Chemistry Reference
In-Depth Information
Table 21.6
Literature review in development and application of outlier detecting chemometric techniques.
Chemometrician
Year
Main idea
D. Rohlf
1975
The largest edge of the minimum spanning tree
P.J. Rousseeuw
1985
Minimum volume estimator (MVE) and minimum covariance
determinant (MCD)
R.G. Garrett
1989
Chi-square plot as a tool for multivariate outlier recognition
D.L. Woodruff
1996
Detection of multiple multivariate outliers which were not always
detectable in data with contamination fractions greater than 35
%
.
D. Jouan-Rimbaud
1999
Mahalanobis distance
A.S. Kosinski
1999
Strongly resistant to such high contamination of data with outliers
R.J. Pell
2000
Use of robust principal component regression (PCR) and iteratively
reweighted partial least squares (PLS) for multiple outlier detection
K.A. Hoo
2002
Develops the approach, discusses the concept of robust statistics and
winsorization, and presents the procedures for robust multivariate
outlier filtering
T. Lillhonga
2005
Replicate analysis and outlier detection in multivariate NIR calibration
M. Khanmohammadi
2009
Outlier detection using the leverage method for quantitative analysis
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
10
30
Data martix element
20
40
50
60
Figure 21.1
Leverage scheme for the detection of an outlier in a data matrix.
examine the residuals from this fit to detect outliers. Table 21.6 reviews the various outlier detection methods
which have been discussed by different chemometricians [76-82].
The recent advances in outlier detection have led to development of several techniques, such as Leverage
method. In this technique a data matrix (X) is formed, trying to detect outliers in the X space examining the
leverage of each sample. The leverage of a sample is a measure of its spatial distance to the main body of the
samples in X. The leverage of a sample in a given data matrix is determined as the elements of P matrix:
P
=
X(X
T
X)
−1
X
T
Large values for each element of P matrix means the sample falls into outlier data. Of course the edge of
leverage discrimination graph is also effective in this step. Typically, Figure 21.1 shows the outlier detection
