Table 1.

Short description and characteristics of the methods for pre- processing.

	Method	Description	Characteristic
Denoise	Kernel smoothing	Smooths the spectra based on a normal kernel function	Parameter free
	Savitzky-Golay differentiation	Estimates the derivative by consecutively fitting window-wised sub-sets of adjoining data points with a degree (custom designed) polynomial using linear least squares	Parameter-free; can be used for both baseline correction and smoothing/noise reduction.
Baseline removal	MPLS	Finds a rough background based on a penalized least squares function	Relatively time-consuming; competitive results; insensitive to the parameters.
	SNV	Transposes and then auto-scales the data.	Parameter free; scales the data
	MSC	Each input spectrum is regressed against a reference (e.g. the mean spectrum) and the results are used to correct the input spectrum.	Reference dependent; scales the data.
Cosmic ray removal	Sharp spike detection	Detects spikes which are significantly narrower than the peaks in the spectrum.	Insensitive to the relatively wide spikes; threshold dependent.
	Abnormal spike detection	A series of replicate spectra are compared. A spike is detected and removed since the probability of a spike occurring at the same point in multiple spectra is considered low.	Time-consuming since multiple spectra must be compared.
	Image curvature correction	Optimizes optical systems by comparing spectra from different rows of pixels on the detector.	User intervention needed for implementation; parameter based; time-consuming.
	Mapping based technique	The abnormal spikes are detected by comparing the neighboring spectra from the map.	A relatively large number of pixels needed for the accuracy of the detection.
Scaling method	Normalization by a peak (e.g. maximal peak).	Divides every row (spectrum) by the value at the selected peak of that row (e.g. maximal peak). ${\mathbf{X}}_{\left(n,:\right)}^{\mathit{scaled}}=\frac{{\mathbf{X}}_{(n,:)}}{{\mathbf{X}}_{(n,peak)}}$	Emphasizes the variation of the Raman bands against the selected peak
	Auto-scaling	Subtracts the mean and then divides the standard deviation of that row. ${\mathbf{X}}_{\left(n,:\right)}^{\mathit{scaled}}=\frac{{\mathbf{X}}_{(n,:)}-\stackrel{-}{{\mathbf{X}}_{(n,:)}}}{\mathit{std}({\mathbf{X}}_{\left(n,peak\right)})}\pi r^2$	The shape of the spectra may be lost; reduces the variation in the objects and gathers the objects towards the center.
	Row normalization (length/area)	Divides every row/ object by the length (Manhattan distance)/area (Euclidean distance) of that row.${\mathbf{X}}_{\left(n,:\right)}^{\mathit{scaled}}=\frac{{\mathbf{X}}_{(n,:)}}{\mathit{sum}(\left|{\mathbf{X}}_{(n,:)}\right|)}$(length)${\mathbf{X}}_{\left(n,:\right)}^{\mathit{scaled}}=\frac{{\mathbf{X}}_{(n,:)}}{\sqrt{\mathit{sum}({{\mathbf{X}}_{(n,:)}}^2)}}$(area)	The variation of objects is reduced.
	Column normalization (length/area)	Divides every column/variable by the length (Manhattan distance)/area (Euclidean distance) of that column. ${\mathbf{X}}_{\left(:,w\right)}^{\mathit{scaled}}=\frac{{\mathbf{X}}_{(:,w)}}{\mathit{sum}(\left|{\mathbf{X}}_{(:,w)}\right|)}$(length) ${\mathbf{X}}_{\left(:,w\right)}^{\mathit{scaled}}=\frac{{\mathbf{X}}_{(:,w)}}{\sqrt{\mathit{sum}({{\mathbf{X}}_{(:,w)}}^2)}}$(area)	The shape of the spectra may be lost; Reduces the variation from variables
	Mean-center	Subtracts the mean of each row for all the elements${\mathbf{X}}_{\left(n,:\right)}^{\mathit{scaled}}={\mathbf{X}}_{(n,:)}-\stackrel{-}{{\mathbf{X}}_{(n,:)}}$	Reduces the deviation of the data from its center; gathers the objects towards the center.

n/w represents the n^th/w^th row /column of the spectral matrix X for scaling. All the X blocks in the paper are arranged in a way that objects are stored in different rows and variables are stored in different columns.