Paper: https://doi.org/10.1186/s12920-017-0302-1 Presentation at InCob2017 http://datamining-web.it.uts.edu.au/bioinformatics/

1. Tensor decomposition­based unsupervised
feature extraction identifies candidate
genes that induce post­traumatic stress
disorder­mediated heart diseases
Y­h. Taguchi, Dept. Phys., Chuo Uinv.,
Tokyo, Japan
Best Paper Awards of BMC Track
of
InCoB 2017 (BMC Med. Geno., Silver)

2. 1. Introduction
PTSD (Post Traumatic Stress Disorder) is
primarily a mental disease that can mediate other
physical diseases, e.g., diabetes (Roberts et al.,
JAMA Psychiatry, 2015).
In this study, we study how PTSD mediates heart
failure in spite of the remote distance between
heart and brain where PTSD primarily takes place.
We hypothesize that similar gene expression
between heart and brain might mediate PTSD
mediated heart diseases.

3. 2. Methods
Applying tensor decomposition (TD) based unsupervised
feature extraction (FE) to gene expression tensor,
treatments treatments  tissuestissues  genesgenes, identify genes co­expressed
between brain and heart, but differentially between control
and treated samples.
Tensor
GenesGenes
Tissues
Tissues
TreatmentsTreatments
Genes expressive selectively at the specific
combination of tissues and conditions

4. 3. Synthetic data
10 treatments  10 tissues = 100 classes
1 sample / 1 class
1st
100 genes:
expressive in 4 tissues at 1st
treatment
2nd
100 genes:
expressive in other 4 tissues at 2nd
treatment
….
10th
100 genes:
expressive in other 4 tissues at 10th
treatment
1,000 expressive genes + 29,000 noise =30,000

5. 1st
100 genes set
2nd
100 genes set
3rd
100 genes set
4th
100 genes set
5th
100 genes set
6th
100 genes set
7th
100 genes set
8th
100 genes set
9th
100 genes set
10th
100 genes set
Total 1,000 genes

6. Task:
Identification of 1000 expressive genes among
30,000 genes composed of 1,000 expressive
genes and 29,000 noise.
Tensor representation:
xi1i2i3
: 1 ≤ i1 ≤ 30,000 genes,
1 ≤ i2 ≤ 10 tissues,
1 ≤ i3 ≤ 10 treatments.

7. HOSVD (Higher Order Singular Value Decomposition)
xi1i2i3
= ∑ l1l2l3
G(l1l2l3) xl1i1
xl2i2
xl3i3
1 ≤ l1 ≤ 30,000, 1 ≤ l2 ≤ 10, 1 ≤ l3 ≤ 10.
G(l1l2l3): core tensor
xl1i1
, xl2i2
, xl3i3
:singular value vectors
(orthogonal matrices)
xi1i2i3
G
xi1l1
xi2l2
xi3l3

8. xl1i1
, 2 ≤ l1 ≤ 5
1,000 genes
are well
separated.
(10 classes
=
5 colors

5 symbols)
29,000 genes
are omitted.

9. Selection of 1,000 genesSelection of 1,000 genes assuming
that xl1i1
, 2 ≤ l1 ≤ 5 obey multiple Gaussian.
In other words, genes not obeying Gaussian are
supposed to be expressive genes.
Pi1
s are attributed to 1 ≤ i1 ≤ 30,000 by 2
distribution.
Pi1
= P
2
[> ∑ 2 ≤ l1 ≤ 5 (xl1i1
/l1
)2
]
P
2
[> x] :Cumulative probability that argument is
larger than x under the 2
distribution.
l1
: standard deviation.
Pi1
are corrected by multiple comparison correction

10. .. . AUC
adjusted Pi1
<0.1
adjusted Pi1
<0.05
adjusted Pi1
<0.01
True positive rate
False positive rate
Benjamini­Hochberg FDR

11. adjusted Pi1
<0.1
Comparison
between true classes
vs two clustering
results of selected
genes
True classes
Clustering
Gaussian mixture
Ward (hierarchical clustering)

12. Conclusions of synthetic data
1. Singular value vectors given by HOSVD clusters 10
classes well.
2. Singular value vectors given by HOSVD discriminate
1,000 expressive genes from 29,000 noise
3. Unsupervised clustering by singular value vectors
given by HOSVD are coincident with 10 classes.
4. Either ANOVA, SAM, or limma, could not achieve
comparative performance for discriminating 1,000 genes
from other 29,000 genes (omittedomitted).

13. 4. Real Data sets
PTSD model mouse: numbers: controls, treated
AY: amygdala, HC: hippocampus, MPFC: medial
prefrontal cortex, SE: septal nucleus,ST: striatum,
VS: ventral striatum.

14. xj1j2j3j4i : 1 ≤ j1 ≤ 2 control vs treated
1 ≤ j2 ≤ 10 tissues,
1 ≤ j3 ≤ 2 stress periods (5 vs 10 days)
1 ≤ j4 ≤ 3 rest periods
1 ≤ i ≤ 43,379 genes,
xj1j2j3j4i=∑l1l2l3l4l5
G(l1l2l3l4l5)xl1j1
xl2j2
xl3j3
xl4j4
xl5i
HOSVD

15. Control vs treated Tissues
xl1=2,j1
xl2=4,j2
AY
HC
heart
hemibrain

16. In order to identify xl3j3
,xl4j4
,xl5i associated
with l1=2 and l2=4, we rank G(2,3,l3,l4,l5) since
G with larger absolute value means more
contributions.
Stress l3=1,2
Rest l4=1,2,3
Gene l5=1,4,11
Gene selection

17. Pi = P
2
[> ∑ l5 =1,4,11 (xl5i/l5
)2
]
BH correction Adjusted Pi <0.01 → 801 genes
Differential expression between control and treated is
checked in raw data.
Successful!

18. Conclusions of real data
1. TD based unsupervised FE applied to real gene
expression identify 801 genes.
2. 801 genes are expressed commonly between heart and
brain, but differently between controls and treated.
3. ANOVA, SAM, and limma failed to identify reasonable
number of genes (omittedomitted).
4. Biological validation of genes are promising (omittedomitted).