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Using Random Forests to explore a complex Metabolomic data set. Susan Simmons Department of Mathematics and Statistics University of North Carolina Wilmington. Collaborators. Dr. David Banks (Duke) Dr. Jacqueline Hughes-Oliver (NC State) Dr. Stan Young (NISS) Dr. Young Truoung (UNC) - PowerPoint PPT Presentation
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Using Random Forests to explore a complex Metabolomic data set
Susan SimmonsDepartment of Mathematics and StatisticsUniversity of North Carolina Wilmington
Collaborators
• Dr. David Banks (Duke)• Dr. Jacqueline Hughes-Oliver (NC State)• Dr. Stan Young (NISS)• Dr. Young Truoung (UNC)• Dr. Chris Beecher (Metabolon)• Dr. Xiaodong Lin (SAMSI)
Large data sets
• Examples– Walmart
• 20 million transactions daily
– AT&T• 100 million customers and carries 200 million calls a day on
its long-distance network
– Mobil Oil • over 100 terabytes of data with oil exploration
– Human genome• Gigabytes of data
– IRA
Dimensionality
Dimensionality
• 3,000 metabolites• 40,000 genes• 100,000 chemicals• Try to find the signal in these data sets (and
not the noise)…..Data mining• Examples of data mining techniques:
pattern recognition, expert systems, genetic algorithms, neural networks, random forests
Today’s talk
• Focus on classification (supervised learning…use a response to guide the learning process)
• Response is categorical (Each observation belongs to a “class”)
• Interested in relationship between variables and the response
• Short, fat data (instead of long, skinny data)
Long, skinny dataX Y Z
2 8 9
3 4 4
7 5 46
8 7 3
4 56 35
6 58 63
12 9 3
14 2 35
24 1 45
2 7 4
13 78 25
14 56 34
18 6 89
35 8 56
Short, fat data
n<p problem
X Y Z S T V M N R Q L H G K B C W
4 36 5 8 30 4 35 7 3 78 9 3 1 40 2 5 34
6 7 34 6 7 67 8 89 8 4 2 6 5 9 8 67 3
7 46 2 4 5 6 7 58 9 7 9 50 4 45 7 8 45
8 4 5 65 57 57 42 2 7 23 4 6 76 8 0 56 90
Random Forests
• Developed by Leo Breiman (Berkeley) and Adele Cutler (Utah State)
• Can handle the n<p problem• Random forests are comparable in accuracy
to support vector machines• Random forests are a combination of tree
predictors
Constructing a tree
Observation Gender Height (inches)1 F 602 F 663 M 684 F 705 F 666 M 727 F 648 M 67
Tree for previous data set
All observations
N=8
Height < 66
N=4
Height > 66
N=4
Male
N=0
Female
N=4
Male
N=3
Female
N=1
Random Forest
• First, the number of trees to be grown must be specified.
• Also, the number of variables randomly selected at each node must be specified (m).
• Each tree is constructed in the following manner:1. At each node, randomly select m variables to
split on.
Random Forest
2. The node is split using the best split among the selected variables.
3. This process is continued until each node has only one observation, or all the observations belong to the same class.
• Do this for each tree in the “forest”
Example: Cereal Data
N=70
(40 G, 30K)
Calories <100
(2 G, 15 K)
Calories <100
(38 G, 15 K)
Fat <1
15 K
Fat >1
2 G
Carbo<12
15 K
Carbo>12
38G
Random Forest• Another important feature is that each tree is
created using a bootstrap sample of the learning set.• Each bootstrap sample contains approximately 2/3
of the data (thus approximately 1/3 is left)• Now, we can use the trees built not containing
observations to get an idea of the error rate (each tree will “vote” on which class the observation belongs to).
• Example
N=70
(40 G, 30K)
Calories <100
(2 G, 15 K)
Calories <100
(38 G, 15 K)
Fat <1
15 K
Fat >1
2 G
Carbo<12
15 K
Carbo>12
38G
Observation withheld from creating this tree
Calories Fat Carbo Mfr
98 2 10 K
Random Forest
• This gives us an “out of bag” error rate• Random forests also give us an idea of
which variables are important for classifying individuals.
• Also gives information about outliers
The era of the “omics” sciences
Just a few of the “omics” sciences
• Genomics• Transcriptomics• Proteomics• Metabolomics• Phenomics• Toxicogenomics• Phylomics• Foldomics
• Kinomics• Interactomics• Behavioromics• Variomics• Pharmacogenomics
Functional Genomics
Genomics
Transciptomics
Proteomics
Metabolomics
Metabolomics
• Metabolites are all the small molecules in a cell (i.e. ATP, sugar, pyruvate, urea)
• 3,000 metabolites in the human body (compared to 35,000 genes and approximately 100,000 proteins)
• Most direct measure of cell physiology• Uses GC/MS and LC/MS to obtain
measurements
Data
• Currently only have GC/MS information• Missing values are very informative (below
detection limits)• Imputed data using uniform random
variables from 0 to minimum value• 105 metabolites• 58 individuals (42 “disease 1”, 6 “disease
2”, and 10 “controls”)
Confusion matrix
1 2 3
1 40 1 8
2 0 5 1
3 2 0 1
Oob error = 20.69%
Outlier
Variable Importance
Visual Data
• Dostat
Conclusions
• Random forests, support vector machines, and neural networks are some of the newest algorithms for understanding large datasets.
• There is still much more to be done.
Thank you