class_docstr: A selector based off a sum redundancy submodular function.
  
  The sum redundancy function is a graph-based function that penalizes 
  redundancy among the selected set. This approach is straightforward, 
  in that it simply involved a sum. It is also fast in comparison to a 
  facility location function because it involves only performing calculation 
  over the selected set as opposed to the entire ground set. Because the sum 
  of the similarities is not submodular, it is subtracted from the sum of 
  the entire similarity matrix, such that examples that are highly similar 
  to each other result in a lower value than examples that are not very 
  similar.
  
  .. note:: 
          All ~pairwise~ values in your data must be positive for this 
          selection to work.
  
  The general form of a sum redundancy function is 
  
  .. math::
          f(X, V) = \sum_{x, y \in V} \phi(x, y) - \sum_{x, y\in X} \phi(x,y)
  
  where :math:`f` indicates the function, :math:`X` is the selected subset, 
  :math:`V` is the ground set, and :math:`\phi` is the similarity measure 
  between two examples. While sum redundancy functions involves calculating 
  the sum of the entire similarity matrix in principle, in practice if one 
  is only calculating the gains this step can be ignored.
  
  This implementation allows users to pass in either their own symmetric
  square matrix of similarity values, or a data matrix as normal and a function
  that calculates these pairwise values.
  
  Parameters
  ----------
  n_samples : int
          The number of samples to return.
  
  metric : str, optional
          The method for converting a data matrix into a square symmetric matrix
          of pairwise similarities. If a string, can be any of the metrics
          implemented in sklearn (see
          https://scikit-learn.org/stable/modules/generated/sklearn.metrics.pairwise_distances.html),
          including "precomputed" if one has already generated a similarity
          matrix. Note that sklearn calculates distance matrices whereas apricot
          operates on similarity matrices, and so a distances.max() - distances
          transformation is performed on the resulting distances. For
          backcompatibility, 'corr' will be read as 'correlation'. Default is
          'euclidean'.
  
  initial_subset : list, numpy.ndarray or None, optional
          If provided, this should be a list of indices into the data matrix
          to use as the initial subset, or a group of examples that may not be
          in the provided data should beused as the initial subset. If indices, 
          the provided array should be one-dimensional. If a group of examples,
          the data should be 2 dimensional. Default is None.
  
  optimizer : string or optimizers.BaseOptimizer, optional
          The optimization approach to use for the selection. Default is
          'two-stage', which makes selections using the naive greedy algorithm
          initially and then switches to the lazy greedy algorithm. Must be
          one of
  
                  'random' : randomly select elements (dummy optimizer)
                  'modular' : approximate the function using its modular upper bound
                  'naive' : the naive greedy algorithm
                  'lazy' : the lazy (or accelerated) greedy algorithm
                  'approximate-lazy' : the approximate lazy greedy algorithm
                  'two-stage' : starts with naive and switches to lazy
                  'stochastic' : the stochastic greedy algorithm
                  'sample' : randomly take a subset and perform selection on that
                  'greedi' : the GreeDi distributed algorithm
                  'bidirectional' : the bidirectional greedy algorithm
  
          Default is 'two-stage'.
  
  optimizer_kwds : dict or None
          A dictionary of arguments to pass into the optimizer object. The keys
          of this dictionary should be the names of the parameters in the optimizer
          and the values in the dictionary should be the values that these
          parameters take. Default is None.
  
  n_neighbors : int or None
          When constructing a similarity matrix, the number of nearest neighbors
          whose similarity values will be kept. The result is a sparse similarity
          matrix which can significantly speed up computation at the cost of
          accuracy. Default is None.
  
  reservoir : numpy.ndarray or None
          The reservoir to use when calculating gains in the sieve greedy
          streaming optimization algorithm in the `partial_fit` method.
          Currently only used for graph-based functions. If a numpy array
          is passed in, it will be used as the reservoir. If None is passed in,
          will use reservoir sampling to collect a reservoir. Default is None.
  
  max_reservoir_size : int 
          The maximum size that the reservoir can take. If a reservoir is passed
          in, this value is set to the size of that array. Default is 1000.
  
  n_jobs : int
          The number of threads to use when performing computation in parallel.
          Currently, this parameter is exposed but does not actually do anything.
          This will be fixed soon.
  
  random_state : int or RandomState or None, optional
          The random seed to use for the random selection process. Only used
          for stochastic greedy.
  
  verbose : bool
          Whether to print output during the selection process.
  
  Attributes
  ----------
  n_samples : int
          The number of samples to select.
  
  pairwise_func : callable
          A function that takes in a data matrix and converts it to a square
          symmetric matrix.
  
  ranking : numpy.array int
          The selected samples in the order of their gain.
  
  gains : numpy.array float
          The gain of each sample in the returned set when it was added to the
          growing subset. The first number corresponds to the gain of the first
          added sample, the second corresponds to the gain of the second added
          sample, and so forth.
code: def __init__(
      self,
      n_samples=10,
      metric="euclidean",
      initial_subset=None,
      optimizer="two-stage",
      n_neighbors=None,
      reservoir=None,
      max_reservoir_size=1000,
      n_jobs=1,
      random_state=None,
      optimizer_kwds={},
      verbose=False,
  ):
      super(SumRedundancySelection, self).__init__(
          n_samples=n_samples,
          metric=metric,
          initial_subset=initial_subset,
          optimizer=optimizer,
          n_neighbors=n_neighbors,
          reservoir=reservoir,
          max_reservoir_size=max_reservoir_size,
          n_jobs=n_jobs,
          random_state=random_state,
          optimizer_kwds=optimizer_kwds,
          verbose=verbose,
      )
  
file_path: apricot/apricot/functions/sumRedundancy.py
imports: import numpy
  from .base import BaseGraphSelection
  from tqdm import tqdm
label_desc: Use image node_id 1 to create a new SumRedundancySelection object from inherited base classes: BaseGraphSelection with example: obj = SumRedundancySelection(n_samples, metric, initial_subset, optimizer, n_neighbors, reservoir, max_reservoir_size, n_jobs, random_state, optimizer_kwds, verbose)