Tensor Decomposition of Spatial Features

Author: Clarence Mah | Last Updated: 6/15/2022

Here we will demonstrate how to use tensor decomposition to generate low dimensional signatures with bento. We will use the included seqFISH+ dataset.

Load Libraries

import bento

Load Data

Let’s start with the preprocessed seqFISH+ data.

# Load precomputed features
adata = bento.datasets.load_dataset('seqfish')

adata.layers

Layers with keys: cell_edge, cell_edge_p, cell_inner_asymmetry, cell_inner_proximity, cell_outer_asymmetry, cell_outer_proximity, cytoplasmic, cytoplasmic_p, l_half_radius, l_max, l_max_gradient, l_min_gradient, l_monotony, none, none_p, nuclear, nuclear_edge, nuclear_edge_p, nuclear_p, nucleus_dispersion, nucleus_inner_asymmetry, nucleus_inner_edge_enrichment, nucleus_inner_proximity, nucleus_outer_asymmetry, nucleus_outer_edge_enrichment, nucleus_outer_proximity, point_dispersion, spliced, unspliced

Tensor Rank Estimation

First we will determine the number of factors used to represent our dataset. To do so, we will perform tensor decomposition for a range of values and calculate the reconstruction loss with the original tensor at each value. Reconstruction accuracy across range of decomposition ranks (1 is perfect, 0 is noise). The best rank is highlighted in red as determined by the elbow method.

Note

Estimating rank can be difficult; here we are using a heuristic and therefore may not generalize perfectly to a different dataset. Try increasing the upper_rank if the error does not flatten, or increasing runs if the confidence interval is too wide.

layers = [
    "cell_inner_proximity",
    "nucleus_inner_proximity",
    "nucleus_outer_proximity",
    "l_half_radius",
    "l_max",
    "l_max_gradient",
    "l_min_gradient",
    "l_monotony",
    "cell_inner_asymmetry",
    "nucleus_inner_asymmetry",
    "nucleus_outer_asymmetry",
    "point_dispersion",
    "nucleus_dispersion",
]

bento.tl.select_tensor_rank(
    adata,
    layers=layers,
    upper_rank=10,
    runs=1
)

Device: cpu

The rank at the elbow is: None

Note

GPU Support: Tensor decomposition runs much faster on the GPU. See bento installation instructions to see how you can take advantage of this and compute signatures much more efficiently.

Generate signatures with tensor decomposition

Bento is able to utilize these feature spaces for predicting RNA localization patterns (see the “Subcellular Localization” tutorial). For unsupervised analysis, Bento implements tensor decomposition to generate interpretable low dimensional signatures.

bento.tl.decompose_tensor(
    adata,
    layers,
    9,
)

Device: cpu

Visualize the signature loadings.

bento.pl.lp_signatures(adata)

Plot the top genes and cells for each signature.

bento.pl.sig_samples(adata)