elephant.spade.approximate_stability

elephant.spade.approximate_stability(concepts, rel_matrix, n_subsets=0, delta=0.0, epsilon=0.0)

Approximate the stability of concepts. Uses the algorithm described in Babin, Kuznetsov (2012): Approximating Concept Stability

Parameters:

conceptslist

All the pattern candidates (concepts) found in the spiketrains. Each pattern is represented as a tuple containing (spike IDs, discrete times (window position) of the occurrences of the pattern). The spike IDs are defined as: spike_id=neuron_id*bin_id with neuron_id in [0, len(spiketrains)] and bin_id in [0, winlen].

rel_matrixscipy.sparse.coo_matrix

A binary matrix with shape (number of windows, winlen*len(spiketrains)). Each row corresponds to a window (order according to their position in time). Each column corresponds to one bin and one neuron, and it is 0 if no spikes or 1 if one or more spikes occurred in that bin for that particular neuron. For example, the entry [0,0] of this matrix corresponds to the first bin of the first window position for the first neuron, the entry [0, winlen] to the first bin of the first window position for the second neuron.

n_subsetsint

Number of subsets of a concept used to approximate its stability. If n_subsets is 0, it is calculated according to to the formula given in Babin, Kuznetsov (2012), proposition 6:

\[n_{\text{subset}} = \frac{1}{2 \cdot \epsilon^2} \ln{\left( \frac{2}{\delta} \right)} +1\]

Default: 0

deltafloat, optional

delta: probability with at least \(1-\delta\) Default: 0.0

epsilonfloat, optional

epsilon: absolute error Default: 0.0

Returns:

outputlist

List of all the pattern candidates (concepts) given in input, each with the correspondent intensional and extensional stability. Each pattern is represented as a tuple (spike IDs, discrete times of the occurrences of the pattern, intensional stability of the pattern, extensional stability of the pattern). The spike IDs are defined as: spike_id=neuron_id*bin_id with neuron_id in [0, len(spiketrains)] and bin_id in [0, winlen].

Notes

If n_subset is larger than the extent all subsets are directly calculated, otherwise for small extent size an infinite loop can be created while doing the recursion, since the random generation will always contain the same numbers and the algorithm will be stuck searching for other (random) numbers.