# Source code for apricot.functions.sumRedundancy

# sumRedundancy.py
# Author: Jacob Schreiber <jmschreiber91@gmail.com>

import numpy

from .base import BaseGraphSelection

from tqdm import tqdm

[docs]class SumRedundancySelection(BaseGraphSelection): """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. """ 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)
[docs] def fit(self, X, y=None, sample_weight=None, sample_cost=None): """Run submodular optimization to select the examples. This method is a wrapper for the full submodular optimization process. It takes in some data set (and optionally labels that are ignored during this process) and selects n_samples from it in the greedy manner specified by the optimizer. This method will return the selector object itself, not the transformed data set. The transform method will then transform a data set to the selected points, or alternatively one can use the ranking stored in the self.ranking attribute. The fit_transform method will perform both optimization and selection and return the selected items. Parameters ---------- X : list or numpy.ndarray, shape=(n, d) The data set to transform. Must be numeric. y : list or numpy.ndarray or None, shape=(n,), optional The labels to transform. If passed in this function will return both the data and th corresponding labels for the rows that have been selected. sample_weight : list or numpy.ndarray or None, shape=(n,), optional The weight of each example. Currently ignored in apricot but included to maintain compatibility with sklearn pipelines. sample_cost : list or numpy.ndarray or None, shape=(n,), optional The cost of each item. If set, indicates that optimization should be performed with respect to a knapsack constraint. Returns ------- self : SumRedundancySelection The fit step returns this selector object. """ return super(SumRedundancySelection, self).fit(X, y=y, sample_weight=sample_weight, sample_cost=sample_cost)
def _initialize(self, X_pairwise, idxs=None): super(SumRedundancySelection, self)._initialize(X_pairwise, idxs=idxs) idxs = idxs if idxs is not None else numpy.arange(X_pairwise.shape[0]) for i, idx in enumerate(idxs): self.current_values[i] = X_pairwise[idx, idx] if self.initial_subset is None: return elif self.initial_subset.ndim == 2: raise ValueError("When using saturated coverage, the initial subset"\ " must be a one dimensional array of indices.") elif self.initial_subset.ndim == 1: if not self.sparse: for i in self.initial_subset: self.current_values += X_pairwise[i] * 2 else: for i in self.initial_subset: self.current_values += X_pairwise[i].toarray()[0] * 2 else: raise ValueError("The initial subset must be either a two dimensional" \ " matrix of examples or a one dimensional mask.") def _calculate_gains(self, X_pairwise, idxs=None): idxs = idxs if idxs is not None else self.idxs return -self.current_values[idxs] def _select_next(self, X_pairwise, gain, idx): """This function will add the given item to the selected set.""" if self.sparse: self.current_values += X_pairwise.toarray()[0] * 2 else: self.current_values += X_pairwise * 2 super(SumRedundancySelection, self)._select_next( X_pairwise, gain, idx)