1. 8/12/14, 1:58 PMMicrobiome Species Data Exploration
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MicrobiomeSpeciesDataExplorationMicrobiomeSpeciesDataExploration
UnsupervisedandSupervisedApproach
Mehrdad Yazdani
August 12, 2014

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Outline
1. Properties of data set
2. Unsupervised Analysis
3. Supervised Analysis
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Where does this data come from?
The data originates from stool samples from the NIH Human Microbiome Project and Professor
Larry Smarr. The NIH HMP has healthy and sick subjects.
Here we focus on different population of species.
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Properties of Species Data Set
The data shows the different compositions of different species for each subject. Hence, it has
the properties of a compositional data set:
1. For each subject, the composition of a specific species is greater than 0.0 and less than 1.0
2. The composition of all species for a single subject must sum to 1.0
In our data, the number of species are:
The number of subjects are:
Note that we have far more species than subjects in this data set.
## [1] 2572
## [1] 249
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Species Compositions for Each Subject
The composition of the species for each subject must sum to 1.0, however this is not the case
for this data set:
Possible reason: numerical "round-off"" errors introduce this discrepancy.
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Zeros
Zeros must be handled carefully. There are two classes of zeros in compositional data sets:
1. Absolute zeros: indicate that the species should be removed
2. Round-off zeros: indicates that the amount of species was below threshold of detection
Absolute zeros are dealt with by removing them. Round-off zeros are trickier and are typically
replaced with "small" values (imputation tricks).
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Number of Absolute Zeros
The number of species that are always zero for all subjects is:
We will treat these species as being absolute zeros and remove them from the data:
## [1] 29
## [1] "Marinilabilia sp. AK2"
## [2] "Desulfovibrio piezophilus"
## [3] "Streptomyces bottropensis"
## [4] "Novosphingobium sp. AP12"
## [5] "Acinetobacter sp. NCTC 7422"
## [6] "Caldisphaera lagunensis"
## [7] "Streptomyces auratus"
## [8] "Candidatus Arthromitus sp. SFB-1"
## [9] "Gillisia sp. CBA3202"
## [10] "Thielavia terrestris"
## [11] "Synechococcus sp. PCC 6312"
## [12] "Alcaligenes faecalis"
## [13] "Aspergillus fumigatus" 7/23

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Number of Round-off Zeros
After removing absolute zeros, we observe that there are also a large number of zeros from
round-off errors:
Since the compositions do not sum to 1.0, we replace these round-off zeros with values so that
our data is a true compositional data set.
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Recall that we are dealing with compositions
1. For each subject, the composition of a specific species is greater than 0.0 and less than 1.0
2. The composition of all species for a single subject must sum to 1.0
Because of these constraints, the usual algebra of additions, multiplications, etc. that we are
used to does not apply. Typically, a transformation function is applied to the composition so
that we can apply the usual Euclidean algebra. There are many possible transformation
functions used.
Here we apply the log transformation on compositions.
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Unsupervised Approach
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PCA
Top 3 PC's explain 80% of variance.
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Species Projected onto Top PC's
Hypothesis: PC2 is the most useful component for discriminating healthy vs. sick subjects.
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What does PC-1 look like?
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What does PC-2 look like?
Many of the loadings are close to zero, therefore PC2 can be approximated by a sparse vector:
this can lead to better interpretable results as to which species "matter." This is in contrast to
PC-1.
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Supervised Approach
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Logistic Regression
We build classifiers to determine which species are important for discriminating healthy from
sick subjects. In our approach, we pool all LS, CD, and UC subjects into one group labeled as
"sick," and all HE subjects are labeled as "healthy."
The classifier that we use is a logistic regression model and we measure the error of the
classifier using the Akaike information criterion (AIC).
Note that since we have an order of magnitude less subjects than species, this is an
undetermined system (more unknowns than equations) and it is not meaningful to use "all" the
data. To mitigate this issue, we take subsets of the species that we have. We first take subsets
from the PCs, followed by subsets of the species.
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Logistic Regression on PCs
We build a logistic regression model on the top 3 PC's to measure just how good these
components are classifying sick from healthy subjects. Recall that our PCA plots from before
appeared to show PC2 to be the most useful for this task. The AIC for the logistic regression
model that uses only PC 1 is:
The AIC for the logistic regression model that uses only PC 2 is:
The AIC for the logistic regression model that uses only PC 3 is:
The lower the AIC, the less error the model has. Therefore these analyses support our earlier
hypothesis that PC2 is more discriminative than the other PCs.
## [1] 163.8
## [1] 61.6
## [1] 190.9
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Logistic Regression on Individual Species
We now build classifiers on each individual species. The AIC for logistic regression models that
use single species is as follows:
We select the pair of species with lowest AIC. Since the AIC was computed for a model that uses
a single species, selecting a pair of species may be sub-optimal.
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Two species with lowest AIC
The two species with the lowest individual AIC are:
Their respective individual AIC's are:
## [1] "Bacteroides.dorei" "Bacteroides.oleiciplenus"
## [1] 24.47 49.38
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Plot of the Two Species with Lowest AIC
This plot shows that the species with the lowest AIC have a larger separability than the PCA plot
from before. However, a lot of interesting structure that the PCA plot revealed is lost (for
example: the sub-cluster within healthy subjects).
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Plot of the Species with Lowest AIC against E. Coli
While E. Coli does not have lowest AIC, comparing it with the lowest AIC specie reveals good
discrimination and interesting structures that PCA had revealed.
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Future Work
1. Instead of selecting a single species to build a logistic regression model, select pairs of
species. This will involve solving over 3 million logistic regression models. Solving a triplet will
require over 2.8 billion! (Dell resources??)
2. Incorporate Ayasdi features
3. Apply similar analysis to the other data sets.
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