Applications of Machine Learning and High Dimensional
Visualization in Cancer Diagnosis and Detection
John McCarthy*, Kenneth A. Marx, Alex Gee,
Philip O’Neil, M.L. Ujwal, Patrick Hoffman, John Hotchkiss
AnVil, Inc.
25 Corporate Drive
Burlington, MA 01803
1
*corresponding author
jmccarthy@verizon.net;
(781) 828-4230
Abstract
Introduction to Data Analysis by Machine Learning
Overview of Machine Learning and Visualization
Three of the major techniques in machine learning are clustering, classification and feature
reduction. Classification and clustering are also broadly known as unsupervised and supervised
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learning. In supervised learning, the object is to learn predetermined class assignments from
other data attributes. For example, given a set of gene expression data for samples with known
diseases, a supervised learning algorithm might learn to classify disease states based on patterns
of gene expression. In unsupervised learning, there either are no predetermined classes or class
assignments are ignored. Cluster analysis is the process by which data objects are grouped
together based on some relationship defined between objects.
In both classification and
clustering an explicit or implicit model is created from the data which can help to predict future
data instances or understand the physical process behind the data. Creating these models can be
a very compute intensive task, such as training a neural network. Feature reduction or selection
reduces the data attributes used in creating a data model. This process can reduce analysis time
and create simpler and (sometimes) more accurate models.
In the three cancer examples presented all three machine learning techniques are used and
will be described, however, one of the primary analysis techniques used is high dimensional
visualizations. One particular visualization, RadViz™, incorporates all three machine learning
techniques in an intuitive, interactive display. Two other high dimensional other visualizations,
Parallel Coordinates and PatchGrid (similar to HeatMap) are also used to analyze and display
results.
Classification techniques used:
RadViz™ – rearranging dimensions based on T-statistic – a visual classifier
Naïve Bayes (Weka)
Support Vector Machines (Weka)
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Instance Based or K – nearest neighbor (Weka)
Logistic Regression (Weka)
Neural Net (Weka)
Neural Net (Clementine)
Validation technique
10-fold
Hold 1 out
Training and Test datasets
Clustering techniques:
RadViz™ – arranging dimensions not based on class label – ex. Principal Components
Hiarchical with Pearson correlation
Feature Reduction techniques used:
Pairwise t-statistic – equal variance used in RadViz™ (other statistics can also be used)
F-statistic – select top dimensions based on the highest F-statistic computed from class labels
PURS™ (patent pending) - Principal Uncorrelated Record Selection
***** Phil/Alex Should have the new algorithm definition *******
Initially selection some “seed” dimensions, say based on high t or F statistic, repeatedly
delete dimensions that correlate highly to seed dimensions, if not correlated add the
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dimension to the “seed” dimension set.
Repeat and slowly reduce the correlation
threshold until “seed” dimensions are reduced to the desired amount.
Random – randomly selected dimensions and build/test classifier
****** This probably should be reduced ********].
The Importance of High-dimensional Data Visualization and its Integration with
Analytic Data Mining Techniques.
Visualization, data mining, statistics, as well as
mathematical modeling and simulation are all methodologies that can be used to enhance the
discovery process [15].. There are numerous visualizations and a good number of valuable
taxonomies (See [16] for an overview of taxonomies). Most information visualization systems
focus on tables of numerical data (rows and columns), such as 2D and 3D scatterplots [17],
although many of the techniques apply to categorical data. Looking at the taxonomies, the
following stand out as high-dimensional visualizations: Matrix of scatterplots [17]; Heat maps
[17]; Height maps [17]; Table lens [18]; Survey plots [19]; Iconographic displays [20];
Dimensional stacking (general logic diagrams) [21]; parallel coordinates [22]; Pixel techniques,
circle segments [23]; Multidimensional scaling [23]; Sammon plots [24]; Polar charts [17];
RadViz™ [25]; Principal component analysis [26]; Principal curve analysis [27]; Grand Tours
[28]; Projection pursuit [29]; Kohonen self-organizing maps [30]. Grinstein et.al., [31] have
compared the capabilities of most of these visualizations. Historically, static displays include
histograms, scatterplots, and large numbers of their extensions. These can be seen in most
commercial graphics and statistical packages (Spotfire, S-PLUS, SPSS, SAS, MATLAB,
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Clementine, Partek, Visual Insight’s Advisor, and SGI’s Mineset, to name a few). Most software
packages provide limited features that allow interactive and dynamic querying of data.
HDVs have been limited to research applications and have not been incorporated into many
commercial products. However, HDVs are extremely useful because they provide insight during
the analysis process and guide the user to more targeted queries. Visualizations fall into two
main categories: (1) low-dimensional, which includes scatterplots, with from 2-9 variables
(fields, columns, parameters) and (2) high-dimensional, with 100-1000+ variables. Parallel
coordinates or a spider chart or radar display in Microsoft Excel can display up to 100
dimensions, but place a limit on the number of records that can be interpreted. There are a few
visualizations that deal with a large number (>100) of dimensions quite well: Heatmaps,
Heightmaps, Iconographic Displays, Pixel Displays, Parallel Coordinates, Survey Plots, and
RadViz™. When more than 1000 records are displayed, the lines overlap and cannot be
distinguished. Of these, only RadViz is uniquely capable of dealing with ultra–high-dimensional
(>10,000 dimensions) datasets, and we discuss it in detail below.
RadViz™ is a visualization and classification/clustering tool that uses a spring analogy for
placement of data points and incorporates machine learning feature reduction techniques as
selectable algorithms. 13-15 The “force” that any feature exerts on a sample point is determined by
Hooke’s law: f  kd . The spring constant, k, ranging from 0.0 to1.0 is the value of the
feature(scaled) for that sample, and d is the distance between the sample point and the perimeter
point on the RadViz™ circle assigned to that feature-see Figure A. The placement of a sample
point, as described in Figure A is determined by the point where the total force determined
vectorially from all features is 0. The RadViz display combines the n data dimensions into a
single point for the purpose of clustering, but it also integrates analytic embedded algorithms in
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order to intelligently select and radially arrange the dimensional axes. This arrangement is
performed through Autolayout, a unique, proprietary set of algorithmic features based upon the
dimensions’ significance statistics that optimizes clustering by optimizing the distance separating
clusters of points. The default arrangement is to have all features equally spaced around the
perimeter of the circle, but the feature reduction and class discrimination algorithms arrange the
features unevenly in order to increase the separation of different classes of sample points. The
feature reduction technique used in all figures in the present work is based on the t statistic with
Bonferroni correction for multiple tests. The circle is divided into n equal sectors or “pie slices,”
one for each class. Features assigned to each class are spaced evenly within the sector for that
class, counterclockwise in order of significance (as determined by the t statistic, comparing
samples in the class with all other samples). As an example, for a 3 class problem, features are
assigned to class 1 based on the sample’s t-statistic, comparing class 1 samples with class 2 and 3
samples combined. Class 2 features are assigned based on the t-statistic comparing class 2 values
with class 1 and 3 combined values, and Class 3 features are assigned based on the t-statistic
comparing class 3 values with class 1 and class 2 combined. Occasionally, when large portions
of the perimeter of the circle have no features assigned to them, the data points would all cluster
on one side of the circle, pulled by the unbalanced force of the features present in other sectors.
In this case, a variation of the spring force calculation is used, where the features present are
effectively divided into qualitatively different forces comprised of high and low k value classes.
This is done via requiring k to range from –1.0 to 1.0. The net effect is to make some of the
features pull (high or +k values) and others ‘push’ (low or –k values) the points to spread them
absolutely into the display space, but maintaining the relative point separations. It should be
stated that one can simply do feature reduction by choosing the top features by t-statistic
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significance and then apply those features to a standard classification algorithm. The t-statistic
significance is a standard method for feature reduction in machine learning approaches,
independently of RadViz. The top significance chemicals selected with the t-statistic are the
same as those selected by RadViz. RadViz has this machine learning feature embedded in it and
is responsible for the selections carried out here.
The advantage of RadViz is that one
immediately sees a “visual” clustering of the results of the t-statistic selection. Generally, the
amount of visual class separation correlates to the accuracy of any classifier built from the
reduced features. The additional advantage to this visualization is that sub clusters, outliers and
misclassified points can quickly be seen in the graphical layout. One of the standard techniques
to visualize clusters or class labels is to perform a Principle Component Analysis and show the
points in a 2d or 3d scatter plot using the first few Principle Components as axes. Often this
display shows clear class separation, but the most important features contributing to the PCA are
not easily seen. RadViz is a “visual” classifier that can help one understand important features
and how many features are related.
The RadViz Layout:
An example of the RadViz layout is illustrated in Figure A. There are 16 variables or dimensions
associated with the 1 point plotted. Sixteen imaginary springs are anchored to the points on the
circumference and attached to one data point. The data point is plotted where the sum of the
forces are zero according to Hooke’s law (F = Kx): where the force is proportional to the
distance x to the anchor point. The value K for each spring is the value of the variable for the
data point. In this example the spring constants (or dimensional values) are higher for the lighter
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springs and lower for the darker springs. Normally, many points are plotted without showing the
spring lines. Generally, the dimensions (variables) are normalized to have values between 0 and
1 so that all dimensions have “equal” weights. This spring paradigm layout as some interesting
features.
For example if all dimensions have the same normalized value the data point will lie exactly in
the center of the circle. If the point is a unit vector then that point will lie exactly at the fixed
point on the edge of the circle (where the spring for that dimension is fixed). Many points can
map to the same position. This represents a non-linear transformation of the data which preserves
certain symmetries and which produces an intuitive display. Some features of this visualization
include:

it is intuitive, higher dimension values “pull” the data points closer to the dimension on the
circumference

points with approximately equal dimension values will lie close to the center

points with similar values whose dimensions are opposite each other on the circle will lie
near the center

points which have one or two dimension values greater than the others lie closer to those
dimensions

the relative locations of the of the dimension anchor points can drastically affect the layout
(the idea behind the “Class discrimination layout” algorithm)

an n-dimensional line gets mapped to a line (or a single point) in RadViz

Convex sets in n-space map into convex sets in RadViz

Computation time is very fast
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
1000’s of dimensions can be displayed in one visualization
We have studied the following systems related to cancer detection:
1. GI50 compound 60 cancer cell lines
2. Microarray lung cancer data
3. proteomics MS dataset
1. Data Mining the Public Domain NCI-60 Cancer Cell Line Compound GI50
Data Set
Introduction to the Cheminformatics Problem.
Important objectives in the overall process of molecular design for drug discovery are: 1)
the ability to represent and identify important structural features of any small molecule, and 2) to
select useful molecular structures for further study, usually using linear QSAR models and based
upon simple partitioning of the structures in n-dimensional space. To date, partitioning using
non-linear QSAR models has not been widespread, but the complexity and high-dimensionality
of the typical data set requires them. The machine learning and visualization techniques that we
describe and utilize here represent an ideal set of methodologies with which to approach
representing structural features of small molecules, followed by selecting molecules via
constructing and applying non-linear QSAR models. QSAR models might typically use
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calculated chemical descriptors of compounds along with computed or experimentally
determined compound physical properties and interaction parameters (G, Ka, kf, kr, LD50,
GI50, etc) with other large molecules or whole cells. Theromodynamic and kinetic parameters
are usually generated in silico (G) or via high throughput screening of compound libraries
against appropriate receptors or important signaling pathway macromolecules (Ka, kf, kr),
whereas the LD50 or GI50 values are typically generated using whole cells that are suitable for
the disease model being investigated. When the data has been generated, then the application of
machine learning can take place. We provide a sample illustration of this process below.
The National Cancer Institute’s Developmental Therapeutics Program maintains a compound
data set (>700,000 compounds) that is currently being systematically tested for cytotoxicity
(generating 50% growth inhibition, GI50, values) against a panel of 60 cancer cell lines
representing 9 tissue types. Therefore, this dataset contains a wealth of valuable information
concerning potential cancer drug pharmacophores. In a data mining study of the 8 largest public
domain chemical structure databases, it was observed that the NCI compound data set contained
by far the largest number of unique compounds of all the databases (32). The application of
sophisticated machine learning techniques to this unique NCI compound dataset represents an
important open problem that motivated the investigation we present in this report. Previously,
this data set has been mined by supervised learning techniques such as cluster correlation,
principle component analysis and various neural networks, as well as statistical techniques
(33,34). These approaches have identified distinct subsets within of a variety of different classes
of chemical compounds (35,36,37,38). More recently, gene expression analysis has been added
to the data mining activity of the NCI compound data set (39) to predict chemosensitivity, using
the GI50 test data for each compound, for a few hundred compound subset of the NCI data set
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(40). After we completed our initial data mining analysis using the GI50 values (41), gene
expression data on the 60 cancer cell lines was combined with NCI compound GI50 data and also
with a 27,000 chemical feature database computed for the NCI compounds. . {Using what
method or software??}
In this study, we use microarray based gene expression data to first establish a number of
‘functional’ classes of the 60 cancer cell lines via a hierarchical clustering technique. These
functional classes are then used to supervise a 3-Class learning problem, using a small but
complete subset of 1400 of the NCI compounds’ GI50 values as the input to a clustering
algorithm in the RadViz™ program (43).
Specific Methods Used.
For the ~ 4% missing values found in the 1400 compound data set, we tried and
compared two approaches to missing value replacement: 1) record average replacement; 2)
multiple imputation using Schafer’s NORM software (44). Since applying either missing value
replacement method to our data had little impact on the final results of our analysis, we chose
the record average replacement method for all subsequent analysis.
Clustering of cell lines was done with R-Project software using the hierarchical clustering
algorithm with “average” linkage method specified and a dissimilarity matrix computed as [1 –
the Pearson correlations] of the gene expression data. AnVil Corporation’s RadViz™ software
(??){ Need to update} was used for feature reduction and initial classification of the cell lines
based on the compound GI50 data. The selected features were validated using several classifiers
as implemented in the Weka (Waikato Environment for Knowledge Analysis, University of
Waikato, New Zealand) software application program . The classifiers used were IB1 (nearest
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neighbor), IB3 (3 nearest neighbor), logistic regression, Naïve Bayes Classifier, support vector
machine, and neural network with back propagation. Both ChemOffice 6.0 (CambridgeSoft
Corp.) and the NCI website were used to identify compound structures via their NSC numbers.
Substructure searching to identify quinone compounds in the larger data set was carried out using
ChemFinder (CambridgeSoft).
Results and Discussion
Identifying functional cancer cell line classes using gene expression data. Based upon
gene expression data, we identified cancer cell line classes that we could use in a subsequent
supervised learning approach. In Figure 1.1, we present a hierarchical clustering dendrogram
using the [1-Pearson] distances calculated from the T-Matrix{?? Not sure what this is. Are you
referring to the t-test statistic in matrix form?} , comprised of 1376 gene expression values
determined for the 60 NCI cancer cell lines (43). There are five well defined clusters observed In
this figure. Clusters 2-5 respectively, represent pure renal, leukemia, ovarian and colonrectal
cancer cell lines. Only in Cluster 1, the melanoma class instance, does the class contain two
members of another clinical tumor type; the two breast cancer cell lines - MDA-MB-435 and
MDA-N. The two breast cancer cell lines behave functionally as melanoma cells and seem to be
related to melanoma cell lines via a shared neuroendocrine origin (43). The remaining cell lines
in this dendrogram, those not found in any of the five functional classes, are defined as being in a
sixth class; the non- melanoma, leukemia, renal, ovarian, colorectal class. In the supervised
learning analysis that follow, we treat these six computational derived functional clusters as
ground truth.
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3-Class Cancer Cell Classifications and Validation of Selected Compounds. High
class number classification problems are difficult to implement in cases where the data are not
clearly separable into distinct classes. Thus, we could not successfully carry out a 6-class
classification of cancer cell lines based upon the starting GI50 compound data. Alternatively, we
implemented a 3-Class supervised learning classification using RadViz™ (25, 45-47). Starting
with the small 1400 compounds’ GI50 data set that contained no missing values for all 60 cell
lines, we selected those compounds that were effective in carrying out a 3-way class
discrimination at the p < .01 (Bonferroni corrected t statistic) significance level. A RadViz
visual classifier for the melanoma, leukemia, and non-melanoma/non-leukemia classes is shown
in Figure 2.1. A clear and accurate class separations of the 60 cancer cell lines can be seen.
There were 14 compounds selected as being most effective against melanoma cells and 30
compounds selected as being most effective against leukemia cells. Similar classification results
were obtained for the two separate 2-Class problems: melanoma vs. non-melanoma and
leukemia vs. non-leukemia. For all other possible 2-Class problems, we found that few to no
compounds could be selected at the significance level we had previously set.
In order to validate our list of computationally selected compounds , we applied six
additional analytical classification techniques, as previously described, , to the original GI50 data
set using the same set of chemical predictors and a hold-one-out cross-validation strategy. Using
these selected compounds resulted in a greater than 6-fold lowered level of error compared to
using the equivalent numbers of randomly selected compounds, thus validating our selection
methodology.
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Quinone Compound Subtypes Upon examining the chemical identity of the compounds
selected as most effective against melanoma and leukemia, an interesting observation was made.
, For the 14 compounds selected as most effective against melanoma, 11 were p-quinones and
all have an internal ring quinone structure.
Alternatively, there were 30
compounds selected as most effective against leukemia, of which 8
contain p-quinones. In contrast to the internal ring quinones in the
melanoma class however, 6 out of the 8 leukemia p-quinones were
external ring quinones. In order to ascertain the uniqueness of the two quinone subsets
we first determined the extent of occurrence of p-quinones of all types in our starting data set, via
substructure searching using the ChemFinder 6.0 software. The internal and external quinone
subtypes represent a significant fraction, 25 % (10/41) of all the internal quinones and 40 %
(6/15) of all the external quinones in the entire data set (41).
Conclusion.
With this cheminformatics example we have demonstrated that the machine learning
approach described above utilizing RadViz™ has produced two novel discoveries . First, a small
group of chemical compounds, enriched in quinones, were found to effectively discriminate
among melanoma, leukemia, and non-melanoma/non-luekemia cell lines on the basis of
experimentally measured GI50 values. Secondly, two quinone subtypes were identified that
possess clearly different and specific toxicity to the leukemia and melanoma cancer cell types.
We believe that this example illustrates the potential of sophisticated machine learning
approaches to uncovering new and valuable relationships in complex high dimensional chemical
compound data sets.
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2. Distinguishing lung tumor types using microarray gene expression data
Introduction to the high-throughput gene expression problem
Completion of the Human Genome Project has made possible the study of the gene
expression levels of over 30,000 genes [14, 15]??{Do these pertain to original references. 14
looks reasonable but I question 15 based on the journals. Please confirm. YES John, these were
reference numbers Ken provided from the original document he moved into this section and I
incorporated the text. The other two references below will need to be provided by Ken or
someone with their sources.} Major technological advances have made possible the use of DNA
microarrays to speed up this analysis. Even though the first microarray experiment was only
published in 1995{Ref ?, Ken?}, by October 2002 a PubMed query of microarray literature
yielded more than 2300 hits{Ref ?, Ken?}, indicating explosive growth in the use of this
powerful technique. DNA microarrays take advantage of the convergence of a number of
technologies and developments including: robotics and miniaturization of features to the micron
scale (currently 20-200 um surface feature sizes for spotting/printing and immobilizing
sequences for hybridization experiments), DNA amplification by PCR, automated and efficient
oligonucleotide synthesis and labeling chemistries, and sophisticated bioinformatics approaches.
An important application of microarray technology is the identification and
differentiation of tissue types using differential gene expressions, either between normal and
cancerous cells or among tumor subclasses. The specific aim of the project described below was
to explore the potential for using machine learning and high dimensional visualization in
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building a classifier which could differentiate normal lung tissue from the various subclasses of
non-small cell lung cancer using microarray based differential expression patterns. We have
previously reported on using such techniques to successfully construct classifiers which can
solve the more general two-class problem of differentiating non-small cell lung cancer from
normal tissue with accuracies greater than 95%. However, the analysis of the three-class problem
of distinguishing normal lung tissue from the two subclasses of non-small cell lung carcinoma
(adenocarcinomas and squamous cell carcinoma) was not directly addressed. Our ultimate aim
was the creation of gene sets with small number of genes that might serve as the basis for
developing a clinically useful diagnostic tool.
In collaboration with the NCI, we examined two data sets of patients with and without
various lung cancers. The first data set was provided directly by the NCI and included 75 patient
samples [1]. This set contained 17 normal samples, 30 adenocarcinomas (6 doubles), and 28
squamous cell carcinomas (2 doubles). Doubles represent replicate samples prepared at different
times, using different equipment, but derived from the same tissue sample.. A second patient set
of 157 samples was obtained from a publically available data repository [2]. This set included
17 normal samples, 139 adenocarcinomas (127 of these with supporting information) and 21
squamous cell carcinomas. Both data sets included gene expression data from tissue samples
using Affymetrix’s Human Genome U95 Set [3]; only the first of five oligonucleotide based
GeneChip® arrays (Chip A) was used in this experiment. Chip A of the HG U95 array set
contains roughly 12,000 full-length genes and a number of controls. Because we were dealing
with two data sets both from different sources and microarray measurements taken at multiple
times we needed to consider a normalization procedure. For this particular analysis we kept with
a simple mean of 200 for each sample. This resulted in a set of 9918 expressed genes of which
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approximately 2000 were found to be statistically significant (p<0.05) in differentiating normal
lung tissue form non-small cell lung cancer. This differentially expressed set of genes was then
used as the starting point for further analysis as described below.
Specific Methods Used
Because the combinatorial scale of trying all possible gene sets requires a significant
amount of time and computational power, we undertook an approach using sample genes sets
defined by three different gene selection methods {What happened to PURS? As PURS did not
provide any addition information to this analysis and did not perform better than radviz I
removed it for simplity. May be a more thorough analysis with the complete set of PURS results
might have provided something.}.?}
First we defined and analyzed the results from ten
independent random gene sets drawn from the set of approximately 2000 differentially expressed
genes as previously described. These random selections provided a lower predictive bound for
each gene set size.
Second, we selected only genes that demonstrated high statistical
significance by a standard F-test.
Finally, we applied the proprietary RadViz™ technique
developed at AnVil, Inc. (Burlington, MA) to identify sets of genes that best distinguished
differences among the subclasses of samples under analysis [4] {Need a reference here. !!! John,
this is a patent pending idea that has not been published yet. Although radviz as a visualization
technique has be published, the algorithm that selected variables to distinguishes classes is
material found in the company’s second patent (pending).}. Applying these three approaches to
the available expression data we were able to generate gene sets that ranged in size from 1 to 100
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genes. The construction of gene sets was accomplished using a collection of custom scripts
written in Python.
To evaluate the resulting sets of genes we applied a collection of predictive algorithms to
each gene set using a ten-fold cross-validation testing methodology, since an initial comparison
of both ten-fold and hold-one-out cross-validation showed that they produced essentially the
same predictive accuracy. The predictive algorithms used in this analysis included but were not
limited to variations on neural networks, support vector machines, Naïve Bayes, and K-nearest
neighbors all implemented using the publically available Weka application program [5].
Throughout our process of evaluating the various gene sets we kept the two data sets separate in
order to perform two distinct testing scenarios. First we used the NCI data set for crossvalidation as described above; second, we used the Meyerson data set as an independent
validation set.
As a final validation of the biological significance of the genes in our our final 3-way
classifier, we mined the scientific literature for references that associated the selected genes with
specific key words found in association with lung cancer. {ML needs to provide the specific
tools used and brief description of methods}[Mesh – Informax, Go-onotlogy]
Results and Discussion
Distinguishing normal and two tumor types
Our analysis of the general two-class problem for distinguishing between normal lung
tissue and non-small cell lung cancer samples has been reported elsewhere [6]. Unlike the twoclass problem however, the three-class problem proved more challenging.
This problem
involved distinguishing normal lung tissue from two subclasses of non-small cell lung cancer;
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adenocarcinoma and squamous cell carcinoma. Our best gene sets performed on average around
88% for the NCI data set and 96% for the Meyerson data set, both resulting in between 8 to 10
misclassifications. {Can we say anything about 2-class FP vs FN rates of this 3-class model as
compared to the previous 2-class model? Are they similar? NO, the amount of work needed to
make this comparison is beyond my allotted time for this paper.}?} As shown in Figure 2.1, sets
constructed from genes that are highly significant for the three-class problem using the F-statistic
performed better overall than gene sets constructed from randomly selected genes. Also shown in
this figure is the fact that the RadViz™ selection method generally outperforms randomly
selected genes and genes selected on the basis of high statistical significance using the F-test..
The RadViz™ display for the three-class problem as shown in Figure 2.2, clearly demonstrates
near perfect discrimination between normal lung tissue and the two non-small cell lung cancer
subclasses using as few as 15 genes..
Identification of problematic samples
Besides examining the classification results for each gene set independently we looked at
the consistency of classification of samples across gene sets using different machine learning
algorithms as previously described. Suprisingly we identified a few samples in both data sets that
were consistently misclassified. Figure 2.3 {Add patchgrid figure back in and generate separate
tiff image file} shows an example visualization of the results for of the various classification
algorithms (displayed horizontally) for each sample (displayed vertically) within the NCI data
set. The two continuous vertical lines, which are readily visible, represent two samples that have
been consistently misclassified by all the classification algorithms. Although it appears likely
that these samples were improperly labeled, we had no supporting information for these patients
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and thus could not clinically validate these findings. In contrast , upon analysis of the Meyerson
data set we were able to identify six misclassified patients. After reviewing these patients’
supporting information we found that two of these samples consisted of mixed tissue types and
the classification algorithms caught this clinical anomoly.
Validation using biological relevance {ML needs to write this section}
Our validation of the various gene sets we constructed and tested included the use of
domain knowledge in an attempt to support the biological relevance of the selected gene set on
the basis of literature references that associated the selected genes with key words found to be
associated with lung cancer.
(ML needs to provide supporting data for the 15 gene model and a discussion of the
biological relevance of the genes selected. A table identifying the gene #, GenBank ID, and
whether or not there is literature support for its role in lung cancer might also prove
interesting).
Conclusion
This microarray high-throughput gene expression example demonstrates the usefulness of
the machine learning and high dimensional visualization approach to the identification of genes
that may play a significant role in the pathogenesis of non-small cell lung cancer. We have
shown that the RadViz™ technique is extremely useful in identifying genes with significant
differential gene expression which can be used as the basis for a clinically useful and accurate
diagnostic model incorporating measurements from as few as 15 genes. Finally, we have
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provided the basis for a comprehensive pipeline based microarray analysis system incorporating
the selection, evaluation, and relevance of genes for multi-class problems in cancer detection.
References
1.
Jin Jen, M.D., Ph.D., Laboratory of Population Genetics, Center for Cancer Research,
National Cancer Institute.
2.
Matthew Meyerson Lab, Dana-Farber Cancer Institute,
http://research.dfci.harvard.edu/meyersonlab/lungca/data.html.
3.
Affymetrix, www.affymetrix.com.
4.
Reference to RadViz and PURS?? Methodology
5.
Weka (Waikato Environment for Knowledge Analysis), The University of Waikato,
http://www.cs.waikato.ac.nz/~ml.
6.
Dracheva, T., Shih, J., Jen, J., Gee, A., McCarthy, J., and Metrogenix; “Distinguishing
lung tumors based on small number of genes using flow-through-chips” (In preparation)
3. Building a Diagnostic Classifier for Ovarian Cancer Using
Proteomic Data
Introduction to the proteomics problem
ML: {One or two paragraph introduction to biological applications of mass spec and
SELDI-TOF. Focus on the value of using machine learning and high dimensional
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visualization to differentiate the unique signatures of diseased vs normal protein
distibutions in relatively unfractioned serum rather than on the more conventional use of
mass spec fingerprinting in identifying unkown proteins after some form of separation. 1
or 2 general references would also be useful}
The specific goal of this project was to classify patients with ovarian cancer on the basis
of their SELDI-TOF mass spectroscopy signature derived from patient whole sera after
processing on the Ciphergen (Freemont, CA) WCX2 protein array. The methods for data
collection and the general approach are described in Petricoin, et al which documents the first
attempt at applying machine learning techniques to the analysis of clinical proteomic data. [1 ]
The data set used here is not the same as in the original paper, but a similar one labeled 8-07-02,
provided by the authors at http://clinicalproteomics.steem.com/download-ovar.php. The
authors indicate that this data set is less variable than the original data as a result of using an
improved protein chip coupled with totally automated processing by a robotic instrument.
The data consist of over 15,000 mass charge ratio (M/Z) intensity measures, below the
20,000 M/Z range, on 253 patient samples. 162 of these samples were from patients with
ovarian cancer and 91 were from controls. The major objective was to select a set of M/Z values
which best distinguishes cancer cases from controls. Since the number of features is much larger
than the number of samples, it is important to do this in a principled manner to avoid classifying
on the basis of noise.
Two aspects of this data set pose interesting technical challenges in its analysis. The first
is the low S/N level associated with many of the features as shown in Figure 3.1, and the second
is the high degree of correlation between different features. There are at least two sources of
correlation. One, illustrated in Figure 3.2 for M/Z ratios near 417, is the high correlation
23
between neighboring features in the vicinity of a peak. Such correlation may be due to the
inherent resolution limitations of this instrument in resolving two peaks when separated by less
than 600 M/Z units. The other, illustrated in Figure 3.3, is correlation between data at peaks
where one M/Z ratio is almost exactly half the other M/Z ratio. The graph at the top of Figure
3.3 shows the spectrum in the M/Z range from 5300 to 10600, while the bottom graph shows the
range from 2650 to 5300, exactly half the range of the top graph. All of the peaks of the top
graph are repeated in the lower graph, consistent with molecules with the same mass and twice
the charge suggesting production of doubly ionized forms of the original protein fragments.
These figures illustrate the power of visualization for data exploration. Clearly there is a high
degree of noise and redundancy in the data. Such data attributes can be problematic for feature
reduction and consequently reduce the accuracy of the predictive model under development.
Specific methods Used.
Initially each sample was randomly assigned (with 50% probability) to either a “train”
group or a “test” group. This resulted in a training group of 88 ovarian cancer samples and 49
controls, and a test group of 74 ovarian cancer samples and 42 controls. In order to avoid any
influence of test group data on the classification results, all feature reduction and modeling was
done on the basis of training group data only.
The first steps in feature reduction were to eliminate all M/Z ratios less than 350, and to
eliminate those for which the maximum intensity value (in the train group) was less than 17.5.
This was done in order to minimize the possibility of choosing a feature based on noise alone,
and resulted in a reduction from over 15,000 to less than 4,000 features. The next step was to
perform a t test on the remaining features to determine which features show a significant
24
difference between cancer patients and controls. We kept features with significance of p < .001
after Bonferroni correction for multiple tests. This left over 400 features, many of which were
redundant in the sense discussed above.
Simply choosing the most significant 5 or 10 features would incorporate this redundancy
into the classifier and could lead to poor performance. Consequently we used the PURS
technique with a correlation parameter of .90 and initialized with two features, the most
significant feature for each of the two classes. The result was a set of twelve features. We
trained two neural network models using SPSS Clementine. One used all twelve features, the
other used the top six features.
Results and Discussion.
Both neural network models classified cancer patients and controls perfectly in both the
training and test groups. On the website with the data
http://clinicalproteomics.steem.com/download-ovar.php, Petricoin et al present a set of seven
M/Z values which also results in perfect classification. These were chosen by means of a genetic
algorithm. Our past experience with genetic algorithms and microarray data has shown us that
genetic algorithms are susceptible to classification by noise. Microarray data are similar to the
proteomics data in that the number of features (genes) is far greater than the number of samples.
With this level of imbalance it is possible to find perfect classifiers in randomly generated data.
Having an independent test set helps to weed out the really noisy models. However, when you
consider the number of ways of choosing seven features out of 15,000 (> 1025), you begin to see
that the chance of finding a set of seven “good” features is small. At a minimum, features should
show a statistically significant difference between the two classes. Of the seven features given
25
on the website, two are not even marginally significant before correcting for multiple tests.
These contribute mostly noise to the classifier. Two or three more features would fail our strict p
< .001 standard after a Bonferroni correction. This is an arbitrary standard, but since it still
leaves more than 400 “good” features there is no reason to relax it.
Figure 3.4 shows parallel coordinates displays of the two feature sets. The display on the
left is the data for the seven features given on the website. The display on the right is the data for
the six features we selected. Five of the seven features on the left in Figure 3.4 have very low
intensities. We eliminated these in the first step of feature reduction because they fail to reach
the 17.5 threshold.
Conclusions.
It is clear that there are significant differences in proteins in serum between ovarian
cancer patients and controls, and that mass spectroscopy is potentially a useful diagnostic tool.
Because of differences in machines and instrumentation, the applicability of our models to a new
data set is an open question. However, by applying intelligent feature reduction to mass
spectroscopy data using high dimensional visualization prior to classification, the development
of clinically accurate and useful diagnostic models using proteomic data should be possible.
Petricoin, E. F., A. M. Ardekani, B. A. Hitt, P. J. Levine, V. A. Fusaro, S. M. Steinberg, G. B.
Mills, C. Simone, D. A. Fishman, E. C. Kohn, L. A. Liotta, Use of proteomic patterns in serum
to identify ovarian cancer, Lancet, 2002, 359:572-77.
26
Conclusions
Acknowledgements
AnVil and the authors gratefully acknowledges support from two SBIR Phase I grants R43
CA94429-01 and R43 CA096179-01 from the National Cancer Institute. Also, support is
acknowledged from ………..X Y Z
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Figure Legends
35
Figure A. One Point with 16 dimensions in RadViz. Spring lines (not usually shown) are
colored by value (K in Hooke’s law) for that variable (light is higher, dark is lower). The
point is plotted were the sum of the forces is zero.
Figure 1.1. Cancer cell line functional class definition using a hierarchical clustering (1-Pearson
coefficient) dendrogram for 60 cancer cell lines based upon gene expression data. Five well
defined clusters are shown highlighted. We treat the highlighted cell line clusters as the truth for
the purpose of carrying out studies to identify which chemical compounds are highly significant
in their classifying ability
Figure 1.2. RadViz™ result for the 3-Class problem classification of melanoma, leukemia and
non-melanoma, non-leukemia cancer cell types at the p < .01 criterion. Cell lines are symbol
coded as described in the figure. A total of 14 compounds (bottom of layout) were most effective
against melanoma and they are layed out on the melanoma sector (counterclockwise from most
36
0.2
Figure 1.2
ME_LOXIMVI
PR_PC-3
PR_DU-145
RE_SN12C
0.6
0.0
LC_HOP-92
BR_MDA-MB-231/ATCC
CNS_SF-295
CNS_SNB-19
CNS_U251
BR_BT-549
CNS_SF-268
CNS_SF-539
CNS_SNB-75
BR_HS578T
RE_A498
RE_CAKI-1
RE_ACHN
RE_UO-31
RE_TK-10
RE_RXF-393
RE_786-0
LC_NCI-H226
LC_HOP-62
OV_OVCAR-8
BR_MCF7/ADF-RES
LC_NCI-H23
LC_NCI-H522
LC_NCI-H460
LC_A549/ATCC
LC_EKVX
LE_SR
LE_RPMI-8226
LE_K-562
LE_HL-60
LE_CCRF-CEM
LE_MOLT-4
OV_SK-OV-3
OV_IGROV1
OV_OVCAR-3
OV_OVCAR-4
OV_OVCAR-5
LC_NCI-H322M
BR_MCF7
BR_T-47D
CO_HCT-116
CO_SW-620
CO_HCT-15
CO_KM12
CO_HT29
CO_HCC-2998
CO_COLO205
BR_MDA-MB-435
BR_MDA-N
0.4
ME_SK-MEL-5
ME_MALME-3M
ME_SK-MEL-28
ME_UACC-257
ME_SK-MEL-2
ME_UACC-62
ME_M14
Height
to least effective). For leukemia, 30 compounds were identified as most effective and are layed
out in that sector. Some 8 compounds were found to be most effective against non-melanoma,
non-leukemia cell lines and are layed out in that sector.
Figure 1.1
Cluster Dendrogram
1.0
0.8
37
Section 2 Figure Captions
38
Figure 2.1
Figure 2.2
Figure 2.1. Classification results for the NCI data set showing the size of the gene sets compared
to their associated best percent correct. Notice how the RadViz algorithm selected genes (black)
generally perform better than either the top F-statistic genes (gray) or the randomly selected
genes (white). As the gene set sizes increased from one to about twenty genes there was a shard
increase in classification accuracy. In addition, as more random genes are selected their
associated performance increases.
Figure 2.2. A RadViz display showing an example of a selected set of 15 genes from the
Myerson data set defined by a balanced layout for the three classes: normal (gray squares),
adenocarcinoma (black circles) and squamous cell carcinoma (white triangles). Ideally, the
patient samples displayed by their associated representative glyph should fall within their
respective regions, however some samples clearly fall into other regions thus being visually
misclassified. This particular gene set performs very will with about 6 misclassifications
visually, and after applying our collection of classification algorithms this gene set performed
with 8 misclassifications. {We should either identify the genes on the diagram or cross reference
them in ML’s table as previously discussed.}
Figure 2.3. Misclassification Patchgrid {Needs to be cnverted to B/W and reformatted as a TIFF
file along with appropriate caption}.
39
Figure 2.3
Table 1: Gene ID crossreference with indication of literature support {ML}
Figure 3.1. This segment of the spectrum around the M/Z ratio of 203 illustrates the high
signal to noise ratio of some features.
40
Figure 3.2. There is a peak at 417.732 but the intensities at nearby M/Z values are very similar.
The correlation between this peak and its two nearest neighbors is about .97, and the correlation
with the two next neighbors is about .91.
Figure 3.3. The top graph shows the portion of the spectrum from M/Z of 5300 to 10600, while
the bottom graph shows the portion from 2650 to 5300. Thus the range at the bottom is exactly
half the range at the top. Notice that all peaks in the top graph are repeated in the bottom graph.
Figure 3.4. On the left are the seven M/Z ratios selected by Petricoin et al. On the right are the
six features selected by the present authors.
41
Figure 3.1
Figure 3.1
Figure 3.1. This segment of the spectrum around the M/Z
ratio of 203 illustrates the high signal to noise ratio of
some features.
42
Figure 3.2
Figure 3.2. There is a peak at 417.732 but the intensities at
nearby M/Z values are very similar. The correlation between
this peak and its two nearest neighbors is about .97, and the
correlation with the two next neighbors is about .91.
43
Figure 3.3
Figure 3.3. The top graph shows the portion
of the spectrum from M/Z of 5300 to 10600,
while the bottom graph shows the portion
from 2650 to 5300. Thus the range at the
bottom is exactly half the range at the top.
Notice that all peaks in the top graph are
repeated in the bottom graph.
44
Figure 3.4
Figure 3.4. On the left are the seven M/Z ratios selected by Petricoin et al.
On the right are the six features selected by the present authors.
45