Retention Time based Peak Clustering in Comprehensive Two-Dimensional Gas Chromatography

1
Retention Time based Peak Clustering in
Comprehensive Two-Dimensional Gas Chromatography
A presentation for Multi-Dimensional
ChromatographySystems, Informatics, and
ApplicationsSeminar

• By
• Shilpa Deshpande
• University of Nebraska-Lincoln

2
Outline of the Presentation

• Brief Introduction to GCxGC
• Motivation for Clustering in GCxGC
• Clustering Overview
• Implementation and Results
• Application
• Challenges
• Conclusion

3
Introduction to GCxGC

• Comprehensive two-dimensional gas chromatography
  (GCxGC) is a new technology for chemical
  separation. The typical system components are
  shown in Figure 1.
• Retention time The retention time of a solute
  is the elapsed time between the time of injection
  of a solute and the time of elution of the peak
  maximum of that solute 1.
• GCxGC images, have two axes for the retention
  times (time required to pass through each of the
  two column), as shown in Figure 2.

Figure 1 System components for GCxGC with
thermal modulation
Figure 2 GCxGC image
4
Motivation

• The relationship between chemical structure and
  position on the retention time plane produces a
  basis for logical chemical interpretation of
  chromatograms and is an important benefit of
  GCxGC 2.
• Clustering, the process of grouping similar
  items, can expedite the process of chemical
  quantification, which is of interest to chemists.

5
Clustering in GC Image

• In GC Image, templates are patterns of peaks and
  graphic objects observed image(s) used to
  recognize similar patterns of peaks in subsequent
  image(s).
• Template matching is the process of assigning the
  known information about peaks in an image to
  similar peaks in other subsequent image.
• A peak template is a set of peaks, whose metadata
  has been identified. A target peak set is a set
  of peaks whose metadata is to be determined.
• Retention time based peak clustering can be used
  to automate the process of construction of peak
  template.

6
Clustering Overview

• Clustering is the process of grouping data items
  into classes or clusters so that data items
  within a cluster are similar to each other, but
  dissimilar to data items in other clusters 4.
• Clustering is an unsupervised learning in pattern
  recognition. The objective of clustering is to
  reveal" the structure of datapoints into
  sensible clusters (groups) which allow to
  discover similarities and differences among
  datapoints and to derive useful conclusions about
  them 9.

7
Clustering Tasks

• Feature Selection Primary and secondary column
  retention time.
• Proximity Measure Definition Euclidean distance.
• Clustering Criterion Selection Minimize or
  maximize proximity measure.
• Clustering Algorithm Definition Reveal the
  structure
• of data.
• Result Validation Cophenetic correlation
  coefficient.
• Result Interpretation Mass spec analysis, CLIC.

8
Clustering Overview Clustering algorithms

• Partitional K-means, K-median, K-mode
• Each partition have at least one datapoint. Every
  datapoint belongs to one and only one partition.
• K-seeds The number of clusters needs to be
  specified, as shown in Figure 3.
• Seed Seed is the representative of datapoints
  in the cluster.
• Iterative Relocation Scheme Iteratively reassign
  the datapoints to the seeds to minimize the
  proximity measure between seed and datapoint.
• K-means is scalable, easy to implement and
  performs well when clusters are compact clouds.

Figure 3 k-means demo 5
9
Clustering Overview Clustering algorithms

• Hierarchical Hierarchical algorithms produce a
  hierarchy of nested clustering 5, also known as
  a dendrogram.
• Approaches
• Agglomerative In these algorithms, the initial
  number of clusters is equal to number of
  datapoints. The clustering produced at each step
  results from previous one by combining two
  clusters into one.
• Divisive In divisive algorithms, the initial
  number of clusters is one. The clustering
  produced at each step results from previous one
  by splitting one cluster into two.
• Advantages of hierarchical clustering are.
• Hierarchical clustering can handle any forms of
  similarity or distance and can be applied to any
  feature type.
• Disadvantages of hierarchical clustering are.
• Stopping criterion not defined.
• Most of the hierarchical algorithms do not
  revisit the constructed clusters, so any
  improvement in clustering is not possible 6.

10
Clustering Overview Clustering algorithms -
Hierarchical

• Single linkage In single linkage algorithm,
  nearest clusters, that is, datapoint from each
  cluster which are nearest from each other, are at
  minimum distance, as shown in figure 4.
• Complete linkage In complete linkage algorithm,
  farthest clusters, that is, datapoint from each
  cluster which are farthest from each other, are
  at minimum distance.
• Average linkage In average linkage algorithm,
  average clusters, that is, datapoint from each
  cluster which are at average distance from each
  other, are at minimum distance.

Figure 4 single linkage cluster distance
calculation
11
Clustering Overview Clustering algorithms

• Complete Linkage with PCA
• Provides a new proximity measure area.
• Figure 5 , shows the two-dimensional data in
  retention time space.
• Figure 6 , shows the data in the PCA space, the
  enclosing box shows the area.
• In principal component analysis, the product of
  standard deviation along major and minor axis is
  proportional to the area generated by the data.

Figure 5 Original Data
- Figures are borrowed from 7
Figure 6 Data in PCA space
12
Implementation and Results

• GC Image This project is implemented in GC
  Image.
• To perform clustering on selected peaks, in blob
  mode, select Cluster blobs from Edit.
• Cluster Dialog
• Clustering algorithm
• Scaling
• Number of clusters
• Include Clusters
• Add to Template
• Convex Hull Convex Hull Gift Wrap is implemented
  to create graphic for each cluster.

Figure 7 Cluster Dialog
13
Results

• Figure 8, shows supelco standard image which has
  27 peaks. These peaks are clustered with k-means
  (shown in Figure 9) and complete linkage with PCA
  (shown in Figure 10).

Figure 8 Peaks selected
Figure
Figure 10 complete linkage with PCA clustering
Figure 9 k-means clustering results
14
Application Automated Template Construction

• Select the interesting blobs in the image.
• Input the desired number of clusters in the data
  for k-means. For other clustering algorithms,
  user can experiment with different number of
  clusters and then set the optimal number as
  desired number of clusters.
• Clustering algorithm computes the clusters. Draw
  the convex hulls of clusters as graphics.
• Quantification can be done on a cluster to
  cluster basis.
• Marker peaks are selected from each cluster which
  are used to create peaks in the template.

15
Application Automated Template Construction
Figure 12 Blob Set Table
Figure 11 Peaks Selected for template
construction
Figure 13 Template construction
16
Challenges

• Number of clusters This is one of the classic
  problems clustering community faces.
• To reduce the dilemma, this project has preview
  option. In this project implementation, for
  hierarchical algorithms, user can select various
  number of clusters with slider and see the
  result, before finally applying desired number of
  clusters.

Figure 14 Initial Clusters Dialog
Figure 15 4 clusters
17
Challenges

• Subjectivity In clustering algorithms, all the
  features are treated the same.
• For example, in this, in k-means clustering, to
  calculate the squared Euclidean distance both the
  features (primary and secondary column retention
  time) are used.
• This equation does not have any weighing factor.
  In GCxGC domain, primary and secondary column
  retention time might have different significance.
• To counter this problem, in this project,
  weighing factor is applied, as shown in Figure
  16, the primary column scaling is 2.0.

Figure 16 First Column Scaling 2.0
18
Challenges

• Choice of clustering algorithm Numerous
  clustering algorithms are available in the field,
  categorized as partitional, hierarchical,
  density-based, grid-based.
• Different types of clustering algorithms can
  extract different clusters from the data.
• The user has to understand the different outputs
  these clustering algorithms produce before making
  any selection of clustering algorithm.
• In this project, different clustering algorithms
  are implemented as shown in Figure 17. Also user
  can undo the clustering and again perform
  clustering on the same set of data using
  different clustering algorithms.

Figure 17 Different Clustering algorithms
19
Conclusion

• Retention time based peak clustering in
  comprehensive two dimensional gas chromatography
  is a new stream of research. Clustering in one
  and two dimensional gas chromatography has
  usually been done in mass spec domain 8.
• Clustering algorithms in one or two dimensional
  gas chromatography, usually use principal
  component analysis to reduce the size of data and
  use different clustering algorithms to cluster in
  reduced domain space.
• This project used a algorithm to perform
  clustering using principal component analysis to
  get natural clusters.
• This project proposes to use these clusters to
  automatically construct templates.
• The choice of clustering algorithm and user
  parameters play an important role in extracting
  clusters which can be validated by experts or
  some other means such as library search of mass
  spec image.

20
Reference

• 1 Retention-time, \http//www.chromatography-onl
  ine.org/topics/ retention/time.html."
• 2 R. B. Gaines, G. S. Frysinger, M. S.
  Hendrick-Smith, and J. D. Stuart, Oil spill
  source identification by comprehensive
  two-dimensional gas chromatography," Environ.
  Sci. Technol., vol. 33, pp. 2106-2112, 1999
• 3 GC Image, http//www.gcimage.com
• 4 J. Han and M. Kamber, Data Mining Concepts
  and Techniques. San Francisco Morgan Kauffann
  Publisher, 2001
• 5 A. W. Moore , K-means and Hierarchical
  Clustering Slides, http//www.cs.cmu.edu/awm/tut
  orials, Carnegie Mellon University
• 6 P. Berkhin, Survey of Clustering Data Mining
  Techniques. Accrue Software, Inc
• 7 L. I. Smith, A tutorial on Principal
  Components Analysis, 2002
• 8 K. Pierce, J. Hopea, K. Johnson, B. Wright,
  and R. Synovec, Classification of gasoline data
  obtained by gas chromatography using a piecewise
  alignment algorithm combined with feature
  selection and principal component analysis,"
  Journal of Chromatography, vol. 1096, pp.
  101-110, 2005.
• 9 S. Theodoridis and K. Koutroumbus, Pattern
  Recognition. Academic Press, 1998.

21
Extra Slides - Results
Figure 18 Single linkage clustering
Figure 19 Complete linkage with PCA clustering
22
Euclidean Distance