2. ● SVD/PCA of Transcriptome Time Series Data
● Optimal Discrete-Time Linear Dynamical System
● Optimal Continuous-Time Linear Dynamical
System
● Projection of Macroscale Interactions onto
Microscale
● Correlation between Inferred Interactions and
known Genetic Landscape
3.
4. SVD/PCA of Transcriptome Time
Series Data
● We compared the effect of normalizing the features of the
transcriptome time series data before performing SVD
with doing singular value decomposition on a non-
normalized dataset.
● While this data has been subjected to analysis through
the SVD, no one has ever performed PCA on this
dataset.
5.
6.
7.
8. Optimal Discrete-Time Linear
Dynamical System
● We followed the approach of D'hasseler et al. and found an
optimal state-space transition matrix to describe the reduced-
order dynamics of the transcriptome which were revealed
through the unsupervised learning step.
● Our approach was novel and differed from D'hasseler et al and
Wu et al in that we measured the performance of the transition
matrix with only one single matrix multiplication.
● The application of L1
regularized multivariate linear regression
to finding an optimal transition matrix is an original contribution
to the study of transcriptome modeling.
9. Optimal Continuous-Time Linear
Dynamical System
● We sought an optimal continous-time linear dynamical
system which could best describe the transcriptome
modes which were discovered through the unsupervised
learning step in our pipeline.
● Similar approaches (e.g. Inferrelator) that use
continuous-time linear dynamical systems model the
interactions of gene clusters and not the interactions of
non-correlating modes of transcriptome dynamics.
10.
11.
12. Projection of Macroscale
Interactions onto Microscale
● We were able to project the inferred relationships
between macroscale modes of the transcriptome onto the
microscale through finding a microscale transition matrix
according to the formula
⃗wk=∑
i
M
∑
j
M
ui
k
σi Ti
j
⃗uj/σ j
● This novel formula has never been applied before as
clustering is usually used to reduced the dimensionality of
the problem whereas our approach of using PCA/SVD
gives us the precise topology of each of our transcriptome
modes.
13.
14. Correlation between Gene-Gene
Interactions and known Genetic
Landscape
● We calculated the Pearson Correlation Coefficient
between our matrix of genetic interactions and the
genetic lanscape of Costanzo et al (2010).
● We found the correlation between the interactions
inferred through our method and the gene-gene
associations of the genetic landscape to be
approximately zero.
● Our approach uses Singular Value Decomposition to
model collective behavior in the transcriptome on the
microscopic level.
