local2global.utils.AlignmentProblem

class AlignmentProblem

Bases: object

Implements the standard local2global algorithm using an unweighted patch graph

__init__(patches: List[local2global.utils.Patch], patch_edges=None, min_overlap=None, copy_data=True, self_loops=False, verbose=False)

Initialise the alignment problem with a list of patches

Parameters

• patches – List of patches to synchronise

• patch_edges – if provided, only compute relative transformations for given patch edges (all pairs of patches with at least min_overlap points in common are included by default)

• min_overlap (int) – minimum number of points in the overlap required for two patches to be considered connected (defaults to dim+1) where dim is the embedding dimension of the patches

• copy_data (bool) – if True, input patches are copied (default: True)

• self_loops (bool) – if True, self-loops from a patch to itself are included in the synchronisation problem (default: False)

• verbose (bool) – if True print diagnostic information (default: False)

Methods

__init__	Initialise the alignment problem with a list of patches
calc_synchronised_rotations	Compute the orthogonal transformations that best align the patches
calc_synchronised_scales	Compute the scaling transformations that best align the patches
calc_synchronised_translations	Compute translations that best align the patches
get_aligned_embedding	Return the aligned embedding
load	restore AlignmentProblem from patch file
mean_embedding	Compute node embeddings as the centroid over patch embeddings
rotate_patches	align the rotation/reflection of all patches
save_embedding	save aligned embedding to json file
save_patches	save patch embeddings to json file :param filename: path to output file
scale_patches	Synchronise scales of the embeddings for each patch
translate_patches	align the patches by translation
weight	Compute the weighting factor for a pair of patches

Attributes

dim	embedding dimension
n_nodes	total number of nodes
n_patches	number of patches
rotations	tracks orthogonal transformations applied to patches (updated by rotate_patches())
scales	tracks scale transformations applied to patches (updated by scale_patches())
shifts	tracks translation transformations applied to patches (updated by scale_patches(), rotate_patches(), and translate_patches())
verbose	print debug output if True

weight(i, j)

Compute the weighting factor for a pair of patches

Parameters

• i – First patch index

• j – Second patch index

Returns

1

Override this in subclasses for weighted alignment

scale_patches(scale_factors=None)

Synchronise scales of the embeddings for each patch

Parameters

scale_factors – if provided apply the given scales instead of synchronising

calc_synchronised_scales(max_scale=100000000.0)

Compute the scaling transformations that best align the patches

Parameters

max_scale – maximum allowed scale (all scales are clipped to the range [1/max_scale, max_scale]) (default: 1e8)

Returns

list of scales

rotate_patches(rotations=None)

align the rotation/reflection of all patches

Parameters

rotations – If provided, apply the given transformations instead of synchronizing patch rotations

calc_synchronised_rotations()

Compute the orthogonal transformations that best align the patches

translate_patches(translations=None)

align the patches by translation

Parameters

translations – If provided, apply the given translations instead of synchronizing

calc_synchronised_translations()

Compute translations that best align the patches

mean_embedding()

Compute node embeddings as the centroid over patch embeddings

get_aligned_embedding(scale=False, realign=False)

Return the aligned embedding

Parameters

• scale (bool) – if True, rescale patches (default: False)

• realign (bool) – if True, recompute aligned embedding even if it already exists (default: False)

Returns

n_nodes x dim numpy array of embedding coordinates

save_patches(filename)

save patch embeddings to json file :param filename: path to output file

classmethod load(filename)

restore AlignmentProblem from patch file

Parameters

filename – path to patch file

save_embedding(filename)

save aligned embedding to json file

Parameters

filename – output filename