Description Usage Arguments Details Value

Since Euclidean distance and Pearson correlation cannot capture the true
geometry of non-linear low dimensional manifolds, a graph-based distance
is used instead in `novoSpaRc`

. This function first computes a k-nearest
neighbor graph among cells or locations. Then it infers the shortest pairwise
path lengths on the graph for cells and locations, resulting in a graph-based
distance matrix, which is then used for the optimal transport reconstruction
of locations of gene expression.

1 2 | ```
calc_graph_dist(X, k, BNINDEX, BNPARAM, BPPARAM = SerialParam(),
transposed = FALSE, ...)
``` |

`X` |
Numeric matrix (can be sparse) with genes in rows and cells in
columns. If genes are in columns, then set |

`k` |
Number of nearest neighbor when constructing k-nearest neighbor graph. |

`BNINDEX` |
A BiocNeighborIndex object, or |

`BNPARAM` |
A BiocNeighborParam object, or |

`BPPARAM` |
An object of |

`transposed` |
Logical, whether the matrix has cells in rows rather than
in columns. Defaults to |

`...` |
Further arguments to pass to |

Whlie the Python implementation of this package uses the Floyd Warshall
algorithm to find the shortest path between vertices in the graph, this
function uses the Johnson algorithm, which is more efficient for sparse
graphs. Let *V* denote the number of vertices in the graph, and *E* number of
edges. The Floyd Warshall algorithm has complexity *O(V^3)*, while the
Johnson algorithm has complexity *O(V^2 \log(V) + VE)*. We expect k-nearest
neighbor graphs to be sparse since k is usually much smaller than the number
of vertices, so the number of edges is much smaller than in the complete
graph, which is *V(V-1)* in directed graphs.

The `BPPARAM`

argument is used for parallel computing in k-nearrest
neighbor search. For instance, use `BPPARAM = MulticoreParam(3)`

for
using 3 threads in shared memory computing.

The `BNINDEX`

argument is for precomputed index information for
different algorithms to find k-nearests neighbors. Using a pre-computed index
will save when multiple KNN search are performed on the same x.
If `BNINDEX`

is to be specified, then x should be missing.

The `BNPARAM`

argument is used for setting parameters for KNN search
algorithms, such as the kind of distance metric used.

Only one of `BNINDEX`

and `BNPARAM`

is needed to determine the
algorithm used, and if both are supplied, they must specify the same algorithm.
If both are missing, then the KmKNN algorithm will be used.

A dense square numeric matrix with n cells columns and rows. The entry at ith row and jth column represents the normalized shortest path length between vertex i and vertex j.

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