Disparity Sum

class submodlib.functions.disparitySum.DisparitySumFunction(n, mode, sijs=None, data=None, metric='cosine', num_neighbors=None)

Implementation of the Disparity-Sum (DispSum) function.

Disparity-Sum models diversity by computing the sum of pairwise distances of all the elements in a subset. It is defined as

\[f(X) = \sum_{i, j \in X} (1 - s_{ij})\]

Parameters

• n (int) – Number of elements in the ground set. Must be > 0.

• mode (str) – Can be “dense” or “sparse”. It specifies whether the Disparity-Sum function should operate in dense mode (using a dense similarity kernel) or sparse mode (using a sparse similarity kernel).

• sijs (numpy.ndarray or scipy.sparse.csr.csr_matrix, optional) – Similarity kernel (dense or sparse) between the elements of the ground set, to be used for getting \(s_{ij}\) entries as defined above. Shape of dense kernel must be n X n. When not provided, it is computed internally in C++ based on the following additional parameters. The implementation requires this simimlarity kernel to be normalized, i.e. entries must be strictly in [0,1].

• data (numpy.ndarray, optional) – Matrix of shape n X num_features containing the ground set data elements. data[i] should contain the num-features dimensional features of element i. Used to compute the similarity kernel. It is optional (and is ignored if provided) if sijs has been provided.

• metric (str, optional) – Similarity metric to be used for computing the similarity kernel. Can be “cosine” for cosine similarity or “euclidean” for similarity based on euclidean distance. Default is “cosine”.

• num_neighbors (int, optional) – Number of neighbors applicable for the sparse similarity kernel. Must not be provided if mode is “dense”. Must be provided if either a sparse kernel is provided or is to be computed.

clearMemoization()

Clear the computed memoized statistics, if any.

evaluate(X)

Computes the score of a set as per the above math.

Parameters

X (set) – The set whose score needs to be computed. Must be a subset of effective ground set.

Returns

The evaluation score of the given set.

Return type

float

evaluateWithMemoization(X)

Efficiently compute the function evaluation of a set assuming that memoized statistics for it are already computed.

Parameters

X (set) – The set on which the function needs to be evaluated. It must be a subset of the effective ground set.

Returns

The function evaluation score on the given set.

Return type

float

getEffectiveGroundSet()

Get the effective ground set of this object.

marginalGain(X, element)

Computes the marginal gain in score of this function when a single item (element) is added to a set (X).

Parameters

• X (set) – Set on which the marginal gain of adding an element has to be calculated. It must be a subset of the effective ground set.

• element (int) – Element for which the marginal gain is to be calculated. It must be from the effective ground set.

Returns

Marginal gain of adding element to X.

Return type

float

marginalGainWithMemoization(X, element)

Efficiently find the marginal gain in score when a single item (element) is added to a set (X) assuming that memoized statistics for X are already computed.

Parameters

• X (set) – Set on which the marginal gain of adding an element has to be calculated. It must be a subset of the effective ground set and its memoized statistics should have already been computed.

• element (int) – Element for which the marginal gain is to be calculated. It must be from the effective ground set.

Returns

Marginal gain of adding element to X.

Return type

float

maximize(budget, optimizer='NaiveGreedy', stopIfZeroGain=False, stopIfNegativeGain=False, epsilon=0.1, verbose=False, show_progress=True, costs=None, costSensitiveGreedy=False)

Compute the optimal subset with maximum score for the given budget.

Parameters

• budget (int) – Desired size of the optimal set.

• optimizer (string) – The optimizer that should be used to compute the optimal set. Can be ‘NaiveGreedy’, ‘StochasticGreedy’, LazyGreedy’ and ‘LazierThanLazyGreedy’.

• stopIfZeroGain (bool) – Set to True if maximization should terminate as soon as gain of adding any other item becomes zero. When True, size of optimal set can thus be potentially less than the budget.

• stopIfNegativeGain (bool) – Set to True if maximization should terminate as soon as the best gain in an iteration is negative. When True, this can potentially lead to optimal set of size less than the budget.

• epsilon (float) – Used by Stochastic (Random) Greedy and Lazier Than Lazy Greedy to compute the size of the random set.

• verbose (bool) – Set to True to trace/debug the execution of the maximization algorithm.

• show_progress (bool) – Set to True to see progress a progress bar.

• costs (list, optional) – List containing cost of each element of the ground set. Cost contributes to the budget. When costSensitiveGreedy is set to True, the marginal gain is divided by the cost to identify the next best element to add in every iteration. Default is None which means all ground set elements have cost = 1. It is possible to specify costs and yet have costSensitiveGreedy set to False. This would correspond use regular marginal gains, but the budget gets filled as per the costs of selected items.

• costSensitiveGreedy (bool, optional) – When set to True, the next best candidate in every iteration is decided based on their marginal gain divided by cost. When True, it is mandatory to provide costs. Defaults to False.

Returns

The optimal set of size budget.

Return type

set

setMemoization(X)

Compute and store the memoized statistics for subset X.

Parameters

X (set) – The set for which memoized statistics need to be computed and set, overwriting any existing memoized statistics.

updateMemoization(X, element)

Update the memoized statistics of a set X due to adding an element to it. Assumes that memoized statistics are already computed for X. Note that the element is not added to the set and only the memoized statistics are updated. The actual insertion of element to X is the responsibility of the caller.

Parameters

• X (set) – Set whose memoized statistics must already be computed and to which the element needs to be added for the sake of updating the memoized statistics.

• element (int) – Element that is being added to X leading to update of memoized statistics. It must be from the effective ground set.