MAF analysis can be extended to the analysis of three-dimensional ion images obtained from SIMS imaging depth profile (3.32) .

22.17

multivariate curve resolution

MCR

non-negative matrix factorization

NMF

factor analysis (22.5) for the decomposition of multicomponent mixtures into a linear sum of chemical components and contributions, when little or no prior information about the composition is available

Note 1 to entry: MCR factors (22.10) are extracted by the iterative minimization of the residual matrix (22.13) using an alternating least squares (ALS) approach, while applying suitable constraints, such as non-negativity, to the loadings (22.12) and scores (22.11) . MCR can be performed on the data matrix (22.8) with or without data preprocessing (22.22) . MCR factors are not required to be orthogonal.

Note 2 to entry: For each data matrix, MCR factors are not unique but are dependent on initial estimates, the number of factors to be resolved, constraints applied, and convergence criteria.

Note 3 to entry: MCR with non-negativity constraints is used in SIMS (19.1) and XPS (11.6) to obtain loadings and scores that resemble physically meaningful chemical-component spectra and contributions, which shall have positive values. However, the assumption of linearity is only a first approximation, and neglects nonlinear effects, such as matrix effects (3.10) , topography, and detector saturation, which can be important in practical analysis.

Note 4 to entry: MCR can be affected by rotational ambiguity, multiplicative ambiguity, and permutation ambiguity. The latter two are considered trivial but rotational ambiguity is a more severe problem and typically results when the data lack selectivity for example in map (8.57) analysis when there is no pure component pixel.

22.18

partial least squares

partial least squares regression

PLS

linear multivariate regression method for assessing relationships among two or more sets of variables (22.7) measured on the same entities

Note 1 to entry: PLS finds factors (22.10) (latent variables) in the observable variables that explain the maximum variance in the predicted variables, using the simultaneous decomposition of the two. It removes redundant information from the regression, i.e. factors describing large amounts of variance in the observed data that does not correlate with the predictions.

Note 2 to entry: PLS can be used for calibration and quantification, provided that an independent validation data set is used to assess the accuracy of the prediction and guard against the over-fitting of the model to the calibration data. In the absence of an independent validation set, cross-validation can be useful in determining the number of PLS factors to retain in the model. However, any predictions made on independent samples (22.6) shall then be treated with caution.

22.19

t-distributed stochastic neighbour embedding

t-SNE

A non-linear dimensionality reduction (22.4) technique where, in the resulting low dimensional space, similar objects have a high probability of being closer together and dissimilar points further apart.

Note 1 to entry: t-SNE operates by constructing a probability distribution over pairs of objects where similar pairs have high probability. It then defines a low dimensional map (8.57) and obtains a similar probability distribution of object pairs by minimising the Kullback-Leibler divergence between the high and the low dimensionality maps.

Note 2 to entry: t-SNE plots often seem to display clusters even for unclustered objects and such clusters can be influenced strongly by the chosen parameterization and therefore a good understanding of the parameters for t-SNE is necessary.

22.20

uniform manifold approximation and projection

UMAP

A non-linear dimensionality reduction (22.4) technique in which the location of objects in the resulting low dimensional space is structurally similar to that in the high dimensional space.

Note 1 to entry: UMAP operates by assuming that the objects are uniformly distributed on a locally connected Riemannian manifold and that the Riemannian metric is locally constant or approximately locally constant.

22.21

artificial neural network

ANN

neural network

computational model utilizing distributed, parallel local processing, and consisting of a network of simple processing elements called artificial neurons, which can exhibit complex global behaviour

Note 1 to entry: The behaviours of ANNs are determined by the connections between the neurons, and neuron parameters (e.g. input weights and bias).

Note 2 to entry: In an adaptive network, the neurons parameters are altered during the learning (training) phase to produce the desired output.

Note 3 to entry: ANNs are used in a wide range of applications including modelling complex relationships, pattern recognition, classification (22.1) , data processing, and decision-making.

Note 4 to entry: ANNs are particularly useful for modelling nonlinear systems.

22.22

data preprocessing

manipulation of raw data prior to a specified data analysis treatment

Note 1 to entry: The terms preprocessing and pretreatment are often used interchangeably, but the latter is deprecated to reduce confusion with sample preparation/treatment prior to experimental analysis.

Note 2 to entry: Aside from the three main categories of data preprocessing method [ centering (22.25) , scaling (22.30) , and transformation (22.33) ], data preprocessing can refer to any other procedures carried out on the raw data, including mass binning and peak selection. In the case of multivariate maps (8.57) , this can also include region-of-interest selection and map filtering or binning.

Note 3 to entry: All data preprocessing methods imply some assumptions about the nature of the variance in the data set. It is important that these assumptions are understood and appropriate for the data set involved.

Note 4 to entry: More than one data preprocessing method can be applied to the same data set. The order of data preprocessing is important and can affect assumptions made on the nature of variance in the data set.

22.23

feature extraction

feature projection

procedure in which high dimensionality data is transformed into informative and non-redundant features

Note 1 to entry: The most common form of feature extraction is factor analysis (22.5) .

22.24

feature selection

procedure in which a subset of relevant variables or predictors are selected for use in model construction

Note 1 to entry: Feature selection methods aim to identify variables that are either correlated or irrelevant and can be eliminated without loss of information.

22.25

centering

<data preprocessing> data preprocessing (22.22) procedure in which each variable (22.7) in the data matrix (22.8) is centered by the subtraction of a reference value across all samples (22.6)

Note 1 to entry: See scaling (22.30) and transformation (22.33) .

Note 2 to entry: Mean centering (22.26) and median centering (22.27) emphasize the differences between samples rather than differences between the samples and the origin.

Note 3 to entry: Centering is generally recommended for PCA (22.14) , PLS (22.18) , and discriminant analysis (22.15) of SIMS (19.1) and XPS (11.6) data ここで, relative intensities of peaks across the samples are more important than their absolute deviation from zero intensities. Centering is not compatible with non-negativity constraints in MCR (22.17) for the resolution of physically meaningful component spectra and contributions, which shall have positive values.

Note 4 to entry: Centering is generally applied after other data preprocessing methods, including data selection and scaling (22.30) .

Note 5 to entry: All data preprocessing methods imply some assumptions about the nature of the variance in the data set with respect to the analysis objective. It is important that these assumptions are understood and appropriate for the data set involved.

22.26

mean centering

<data preprocessing> data preprocessing (22.22) procedure in which each variable (22.7) in the data matrix (22.8) is centered by the subtraction of its mean value across all samples (22.6)

Note 1 to entry: See centering (22.25) .

Note 2 to entry: All data-preprocessing methods imply some assumptions about the nature of the variance in the data set with respect to the analysis objective. It is important that these assumptions are understood and appropriate for the data set involved.

22.27

median centering

<data preprocessing> data preprocessing (22.22) procedure in which each variable (22.7) in the data matrix (22.8) is centered by the subtraction of its median value across all samples (22.6)

Note 1 to entry: See centering (22.25) .

Note 2 to entry: All data preprocessing methods imply some assumptions about the nature of the variance in the data set with respect to the analysis objective. It is important that these assumptions are understood and appropriate for the data set involved.

22.28

normalization

<data preprocessing> scaling (22.30) method used in data preprocessing (22.22) in which the scaling matrix consists of a constant for each sample (22.6)

Note 1 to entry: See variance scaling (22.32) , auto scaling (22.31) , and Poisson scaling (22.29) .

Note 2 to entry: The scaling constant can be the value of a specific variable (22.7) , the sum of selected variables, or the sum of all variables for the sample.

Note 3 to entry: Normalization is commonly used in SIMS (19.1) to compensate for differences in total ion yield (20.7) that arise from instrumental conditions, since the relative intensities within a SIMS spectrum are more repeatable than absolute intensities.

Note 4 to entry: All data preprocessing methods imply some assumptions about the nature of the variance in the data set. It is important that these assumptions are understood and appropriate for the data set involved.

22.29

Poisson scaling

<data preprocessing> scaling (22.30) method used in the data preprocessing (22.22) of data based on Poisson statistics, in which the scaling matrix consists of the outer product of two vectors containing the square root of the mean sample intensity and the square root of the mean spectrum, respectively

Note 1 to entry: See normalization (22.28) and variance scaling (22.32) .

Note 2 to entry: Poisson scaling is only valid for SIMS (19.1) and XPS (11.6) raw data where the detector is operating within linearity, and cannot be applied in conjunction with other data-scaling methods.

Note 3 to entry: It has been shown that Poisson scaling often improves the results obtained in multivariate analysis (22.3) of SIMS data, including PCA (22.14) and MCR (22.17) , by scaling the data such that each element of the data matrix (22.8) has the same experimental uncertainty. In SIMS, this experimental uncertainty can be dominated by the Poisson counting statistics of the detector, such that high-intensity peaks have a higher absolute measurement uncertainty than low-intensity peaks. Poisson scaling weights each peak in each spectrum (i.e. each element of the data matrix) by this uncertainty, which is estimated from the raw data, using the fact that uncertainty arising from Poisson statistics is equal to the average counted intensity.

Note 4 to entry: Poisson scaling is especially valuable for ToF-SIMS ion images (20.63) , which have low counts (3.18) per pixel and can therefore be dominated by Poisson counting noise (3.19) .

Note 5 to entry: In Poisson scaling, it is customary to transform the results obtained by multivariate analysis, such as loadings (22.12) and scores (22.11) from PCA and MCR, from the Poisson scaled space back to the original physical space by the multiplication of the original scaling vectors.

Note 6 to entry: It is usual to add a small constant to the Poisson scaling factors to avoid division by zero.

22.30

scaling

weighting

<data preprocessing> data preprocessing (22.22) procedure in which the data matrix (22.8) is divided element-wise by a scaling matrix

Note 1 to entry: See centering (22.25) and transformation (22.33) .

Note 2 to entry: Common methods of data scaling are normalization (22.28) , variance scaling (22.32) , auto scaling (22.31) , and, in the case of SIMS (19.1) data, and Poisson scaling (22.29) .

Note 3 to entry: Data scaling can affect both the total variance of the data and the relative variance contained in each variable, and can introduce bias in the analysis of data.

Note 4 to entry: Data scaling is generally applied after appropriate data selection, prior to the centering of the data.

Note 5 to entry: All data preprocessing methods imply some assumptions about the nature of the variance in the data set. It is important that these assumptions are understood and appropriate for the data set involved.

22.31

auto scaling

<data preprocessing> data preprocessing (22.22) method involving the application of variance scaling (22.32) followed by centering (22.25)

Note 1 to entry: See variance scaling (22.32) , normalization (22.28) , and Poisson scaling (22.29) .

Note 2 to entry: Auto scaling equalizes the importance of each variable in multivariate analysis (22.3) and is commonly applied in conjunction with peak selection in SIMS.

Note 3 to entry: All data preprocessing methods imply some assumptions about the nature of the variance in the data set. It is important that these assumptions are understood and appropriate for the data set involved.

22.32

variance scaling

<data preprocessing> scaling (22.30) method, used in data preprocessing (22.22) , in which the scaling matrix consists of the standard deviation of each variable (22.7) across the samples (22.6)

Note 1 to entry: See auto scaling (22.31) , normalization (22.28) , and Poisson scaling (22.29) .

Note 2 to entry: Variance scaling is referred to as auto scaling when combined with mean centering (22.26) .

Note 3 to entry: Variance scaling equalizes the importance of each variable in multivariate analysis (22.3) , and is commonly applied in conjunction with peak selection in SIMS.

Note 4 to entry: All data preprocessing methods imply some assumptions about the nature of the variance in the data set. It is important that these assumptions are understood and appropriate for the data set involved.

22.33

transformation

<data preprocessing> data preprocessing (22.22) procedure in which each element in the data matrix (22.8) is transformed by a defined function

Note 1 to entry: See centering (22.25) and scaling (22.30) .

Note 2 to entry: Examples of defined functions are logarithm and square root.

Note 3 to entry: Transformation by a linear function is equivalent to scaling and centering.

Note 4 to entry: All data preprocessing methods imply some assumptions about the nature of the variance in the data set. It is important that these assumptions are understood and appropriate for the data set involved.