SiFT kernels

We provide examples for the different SiFT kernels

We use the Drosophila wing disc development single cell data [1] for the demonstration.

[1] Everetts, N. J., Worley, M. I., Yasutomi, R., Yosef, N., & Hariharan, I. K. (2021). Single-cell transcriptomics of the Drosophila wing disc reveals instructive epithelium-to-myoblast interactions. Elife, 10, e61276.

import numpy as np
import scanpy as sc

import sift

Load and set the adata

DATA_DIR = ".../drosophila.annotated.h5ad"  # set path to anndata

adata = sc.read(DATA_DIR)

nuisance_genes = np.concatenate((adata.uns["sex_genes"], adata.uns["cell_cycle_genes"]))
adata.obsm["nuisance_genes"] = adata[:, nuisance_genes].X
adata.uns["nuisance_genes"] = nuisance_genes

gene_subset = [g for g in adata.var_names if g not in nuisance_genes]
adata = adata[:, gene_subset].copy()

Define SiFT kernels

RBF kernel

The RBF kernel, aka squared-exponential kernel, defines distances between cells in the given space using:

\[k(x_i, x_j) = \exp\left(\frac{d(x_i, x_j)}{l}\right),\]

where \(l\) is the length_scale parameter.

Here we consider distances based on the nuisance_genes by setting kernel_key=nuisance_genes. We define adjust the length_scale by passing kernel_params = {"length_scale":0.5}

metric_ = "rbf"
kernel_key_ = "nuisance_genes"
kernel_params_ = {"length_scale": 0.5}

sft = sift.SiFT(
    adata=adata,
    kernel_key=kernel_key_,
    metric=metric_,
    kernel_params=kernel_params_,
    copy=True,
)

INFO     sift: initialized a SiFTer with rbf kernel.

Visualize the kernel using plot_kernel().

• groupby: the key in the anndata we can group the cells by.

• color_palette: colors for the groupby groups.

sft.plot_kernel(groupby="phase_sex", color_palette=adata.uns["phase_sex_colors"])

k-NN kernel

The k-NN connectivity graph defines the cell-cell similarity kernel. The connectivity graph is computed over the attributes given in kernel_key (a key in the adata object), here we consider kernel_key=nuisance_genes.

The n_neighbors parameter defines the number of neighbors in the connectivity graph.

metric_ = "knn"
n_neighbors_ = 5
kernel_key_ = "nuisance_genes"

sft = sift.SiFT(
    adata=adata,
    kernel_key=kernel_key_,
    n_neighbors=n_neighbors_,
    metric=metric_,
    copy=True,
)

INFO     sift: initialized a SiFTer with knn kernel.

Visualize the kernel using plot_kernel().

sft.plot_kernel(groupby="phase_sex", color_palette=adata.uns["phase_sex_colors"])

Mapping kernel

The mapping kernel takes a mapping of the cells to a given signal. Here we use the deterministic mapping of the cells to the cell cycle phase & sex label, using kernel_key ="phase_sex".

metric_ = "mapping"
kernel_key_ = "phase_sex"

sft = sift.SiFT(
    adata=adata,
    kernel_key=kernel_key_,
    metric=metric_,
    copy=True,
)

INFO     sift: initialized a SiFTer with mapping kernel.

Visualize the kernel using plot_kernel().

sft.plot_kernel(groupby="phase_sex", color_palette=adata.uns["phase_sex_colors"])

[KeOps] Generating code for formula Sum_Reduction((Var(0,6,0)|Var(1,6,1))*Var(2,19885,1),0) ... OK