Fuzzy Clustering in the Analysis of Fourier Transform Infrared Spectra for Cancer Diagnosis

214 Pages·2007·3.5 MB·English

Fuzzy Clustering in the Analysis of
Fourier Transform Infrared Spectra
for Cancer Diagnosis

by Xiao Ying Wang, BSc

Thesis Submitted to the University of Nottingham
for the degree of Doctor of Philosophy
School of Computer Science and Information Technology
September 2006
Table of Contents
Table of Contents

1 Introduction .................................................................................................... 1
1.1 Background and Motivation ............................................................................. 1
1.2 Aims of this project .......................................................................................... 6
1.3 Overview of the Thesis..................................................................................... 7
2 Literature Review......................................................................................... 11
2.1 Clustering Techniques .................................................................................... 11
2.2 Cluster Validity .............................................................................................. 31
2.3 Auto Clustering .............................................................................................. 38
2.4 Cluster Merging.............................................................................................. 46
2.5 Clustering in FTIR Spectroscopy ................................................................... 49
2.6 Summary......................................................................................................... 61
3 Medical Background .................................................................................... 63
3.1 Introduction .................................................................................................... 63
3.2 Instrumentation............................................................................................... 67
3.3 Sample Preparation and Data Collection........................................................ 71
3.4 Data Pre-processing........................................................................................ 73
3.5 Summary......................................................................................................... 74
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Table of Contents
4 A Comparison of Hierarchical, K-Means and Fuzzy C-Means
Clustering of Oral Cancer Cells ............................................................... 76
4.1 Introduction .................................................................................................... 76
4.2 Oral Cancer Datasets Description................................................................... 77
4.3 Experiments on Oral Cancer Datasets ............................................................ 86
4.4 Summary......................................................................................................... 91
5 Methods for Automatically Determining the Number of Clusters .......... 93
5.1 Introduction .................................................................................................... 93
5.2 VFC-SA Clustering Algorithm....................................................................... 94
5.3 SAFC Clustering Algorithm........................................................................... 98
5.4 Evaluation of VFC−SA and SAFC Clustering of Oral Cancer Cells ........... 103
5.5 Summary....................................................................................................... 115
6 Methods for the Examination of Tissue Sections..................................... 117
6.1 Introduction .................................................................................................. 117
6.2 Lymph Node Dataset Description ................................................................ 118
6.3 A Combination of Principal Component Analysis and Fuzzy C-
Means Clustering.......................................................................................... 121
6.4 Comparison of K−Means and Fuzzy C−Means in Lymph Node
Tissue Sections ............................................................................................. 137
6.5 Summary....................................................................................................... 143

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7 A Cluster Merging Algorithm ................................................................... 145
7.1 Introduction .................................................................................................. 145
7.2 Feature Extraction......................................................................................... 147
7.3 Fuzzy C-Means Based Clustering Algorithm............................................... 148
7.4 The Basis of a New Automated Method to Merge Clusters......................... 149
7.5 Experimental Results.................................................................................... 159
7.6 Discussion of Results ................................................................................... 168
7.7 Summary....................................................................................................... 172
8 Conclusions ................................................................................................. 173
8.1 Contributions ................................................................................................ 174
8.2 Future Work.................................................................................................. 180
8.3 Dissemination ............................................................................................... 184
9 References.................................................................................................... 188
10 Appendix ..................................................................................................... 198

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List of Figures
LIST OF FIGURES
Figure 1.1 FTIR Microscopy spectra for paint analysis [24]. .................................. 5
Figure 1.2 An overview of the project collaboration. .............................................. 6
Figure 2.1 Two dimensional dataset with 3 clusters [27]. ..................................... 15
Figure 2.2 Dendrogram obtained from Figure 2.1 [27].......................................... 15
Figure 2.3 The k-means clustering algorithm. ....................................................... 18
Figure 2.4 The fuzzy c-means clustering algorithm [47]. ...................................... 20
Figure 2.5 Outline of the SA based clustering algorithm....................................... 22
Figure 2.6 The perturbation process in Brown and Huntley [53]. ......................... 25
Figure 2.7 Identification of the number of clusters by using a validity index [56].33
Figure 2.8 Two dimensional dataset strips in four directions. ............................... 44
Figure 2.9 Effective merging radius for clusters i and j......................................... 48
Figure 3.1 Typical location of lymph nodes that drain lymph from the breast...... 67
Figure 3.2 Perkin elmer spotlight imager............................................................... 68
Figure 4.1 Tissue sample from Dataset 1; (a) 4× stained picture; (b) 32× unstained
picture. .................................................................................................. 78
Figure 4.2 FITR spectra from Dataset 1................................................................. 78
Figure 4.3 32× unstained picture from tissue sample Dataset 2............................. 79
Figure 4.4 32× unstained picture from tissue sample Dataset 3............................. 80
Figure 4.5 White light image of tissue sample Dataset 4....................................... 81
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List of Figures
Figure 4.6 Tissue section from dataset 5 (a) white light image (b) spectroscopic-
staining image. ...................................................................................... 83
Figure 4.7 White image of tissue sample for dataset 6 (a) part 1 (b) part 2........... 84
Figure 4.8 White image of tissue sample for Dataset 7. ........................................ 85
Figure 5.1 VFC-SA clustering algorithm procedure. ............................................. 96
Figure 5.2 The split centre procedure................................................................... 100
Figure 5.3 An illustration of Split Centre from the original algorithm with distinct
clusters (where µ
11 and µ12 represent the membership degree of w1 to
the centres v1 and v2 respectively)....................................................... 101
Figure 5.4 The new Split Centre applied to the same dataset as Figure 5.3, above,
(where w1 is now the data point that is closest to the mean value of the
membership degree above 0.5). .......................................................... 101
Figure 5.5 The SAFC clustering algorithm.......................................................... 102
Figure 5.6 Fuzzy C-Means, VFC-SA and SAFC cluster results for dataset 1. .... 108
Figure 5.7 Cluster results for dataset 2 obtained from (a) Fuzzy C-Means, VFC-SA
and 3/10 runs from SAFC (b) 7/10 runs from SAFC. ........................ 108
Figure 5.8 Cluster results for dataset 3 obtained from (a) Fuzzy C-Means and
VFC-SA (b) SAFC.............................................................................. 109
Figure 5.9 Cluster results for dataset 4 obtained from (a) Fuzzy C-Means (b) VFC-
SA and SAFC...................................................................................... 109
Figure 5.10 Cluster results for dataset 5 obtained from (a) Fuzzy C-Means and 5/10
runs from VFC-SA (b) SAFC and 5/10 runs from VFC-SA. ............. 109
Figure 5.11 Fuzzy C-means, VFC-SA and SAFC cluster results for dataset 6...... 110
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List of Figures
Figure 5.12 Cluster results for dataset 7 obtained from (a) Fuzzy C-Means, 9 runs
from VFC-SA and SAFC (b) 1 run from VFC-SA............................. 110
Figure 6.1 (a) Photomicrograph of the H&E stained parallel lymph node tissue
section used for IR analysis (b) selected area – LNII5 at high
magnification (c) different tissue types description (d) LNII5 spectral
image................................................................................................... 120
Figure 6.2 IR imaging of lymph node tissue section LNII5 by PCA (a) H&E
stained image of LNII5 (b)−(k) false colour weighted images for
PC1−PC10 respectively. ..................................................................... 124
Figure 6.3 Clustering results from three separate runs with fuzzy c-means. ....... 125
Figure 6.4 A three – dimensional scatter plot of the tissue section spectra projected
onto the first 3 PCs.............................................................................. 127
Figure 6.5 IR imaging of lymph node tissue section LNII5 by fuzzy c-means (a)
H&E stained image of LNII5 (b)−(i) fuzzy c-means false colour
weighted clustering results, the number of clusters were from 2 – 9
respectively. ........................................................................................ 130
Figure 6.6 IR imaging of lymph node tissue section LNII5 by PCA–fuzzy c-means
(a) H&E stained image of LNII5 (b)−(i) fuzzy c-means false colour
weighted clustering results, the number of clusters were from 2 – 9
respectively. ........................................................................................ 132
Figure 6.7 LNII5 tissue section spectra plot in three dimensional PCs space (a)
original plot with 5 clusters (b) rotated plot of picture (a).................. 136
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List of Figures
Figure 6.8 Clustering results from k-means (a&b) and fuzzy c-means (c) in 2
clusters. ............................................................................................... 138
Figure 6.9 K-means clustering results in 3 − 9 clusters. ...................................... 139
Figure 6.10 Fuzzy c-means clustering results in 3 − 9 clusters.............................. 139
Figure 6.11 Variation in k-means clustering results for 5 clusters......................... 139
Figure 6.12 Variation in k-means clustering results for 6 clusters......................... 140
Figure 6.13 Variation in k-means clustering results for 7 clusters......................... 140
Figure 6.14 Variation in k-means clustering results for 9 clusters......................... 140
Figure 7.1 The fuzzy c-means based clustering algorithm................................... 150
Figure 7.2 An extracted spectral dataset after applying fuzzy c-means based
clustering algorithm. ........................................................................... 151
Figure 7.3 The procedure of determining a reference wave-number. .................. 153
Figure 7.4 Mean infrared spectra obtained from different clusters...................... 154
Figure 7.5 Enlarged region of Figure 7.4. ............................................................ 154
Figure 7.6 The procedure of automated merge clusters. ...................................... 156
Figure 7.7 Four mean spectra absorbance at reference wave-number. ................ 157
Figure7.8 The resultant absorbance distribution obtained after merging the two
most similar clusters. .......................................................................... 157
Figure 7.9 The merging situation when there are two dist left (type 1). .............. 158
Figure 7.10 The merging situation when there are two dist left (type 2). .............. 158
Figure 7.11 Entire automated merging clustering procedure. ................................ 158
Figure 7.12 The extracted spectral dataset after applying the proposed automated
merging cluster method. ..................................................................... 159
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List of Figures
Figure 7.13 An example of an extracted dataset. ................................................... 160
Figure 7.14 An example of a whole sub area of lymph node dataset. ................... 161
Figure 7.15 (a) Extracted LNII7 clustering results after applying fuzzy c-means
based clustering algorithm. (b) Extracted LNII7merged clusters results.
............................................................................................................ 162
Figure 7.16 (a) Dataset 3 clustering results obtained from SAFC algorithm. (b)
Dataset 3 merged clusters results. ...................................................... 163
Figure 7.17 (a) Dataset 5 clustering results obtained from SAFC algorithm. (b)
Dataset 5 merged clusters results. ...................................................... 163
Figure 7.18 Lymph node tissue section LNII7. Sampled area was 275µm ×
818.75µm in size. (a) Total absorbance IR image (b) H&E stained
image. Clustering results after fuzzy c-means based clustering
algorithm. Each colour represents a different cluster of IR spectra (c) 5
cluster image (d) 6 cluster image (e) 9 cluster image (f) Final results
obtained from automated merge clustering algorithm – this image
contained two final clusters of IR spectra........................................... 164
Figure 7.19 Lymph node tissue section LNII5. Sampled area was 30625µm ×
95625µm in size. (a) Total absorbance IR image (b) H&E stained
image. Results after fuzzy c-means based clustering algorithm. Each
colour represents a different cluster of IR spectra (c) 5 cluster image (d)
merged cluster result from 5 cluster image (e) 4 cluster image (f)
merged cluster result from 4 cluster image. Both merged cluster results
contained three clusters of IR spectra. ................................................ 166
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List of Figures
Figure 7.20 Lymph node tissue section LN57. Sampled area was 550µm × 512.5µm
in size. (a) Total absorbance IR image (b) H&E stained image.
Clustering results after fuzzy c-means based clustering algorithm. Each
colour represents a different cluster of IR spectra (c) 3 cluster image (d)
4 cluster image (e) 5 cluster image (f) Final result obtained from
automated merge clustering algorithm. Image contained three final
clusters of IR spectra........................................................................... 166

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