Viktor Petukhov
PhD student at the University of Copenhagen
Boundary detection
V. Petukhov, P. Kharchenko
Goal
Estimate
boundaries
Set of molecules
Split molecules by cells
Basic idea
| X | Y | Gene |
|---|---|---|
| ... | ... | ... |
We know:
What is the source?
Gene 1: 20%
Gene 2: 80%
Gene 1: 80%
Gene 2: 20%
Basic idea
| Gene 1 | ... | Gene k |
|---|---|---|
| N1 | Nk |
Gene vector
Embedding to 3d space
k nearest
neighbors
Model description
Global scale
Cell type
Shape / size
Position of center
scRNA-seq data
Composition
Nuclei stains
Membrane stains
Molecules
Boundaries
Model description
Transcript composition
Center position, ellipsoid shape
2D Normal distribution
Multinomial distribution
| 0.43 | 0.12 | 0.12 | 0.03 | 0.24 | 0.06 |
| 10 | 20 |
| 3.5 | -1.5 |
| -1.5 | 3.5 |
\Sigma:
M:
Position
Shape
Composition
P:
Cell is a distribution:
f(x, y, g) = N(x, y | M, \Sigma) P(g)
Goal v2.0
Separate probability distributions from a mixture model
EM on spatial data
Algorithm v0.01
Initial approximation
Expect
Maximize
EM on spatial data
Problem: spatial constraints
EM on spatial data
Solution: Graph Cut Optimization
EM on spatial data
Algorithm v0.02
Initial approximation
Expect
Maximize
GCO
EM on spatial data
Algorithm v0.02: Results
EM on spatial data
Algorithm v0.1: Stochastic EM
Expect
Sample
Maximize
- Convergence to global optimum
- Doesn't require specification of number of clusters
EM on spatial data
Algorithm v0.1: Stochastic EM
Hierarchical Bayesian Models
Composition prior
Expect
Sample
Maximize
SpaceTx presentation
By Viktor Petukhov
