elephant.spade module
SPADE is the combination of a mining technique and multiple statistical tests
to detect and asses the statistical significance of repeated occurrences of
spike sequences (spatio-temporal patterns, STP).
Given a list of Neo Spiketrain objects, assumed to be recorded in parallel, the
SPADE analysis can be applied as demonstrated in this short toy example of 10
artificial spike trains of exhibiting fully synchronous events of order 10.
This modules relies on the implementation of the fp-growth algorithm contained
in the file fim.so which can be found here (http://www.borgelt.net/pyfim.html)
and should be available in the spade_src folder (elephant/spade_src/).
If the fim.so module is not present in the correct location or cannot be
imported (only available for linux OS) SPADE will make use of a python
implementation of the fast fca algorithm contained in
elephant/spade_src/fast_fca.py, which is about 10 times slower.
import elephant.spade
import elephant.spike_train_generation
import quantities as pq
# Generate correlated data
sts = elephant.spike_train_generation.cpp(
rate=5*pq.Hz, A=[0]+[0.99]+[0]*9+[0.01], t_stop=10*pq.s)
# Mining patterns with SPADE using a binsize of 1 ms and a window length of 1
# bin (i.e., detecting only synchronous patterns).
patterns = spade.spade(
data=sts, binsize=1*pq.ms, winlen=1, dither=5*pq.ms,
min_spikes=10, n_surr=10, psr_param=[0,0,3],
output_format=’patterns’)[‘patterns’][0]
# Plotting
plt.figure()
for neu in patterns[‘neurons’]:
- if neu == 0:
- plt.plot(
- patterns[‘times’], [neu]*len(patterns[‘times’]), ‘ro’,
label=’pattern’)
- else:
- plt.plot(
- patterns[‘times’], [neu] * len(patterns[‘times’]), ‘ro’)
# Raster plot of the data
for st_idx, st in enumerate(sts):
- if st_idx == 0:
- plt.plot(st.rescale(pq.ms), [st_idx] * len(st), ‘k.’, label=’spikes’)
- else:
- plt.plot(st.rescale(pq.ms), [st_idx] * len(st), ‘k.’)
plt.ylim([-1, len(sts)])
plt.xlabel(‘time (ms)’)
plt.ylabel(‘neurons ids’)
plt.legend()
plt.show()
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elephant.spade.
approximate_stability
(concepts, rel_matrix, n_subsets, delta=0, epsilon=0)[source]
Approximate the stability of concepts. Uses the algorithm described
in Babin, Kuznetsov (2012): Approximating Concept Stability
Parameters: | concepts: list
All the pattern candidates (concepts) found in the data. 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(data)] and
bin_id in [0, winlen].
rel_matrix: numpy.array
A binary matrix with shape (number of windows, winlen*len(data)). Each
row corresponds to a window (order according to their position in
time). Each column correspond 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_subsets: int
Number of subsets of a concept used to approximate its stability. If
n_subset is set to 0 the stability is not computed. If, however,
for parameters delta and epsilon (see below) delta + epsilon == 0,
then an optimal n_subsets is calculated according to the formula given
in Babin, Kuznetsov (2012), proposition 6:
- ..math::
n_subset = frac{1}{2eps^2} ln(frac{2}{delta}) +1
Default:0
delta: float
delta: probability with at least ..math:$1-delta$
Default: 0
epsilon: float
epsilon: absolute error
Default: 0
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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
-
elephant.spade.
concept_output_to_patterns
(concepts, winlen, binsize, pvalue_spectrum=None, t_start=array(0.) * ms)[source]
Construction of dictionaries containing all the information about a pattern
starting from a list of concepts and its associated pvalue_spectrum.
Parameters: | concepts: tuple
Each element of the tuple correspond to a pattern and it is itself a
tuple consisting of:
((spikes in the pattern), (occurrences of the patterns))
winlen: int
Length (in bins) of the sliding window used for the analysis
pvalue_spectrum: None or tuple
Contains a tuple of signatures and the corresponding p-value. If equal
to None all the pvalues are set to -1
t_start: Quantity
t_start of the analyzed spike trains
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Returns: | output: list
List of dictionaries. Each dictionary correspond to a patterns and
has the following entries:
[‘neurons’] array containing the idx of the neurons of the pattern
[‘lags’] array containing the lags (integers corresponding to the
number of bins) between the spikes of the patterns. The first
lag is always assumed to be 0 and correspond to the first
spike.
- [‘times’] array contianing the times (integers corresponding to the
bin idx) of the occurrences of the patterns.
- [‘signature’] tuple containing two integers
(number of spikes of the patterns,
number of occurrences of the pattern)
- [‘pvalue’] the pvalue corresponding to the pattern. If n_surr==0
the pvalues are set to -1.
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-
elephant.spade.
concepts_mining
(data, binsize, winlen, min_spikes=2, min_occ=2, max_spikes=None, max_occ=None, min_neu=1, report='a')[source]
Find pattern candidates extracting all the concepts of the context formed
by the objects defined as all windows of length winlen*binsize slided
along the data and the attributes as the spikes occurring in each of the
window discretized at a time resolution equal to binsize. Hence, the output
are all the repeated sequences of spikes with maximal length winlen, which
are not trivially explained by the same number of occurrences of a superset
of spikes.
Parameters: | data: list of neo.SpikeTrains
List containing the parallel spike trains to analyze
binsize: Quantity
The time precision used to discretize the data (binning).
winlen: int (positive)
The size (number of bins) of the sliding window used for the analysis.
The maximal length of a pattern (delay between first and last spike) is
then given by winlen*binsize
min_spikes: int (positive)
Minimum number of spikes of a sequence to be considered a pattern.
Default: 2
min_occ: int (positive)
Minimum number of occurrences of a sequence to be considered as a
pattern.
Default: 2
max_spikes: int (positive)
Maximum number of spikes of a sequence to be considered a pattern. If
None no maximal number of spikes is considered.
Default: None
max_occ: int (positive)
Maximum number of occurrences of a sequence to be considered as a
pattern. If None, no maximal number of occurrences is considered.
Default: None
min_neu: int (positive)
Minimum number of neurons in a sequence to considered a pattern.
Default: 1
report: str
Indicates the output of the function.
‘a’: all the mined patterns
‘#’: pattern spectrum
Default: ‘a’
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Returns: | mining_results: list
- If report == ‘a’:
All the pattern candidates (concepts) found in the data. 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(data)] and
bin_id in [0, winlen].
- If report == ‘#’:
The pattern spectrum is represented as a list of triplets each
formed by:
(pattern size, number of occurrences, number of patterns)
rel_matrix : numpy.array
A binary matrix with shape (number of windows, winlen*len(data)). Each
row corresponds to a window (order according to their position in
time). Each column correspond 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.
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-
elephant.spade.
pattern_set_reduction
(concepts, excluded, winlen, h=0, k=0, l=0, min_spikes=2, min_occ=2)[source]
Takes a list concepts and performs pattern set reduction (PSR).
Same as psr(), but compares each concept A in concepts_psf to each other
one which overlaps with A.
PSR determines which patterns in concepts_psf are statistically significant
given any other pattern, on the basis of the pattern size and
occurrence count (“support”). Only significant patterns are retained.
The significance of a pattern A is evaluated through its signature
(|A|,c_A), where |A| is the size and c_A the support of A, by either of:
* subset filtering: any pattern B is discarded if cfis contains a
superset A of B such that (z_B, c_B-c_A+*h*) in excluded
- superset filtering: any pattern A is discarded if cfis contains a
subset B of A such that (z_A-z_B+*k*, c_A) in excluded
- covered-spikes criterion: for any two patterns A, B with A subset B, B
is discarded if (z_B-l)*c_B <= c_A*(z_A-l), A is discarded otherwise.
- combined filtering: combines the three procedures above
takes a list concepts (see output psf function) and performs
combined filtering based on the signature (z, c) of each pattern, where
z is the pattern size and c the pattern support.
For any two patterns A and B in concepts_psf such that B subset A, check:
1) (z_B, c_B-c_A+*h*) in excluded, and
2) (z_A-z_B+*k*, c_A) in excluded.
Then:
* if 1) and not 2): discard B
* if 2) and not 1): discard A
* if 1) and 2): discard B if c_B*(z_B-l) <= c_A*(z_A-l), A otherwise;
* if neither 1) nor 2): keep both patterns.
-
elephant.spade.
pvalue_spectrum
(data, binsize, winlen, dither, n_surr, min_spikes=2, min_occ=2, min_neu=1)[source]
Compute the p-value spectrum of pattern signatures extracted from
surrogates of parallel spike trains, under the null hypothesis of
independent spiking.
- n_surr surrogates are obtained from each spike train by spike dithering
- pattern candidates (concepts) are collected from each surrogate data
- the signatures (number of spikes, number of occurrences) of all patterns
are computed, and their occurrence probability estimated by their
occurrence frequency (p-value spectrum)
Parameters: | data: list of neo.SpikeTrains
List containing the parallel spike trains to analyze
binsize: Quantity
The time precision used to discretize the data (binning).
winlen: int (positive)
The size (number of bins) of the sliding window used for the analysis.
The maximal length of a pattern (delay between first and last spike) is
then given by winlen*binsize
dither: Quantity
Amount of spike time dithering for creating the surrogates for
filtering the pattern spectrum. A spike at time t is placed randomly
within ]t-dither, t+dither[ (see also
elephant.spike_train_surrogates.dither_spikes).
Default: 15*pq.s
n_surr: int
Number of surrogates to generate to compute the p-value spectrum.
This number should be large (n_surr>=1000 is recommended for 100
spike trains in sts). If n_surr is 0, then the p-value spectrum is
not computed.
Default: 0
min_spikes: int (positive)
Minimum number of spikes of a sequence to be considered a pattern.
Default: 2
min_occ: int (positive)
Minimum number of occurrences of a sequence to be considered as a
pattern.
Default: 2
min_neu: int (positive)
Minimum number of neurons in a sequence to considered a pattern.
Default: 1
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elephant.spade.
spade
(data, binsize, winlen, min_spikes=2, min_occ=2, min_neu=1, n_subsets=0, delta=0, epsilon=0, stability_thresh=None, n_surr=0, dither=array(15.) * ms, alpha=1, stat_corr='fdr', psr_param=None, output_format='concepts')[source]
Perform the SPADE [1,2] analysis for the parallel spike trains given in the
input. The data are discretized with a temporal resolution equal binsize
in a sliding window of winlen*binsize milliseconds.
First, spike patterns are mined from the data using a technique termed
frequent itemset mining (FIM) or formal concept analysis (FCA). In this
framework, a particular spatio-temporal spike pattern is termed a
“concept”. It is then possible to compute the stability and the signature
significance of all pattern candidates. In a final step, it is possible to
select a stability threshold and the significance level to select only
stable/significant concepts.
Parameters: | data: list of neo.SpikeTrains
List containing the parallel spike trains to analyze
binsize: Quantity
The time precision used to discretize the data (binning).
winlen: int (positive)
The size (number of bins) of the sliding window used for the analysis.
The maximal length of a pattern (delay between first and last spike) is
then given by winlen*binsize
min_spikes: int (positive)
Minimum number of spikes of a sequence to be considered a pattern.
Default: 2
min_occ: int (positive)
Minimum number of occurrences of a sequence to be considered as a
pattern.
Default: 2
min_neu: int (positive)
Minimum number of neurons in a sequence to considered a pattern.
Default: 1
n_subsets: int
Number of subsets of a concept used to approximate its stability. If
n_subset is set to 0 the stability is not computed. If, however,
for parameters delta and epsilon (see below) delta + epsilon == 0,
then an optimal n_subsets is calculated according to the formula given
in Babin, Kuznetsov (2012), proposition 6:
- ..math::
n_subset = frac{1}{2eps^2} ln(frac{2}{delta}) +1
Default:0
delta: float
delta: probability with at least ..math:$1-delta$
Default: 0
epsilon: float
epsilon: absolute error
Default: 0
stability_thresh: None or list of float
List containing the stability thresholds used to filter the concepts.
If stab_thr is None, then the concepts are not filtered. Otherwise,
only concepts with intensional stability > stab_thr[0] or extensional
stability > stab_thr[1] are returned and used for further analysis
within SPADE.
Default: None
n_surr: int
Number of surrogates to generate to compute the p-value spectrum.
This number should be large (n_surr>=1000 is recommended for 100
spike trains in sts). If n_surr is 0, then the p-value spectrum is
not computed.
Default: 0
dither: Quantity
Amount of spike time dithering for creating the surrogates for
filtering the pattern spectrum. A spike at time t is placed randomly
within ]t-dither, t+dither[ (see also
elephant.spike_train_surrogates.dither_spikes).
Default: 15*pq.s
alpha: float
The significance level of the hypothesis tests performed. If alpha=1
all the concepts are returned. If 0<alpha<1 the concepts
are filtered according to their signature in the p-value spectrum.
Default: 1
stat_corr: str
- Statistical correction to be applied:
‘’ : no statistical correction
‘f’, ‘fdr’ : false discovery rate
‘b’, ‘bonf’: Bonferroni correction
Default: ‘fdr’
psr_param: None or list of int
- This list contains parameters used in the pattern spectrum filtering:
- psr_param[0]: correction parameter for subset filtering
(see parameter h of psr()).
- psr_param[1]: correction parameter for superset filtering
(see parameter k of psr()).
- psr_param[2]: correction parameter for covered-spikes criterion
(see parameter l for psr()).
output_format: str
distinguish the format of the output (see Returns). Can assume values
‘concepts’ and ‘patterns’.
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Returns: | The output depends on the value of the parameter output_format.
If output_format is ‘concepts’:
- output: dict
Dictionary containing the following keys:
patterns: tuple
Each element of the tuple corresponds to a pattern and is
itself a tuple consisting of:
(spikes in the pattern, occurrences of the patterns)
For details see function concepts_mining().
- If n_subsets>0:
(spikes in the pattern, occurrences of the patterns,
(intensional stability, extensional stability))
corresponding pvalue
The patterns are filtered depending on the parameters in input:
If stability_thresh==None and alpha==None:
output[‘patterns’] contains all the candidates patterns
(all concepts mined with the fca algorithm)
- If stability_thresh!=None and alpha==None:
- output contains only patterns candidates with:
intensional stability>stability_thresh[0] or
extensional stability>stability_thresh[1]
- If stability_thresh==None and alpha!=1:
output contains only pattern candidates with a signature
significant in respect the significance level alpha corrected
- If stability_thresh!=None and alpha!=1:
output[‘patterns’] contains only pattern candidates with a
signature significant in respect the significance level alpha
corrected and such that:
intensional stability>stability_thresh[0] or
extensional stability>stability_thresh[1]
In addition, output[‘non_sgnf_sgnt’] contains the list of
non-significant signature for the significance level alpha.
- If n_surr>0:
output[‘pvalue_spectrum’] contains a tuple of signatures and
the corresponding p-value.
If output_format is ‘patterns’:
- output: list
List of dictionaries. Each dictionary corresponds to a patterns and
has the following keys:
- neurons: array containing the indices of the neurons of the
pattern.
- lags: array containing the lags (integers corresponding to the
number of bins) between the spikes of the patterns. The
first lag is always assumed to be 0 and correspond to the
first spike [‘times’] array containing the times.
(integers corresponding to the bin idx) of the occurrences of the
patterns
- signature: tuple containing two integers:
(number of spikes of the patterns,
number of occurrences of the pattern)
- pvalue: the p-value corresponding to the pattern. If n_surr==0 the
p-values are set to 0.0.
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Notes
If detected, this function will utilize MPI to parallelize the analysis.
References
- [1] Torre, E., Picado-Muino, D., Denker, M., Borgelt, C., & Gruen, S.(2013)
- Statistical evaluation of synchronous spike patterns extracted by
frequent item set mining. Frontiers in Computational Neuroscience, 7.
- [2] Quaglio, P., Yegenoglu, A., Torre, E., Endres, D. M., & Gruen, S.(2017)
- Detection and Evaluation of Spatio-Temporal Spike Patterns in Massively
Parallel Spike Train Data with SPADE.
Frontiers in Computational Neuroscience, 11.
‘’‘
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elephant.spade.
test_signature_significance
(pvalue_spectrum, alpha, corr='', report='#')[source]
Compute the significance spectrum of a pattern spectrum.
Given pvalue_spectrum as a list of triplets (z,c,p), where z is pattern
size, c is pattern support and p is the p-value of the signature (z,c),
this routine assesses the significance of (z,c) using the confidence level
alpha.
Bonferroni or FDR statistical corrections can be applied.
Parameters: | pvalue_spectrum: list
A list of triplets (z,c,p), where z is pattern size, c is pattern
support and p is the p-value of signature (z,c)
alpha: float
Significance level of the statistical test
corr: str
Statistical correction to be applied:
‘’ : no statistical correction
‘f’|’fdr’ : false discovery rate
‘b’|’bonf’: Bonferroni correction
report: str
Format to be returned for the significance spectrum:
‘#’: list of triplets (z,c,b), where b is a boolean specifying
whether signature (z,c) is significant (True) or not (False)
- ‘s’: list containing only the significant signatures (z,c) of
pvalue_spectrum
‘e’: list containing only the non-significant signatures
Defualt: ‘#’
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