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)

• 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 60

2 F 66

3 M 68

4 F 70

5 F 66

6 M 72

7 F 64

8 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