kmapper.Cover

class kmapper.Cover(n_cubes=10, perc_overlap=0.5, limits=None, verbose=0)

Bases: object

Helper class that defines the default covering scheme

It calculates the cover based on the following formula for overlap. (https://arxiv.org/pdf/1706.00204.pdf)

             |cube[i] intersection cube[i+1]|
overlap = --------------------------------------
                      |cube[i]|

Parameters

• n_cubes (int) – Number of hypercubes along each dimension. Sometimes referred to as resolution.

• perc_overlap (float) – Amount of overlap between adjacent cubes calculated only along 1 dimension.

• limits (Numpy Array (n_dim,2)) – (lower bound, upper bound) for every dimension If a value is set to float(‘inf’), the bound will be assumed to be the min/max value of the dimension Also, if limits == None, the limits are defined by the maximum and minimum value of the lens for all dimensions. i.e. [[min_1, max_1], [min_2, max_2], [min_3, max_3]]

Example

>>> import numpy as np
>>> from kmapper.cover import Cover
>>> data = np.random.random((100,2))
>>> cov = Cover(n_cubes=15, perc_overlap=0.75)
>>> cube_centers = cov.fit(data)
>>> cov.transform_single(data, cube_centers[0])
array([[0.3594448 , 0.07428465],
       [0.14490332, 0.01395559],
       [0.94988668, 0.03983579],
       [0.73517978, 0.09420806],
       [0.16903735, 0.06901085],
       [0.81578595, 0.10708731],
       [0.26923572, 0.12216203],
       [0.89203167, 0.0711279 ],
       [0.80442115, 0.10220901],
       [0.33210782, 0.04365007],
       [0.52207707, 0.05892861],
       [0.26589744, 0.08502856],
       [0.02360067, 0.1263653 ],
       [0.29855631, 0.01209373]])
>>> hyper_cubes = cov.transform(data, cube_centers)

__init__(n_cubes=10, perc_overlap=0.5, limits=None, verbose=0)

Methods

__init__([n_cubes, perc_overlap, limits, ...])
find(data_point)	Finds the hypercubes that contain the given data point.
fit(data)	Fit a cover on the data.
fit_transform(data)
transform(data[, centers])	Find entries of all hypercubes.
transform_single(data, center[, i])	Compute entries of data in hypercube centered at center

find(data_point)

Finds the hypercubes that contain the given data point.

Parameters

data_point (array-like) – The data point to locate.

Returns

cube_ids (list of int) – list of hypercube indices, empty if the data point is outside the cover.

fit(data)

Fit a cover on the data. This method constructs centers and radii in each dimension given the perc_overlap and n_cube.

Parameters

data (array-like) – Data to apply the cover to. Warning: First column must be an index column.

Returns

centers (list of arrays) – A list of centers for each cube

transform(data, centers=None)

Find entries of all hypercubes. If centers=None, then use self.centers_ as computed in self.fit.

Empty hypercubes are removed from the result

Parameters

• data (array-like) – Data to find in entries in cube. Warning: first column must be index column.

• centers (list of array-like) – Center points for all cubes as returned by self.fit. Default is to use self.centers_.

Returns

hypercubes (list of array-like) – list of entries in each hypercube in data.

transform_single(data, center, i=0)

Compute entries of data in hypercube centered at center

Parameters

• data (array-like) – Data to find in entries in cube. Warning: first column must be index column.

• center (array-like) – Center points for the cube. Cube is found as all data in [center-self.radius_, center+self.radius_]

• i (int, default 0) – Optional counter to aid in verbose debugging.