phot_class.fom

The fom module calculates the Figure of Merit (FOM) parameter defined as:

\[FOM = \frac{N_{true}}{N_{total}} \times \frac{N_{true}}{N_{true} + N_{false}}\]

where \(N_{true}\) is the number of objects correctly classified as a given type, \(N_{false}\) is the number of objects falsely classified as the given type, and \(N_{total}\) is the total number of objects with that type.

This module specifically focuses on classification techniques that classify targets based on their (x, y) position in some two dimensional phase space. Functions are provided for calculating the FOM according to multiple classification schemes:

Function Classification Scheme
rectangular Uses a pair of rectangular axes to classify targets in the upper right quadrant as a given type.
vertical Classifies targets with an x coordinate greater than some value as a given type.
horizontal Classifies targets with a y coordinate greater than some value as a given type.
linear Classifies targets above a linear boundary y = mx + b as a given type.
diagonal Classifies targets above a diagonal boundary y = x + b as a given type. Note the difference in slope between this option and the linear option.

Alternatively, the fom method can be used to calculate the FOM for a set of predetermined classifications, independent of the chosen classification technique (i.e. using the results of an already run classification).

Usage Example

>>> from phot_class.fom import fom
>>>
>>> # The true "spectroscopic" classification of an object
>>> truth = ['normal', 'normal', 'normal', '91bg', '91bg']
>>>
>>> # The result of some classification piepline
>>> classifications = ['normal', 'normal', '91bg', 'normal', '91bg']
>>>
>>> # Classify the FOM for the "91bg" type
>>> bg_fom = fom(truth, classifications, '91bg')
>>>
>>> # Classify the FOM for the "normal" type
>>> normal_fom = fom(truth, classifications, 'normal')

Function Documentation

phot_class.fom.diagonal(truth, x, y, b, check_type)[source]

Calculate the figure of merit using a diagonal lower bound: y = -x + b

Expected classifications are “normal” or “91bg” (case insensitive). All other classifications are ignored.

Parameters:
  • truth (ndarray) – Array of classifications to take as truth
  • x (ndarray) – The classification x coordinate
  • y (ndarray) – The classification y coordinate
  • b (float) – The y-intercept of the boundary
  • check_type (str) – The classification to calculate the FOM for
Returns:

The figure of merit value
phot_class.fom.fom(truth, classification, check_type)[source]

Calculate the figure of merit for a given set of classifications

Parameters:
  • truth (ndarray) – The true classifications
  • classification (ndarray) – The assigned classifications
  • check_type (str) – The classification to calculate the FOM for
Returns:

(n_true / n_total_type) * (n_true / (n_true + n_false))
phot_class.fom.horizontal(truth, x, x_cutoff, check_type)[source]

Calculate the figure of merit using a vertical lower boundary (i.e. using only the x coordinate)

Parameters:
  • truth (ndarray) – Array of classifications to take as truth
  • x (ndarray) – The classification x coordinate
  • x_cutoff (float) – The x boundary to use for separating 91bg / normal
  • check_type (str) – The classification to calculate the FOM for
Returns:

The figure of merit value
phot_class.fom.linear(truth, x, y, m, b, check_type)[source]

Calculate the figure of merit using a diagonal lower bound: y = mx + b

Parameters:
  • truth (ndarray) – Array of classifications to take as truth
  • x (ndarray) – The classification x coordinate
  • y (ndarray) – The classification y coordinate
  • m (float) – The slope of the boundary
  • b (float) – The y-intercept of the boundary
  • check_type (str) – The classification to calculate the FOM for
Returns:

The figure of merit value
phot_class.fom.rectangular(truth, x, y, x_cutoff, y_cutoff, check_type)[source]

Calculate the figure of merit using a pair of rectangular lower bounds

Parameters:
  • truth (ndarray) – Array of classifications (str) to take as truth
  • x (ndarray) – The classification x coordinate
  • y (ndarray) – The classification y coordinate
  • x_cutoff (float) – The x boundary to use for separating 91bg / normal
  • y_cutoff (float) – The y boundary to use for separating 91bg / normal
  • check_type (str) – The classification to calculate the FOM for
Returns:

The figure of merit value
phot_class.fom.vertical(truth, y, y_cutoff, check_type)[source]

Calculate the figure of merit using a horizontal lower boundary (i.e. using only the y coordinate)

Expected classifications are “normal” or “91bg” (case insensitive). All other classifications are ignored.

Parameters:
  • truth (ndarray) – Array of classifications to take as truth
  • y (ndarray) – The classification y coordinate
  • y_cutoff (float) – The y boundary to use for separating 91bg / normal
  • check_type (str) – The classification to calculate the FOM for
Returns:

The figure of merit value