Element_PI.PersImage

Note

The implementation of this class is adapted from the scikit-tda/PerSim package, whose code can be found at this link.

class Element_PI.PersImage(pixels=20, 20, spread=None, specs=None, kernel_type='gaussian', weighting_type='linear', verbose=True)

Initialize a persistence image generator.

Parameters

• pixels (pair of ints like (int, int)) –

  • Tuple representing number of pixels in return image along x and y axis.

• spread (float) –

  • Standard deviation of gaussian kernel

• specs (dict) –

  • Parameters for shape of image with respect to diagram domain.

  • Units are specified in Angstroms.

  • This is used if you would like images to have a particular range. Shaped like:

    {
        "maxBD": float,
        "minBD": float
    }
    

• kernel_type (string or ..) –

  • TODO: Implement this feature.

  • Determine which type of kernel used in the convolution, or pass in custom kernel. Currently only implements Gaussian.

• weighting_type (string or ..) –

  • TODO: Implement this feature.

  • Determine which type of weighting function used, or pass in custom weighting function.

  • Currently only implements linear weighting.

Methods

__init__([pixels, spread, specs, …])	Initialize self.
transform(diagrams)	Convert diagram or list of diagrams to a persistence image.
weighting([landscape])	Define a weighting function.
kernel([spread])	This will return whatever kind of kernel we want to use.
to_landscape(diagram)	Convert a diagram to a landscape (birth, death) -> (birth, death-birth)
show(imgs[, ax])	Visualize the persistence image.

__init__(pixels=20, 20, spread=None, specs=None, kernel_type='gaussian', weighting_type='linear', verbose=True)

Initialize self. See help(type(self)) for accurate signature.

transform(diagrams)

Convert diagram or list of diagrams to a persistence image.

Parameters

diagrams (list of or singleton diagram, list of pairs. [(birth, death)]) –

• Persistence diagrams to be converted to persistence images.

• It is assumed they are in (birth, death) format.

• Can input a list of diagrams or a single diagram.

Returns

imgs –

• Persistence images converted from corresponding diagrams

Return type

list or singular

weighting(landscape=None)

Define a weighting function.

Note

For stability results to hold, the function must be 0 at y=0.

Parameters

landscape (Numpy array) –

• Converted diagram feature (see diagram argument in tranform function)

• Note: diagram converted to landscape in to_landscape function

Returns

weighting_fn –

• The weighting function based on specifications in __init__

Return type

function

kernel(spread=1)

This will return whatever kind of kernel we want to use.

Must have signature (ndarray size NxM, ndarray size 1xM) -> ndarray size Nx1.

Parameters

spread (float, optional) –

• Default: 1

• Variance/covariance for the kernel

Returns

kernel_fn –

• Kernel function based on specification in __init__

Return type

function

static to_landscape(diagram)

Convert a diagram to a landscape (birth, death) -> (birth, death-birth)

Parameters

diagram (list of pairs, [(birth, death)]) –

• Persistence diagram to be converted to persistence image.

• It is assumed to be in (birth, death) format.

Returns

diagram –

• Converted persistence diagram with coordinates [(birth, death-birth)]

Return type

list of pairs, [(birth, death)]

show(imgs, ax=None)

Visualize the persistence image.

Parameters

• imgs (Numpy array) –

  • Persistence images to show

  • Can be list of images or single image

• ax (Axes instance from matplotlib.pyplot, optional) –

  • Option to provide a plotting object for plotting PI

Returns

• None (None)

• No explicit return. Plots the PI on the given Axes (or a new one if not given).