Using Self-referencing Interlaced Submatrices To Determine The Number Of Chemical Species In A Mixture

Determination of chemical species number is the first step to analyze a chemical or biological mixture.Due to advances in analytical instrumentation,two-way data matrices become more accessible besides one-way data vectors.Two-way data matrices are rich in chemical information and,inevitably,contain various types of noise.The complexity of two-way data matrices poses a challenge to qualitative and quantitative analyses.Determining the number of chemical species makes a difference and contributes to examining intermediaries involved in chemical kinetics or detecting impurities.Additionally,the correct number of chemical species enables self-modeling curve resolution(SMCR)to extract pure components from a mixture without a prior knowledge.Common methods of estimating the chemical species number largely depend on the size of data matrices,data type and noise distribution,which leads to their failure to deal with various types of data.In this report,the number of chemical species is estimated using self-referencing interlaced submatrices(SRISM).The proposed methods separate chemical information and noise as making use of the frequency differences between them.An original bilinear two-way data matrix is downsampled to generate two interlaced submatrices in an interlacing manner.The interlaced submatrices consist of completely sampled chemical information and undersampled noise of the original data matrix.Chemical information and noise contained in the interlaced submatrices are divided into separate vectors with pairwise comparison of which the chemical species number is determined.There are three main researches included below:1.A fast and effective method was proposed to determine the chemical species in a mixture with two self-referencing interlaced submatrices of a two-way bilinear data matrix.This method is designated as SRISM.The interlaced submatrices comprise the odd or even columns of the original data matrix so that chemical information is completely sampled and noise is undersampled.The interlaced submatrices are divided by principal component analysis(PCA)into principal components(PCs)of chemical information and that of noise.Comparing the pairs of PCs of the two interlaced submatrices yields the chemical species number.SRISM can deal with simulated data containing various interference factors,such as chromatographic overlapping,minor component and noise.It also shows great potential to determine the number of chemical species in various types of experimental data.Moreover,the same data were analyzed using mathematical,empirical and statistical methods to determine the number of chemical species.SRISM has been proven to be effective when dealing with various types of experimental data.2.SRISM is further evaluated with the consideration of how to downsample data matrices and obtain interlaced submatrices.First,an original data matrix is downsampled using the columns and rows in an interlacing manner to construct two submatrices,respectively.The two column-or row-wise interlaced submatrices are then decomposed into PCs by PCA.Pairwise comparison of PCs allows the determination of chemical species number.Second,several interlaced submatrices are obtained by downsamlpling an original data matrix with various frequencces.All the interlaced submatrices are analyzed by PCA.And then the pairs of PCs of two interlaced submatrices are compared to estimate the number of chemical species.Other common methods are also applied to determine the chemical species number under the consideration of the column and row dimensions.3.Several new methods are derived from SRISM to determine the number of chemical species.The derivations use functional principal component analysis(FPCA),simple-to-use interactive self-modeling mixture analysis(SIMPLISMA)and orthogonal projection approach(OPA)rather than PCA to separate chemical information from noise.FPCA involving roughness penalty improves SRISM method to resist to noise.SIMPLISMA and OPA allow the differentiation of chemical information and noise using purity analysis in a straightforward way.