Select Git revision
elephant.tex.backup
elephant.tex.backup 14.80 KiB
\chapter{Elephant functions}
\label{cha:ele}
List of Elephant functions.
\begin{itemize}
\item Statistics:
\begin{itemize}
\item ISI - Inter Spike Intervals
\item Mean Firing Rate
\item CV - Coefficient of Variation (also: LV,CV2)
\item Instantaneous Firing Rate
\item Time Histogram
\item Complexity PDF
\end{itemize}
\item ASSET - Analysis of Sequence of Synchronous Events in massively parallel spikeTrains
\item SPADE - spatio-temporal Spike PAttern Detection and Evaluation
\item (\textit{UE - Unitary Events})
\end{itemize}
\begin{itshape}
NOTE:
\begin{itemize}
\item ASSET:\\
line 376/377: signal.view(pq.Quantities)[elements\_to\_keep] \\
line 631: mask[\textasciitilde(mask >= -np.inf)] = False
\item Statistics, IFR:\\
line 754: sskernel['optw] with 'bootstrap = TRUE'...not needed?
\item SPADE: FIM instead of fast_fca:\\
line 558ff, fpgrowth with FIM: keyword argument min/max (now) zmin/zmax
\end{itemize}
\end{itshape}
\section{Required modules and imports}
\label{sec:mod}
\begin{itemize}
\item Neo Framework\\
imported within elephant
\item Numpy\\
imported within elephant
\item Quantities\\
\textit{ >> import quantities as pq}
\item Elephant\\
\begin{itshape}
>> import elephant.spike\_train\_generation as stg\\
>> import elephant.asset as asset\\
>> import elephant.statistics as stat\\
>> import elephant.spade as spade
\end{itshape}
\end{itemize}
\section{Required input parameters}
\label{sec:inp}
\begin{itemize}
%%% GLOBAL
\item Global parameters
\begin{itemize}
\item List of <neo.SpikeTrain> objects\\
-> list of neurons
\item Firing rate\\ -> Quantities datatype\\
\textit{>> rate = 15 * pq.Hz}
\item Length of the Signal/SpikeTrain\\
-> Quantities datatype\\
\textit{>> T = 1 * pq.s}
\item Binsize or sampling period\\
-> Quantities datatype\\
\textit{binsize = 5 * pq.ms}
\end{itemize}
%%% Modules
\item Additional parameters per module:
\begin{itemize}
% Statistics
\item Statistics:
\begin{itemize}
\item Kernel for Instantaneous Firing Rate
\end{itemize}
% ASSET
\item ASSET:
\begin{itemize}
\item neo.SpikeTrain objects need additional t\_stop attribute if signal length > 1s (standard is 1s).
\item Build the intersection matrix \textit{'imat'} and probability matrix \textit{'pmat'}:\\
- Number of surrogates for the bootstrapping method\\
- Window size for spike train dithering
\item Joint probability matrix \textit{'jmat'}, using a suitable filter:\\
- Filter shape (length, width)\\
- Number of largest neighbors
\item Create from \textit{'pmat'} and \textit{'jmat'} a masked version of \textit{'imat'}:\\
- alpha1\\
- alpha2
\item Cluster significant elements of \textit{'imat'} into diagonal structures:\\
- epsilon\\
- minimum size\\
- stretch
\end{itemize}
% SPADE
\item SPADE:
\begin{itemize}
\item Window length
\item Some optional parameters
\end{itemize}
\end{itemize}
\end{itemize}
\begin{itshape}
NOTE: convert input (numpy array) from simulation to Neo.SpikeTrain and get the needed global parameters
\end{itshape}
\section{Profiling}
\label{sec:prof}
% \textit{TODO: \\
% - list of test results (runtime)\\
% - rough complexity estimation (Landau Notation?) }
\subsection{Statistics}
\label{subsec:stat}
\begin{figure}[tbhp]
\centering
\includegraphics[width=\linewidth]{graphics/runtime_stat_nn.png}
\caption[]{Statistics runtime with Signal length of 1 second, rate of 20 Hz and binsize of 5 ms.
\textbf{Runtime $<$ Signal length, except for IFR}.}
\label{fig:stat_nn}\end{figure}
\begin{figure}[tbhp]
\centering
\includegraphics[width=\linewidth]{graphics/runtime_stat_slen.png}
\caption[]{Statistics runtime with 10 neurons, rate of 20 Hz and binsize of 5 ms.}
\label{fig:stat_slen}
\end{figure}
Number of Neurons: 1000\\
Length of Signal: 1000ms
\begin{verbatim}
% : name : (count) : total time spend
==================================================
0 : start : 1 : 0.0
4 : DATA : 1000 : 0.877937078476
0 : ISIs : 1000 : 0.0740790367126
2 : MFR : 1000 : 0.33157491684
0 : IFR_start : 1000 : 0.00199174880981
3 : IFR_sskernel_density : 1000 : 0.682367086411
25 : IFR_sskernel_optw : 1000 : 5.00267696381
14 : IFR_rescale : 1000 : 2.86129784584
11 : IFR_slice : 1000 : 2.28599452972
14 : IFR_fft : 1000 : 2.75114107132
17 : IFR_rest : 1000 : 3.52695941925
0 : IFR_end : 1000 : 0.00867342948914
0 : CV : 1000 : 0.06112408638
4 : HIST : 1 : 0.858650922775
0 : FANO : 1 : 0.000443935394287
4 : cPDF : 1 : 0.858818054199
0 : end : 1 : 0.00200796127319
Total time : 20.1857380867
\end{verbatim}
% Number of Neurons: 1000\\
% Length of Signal: 2000ms
% \begin{verbatim}
%
% % : name : (count) : total time spend
% ==================================================
% 0 : start : 1 : 0.0
% 4 : DATA : 1000 : 0.883128166199
% 0 : ISIs : 1000 : 0.0742020606995
% 1 : MFR : 1000 : 0.335043907166
% 0 : IFR_start : 1000 : 0.0019428730011
% 3 : IFR_sskernel_density : 1000 : 0.691978693008
% 26 : IFR_sskernel_optw : 1000 : 5.90263366699
% 12 : IFR_rescale : 1000 : 2.87390136719
% 18 : IFR_slice : 1000 : 4.24568390846
% 12 : IFR_fft : 1000 : 2.77198982239
% 15 : IFR_rest : 1000 : 3.54691672325
% 0 : IFR_end : 1000 : 0.00878882408142
% 0 : CV : 1000 : 0.0607461929321
% 4 : HIST : 1 : 0.868949890137
% 0 : FANO : 1 : 0.000442028045654
% 4 : cPDF : 1 : 0.868922948837
% 0 : end : 1 : 0.00205397605896
% Total time : 23.1373250484
%
% \end{verbatim}
%
% Number of Neurons: 1000\\
% Length of Signal: 3000ms
% \begin{verbatim}
%
% % : name : (count) : total time spend% ==================================================
% 0 : start : 1 : 0.0
% 4 : DATA : 1000 : 0.896424055099
% 0 : ISIs : 1000 : 0.0755770206451
% 1 : MFR : 1000 : 0.334756851196
% 0 : IFR_start : 1000 : 0.00195527076721
% 3 : IFR_sskernel_density : 1000 : 0.689239501953
% 24 : IFR_sskernel_optw : 1000 : 6.05566334724
% 11 : IFR_rescale : 1000 : 2.85995459557
% 25 : IFR_slice : 1000 : 6.18957233429
% 11 : IFR_fft : 1000 : 2.76875591278
% 14 : IFR_rest : 1000 : 3.52816939354
% 0 : IFR_end : 1000 : 0.00865769386292
% 0 : CV : 1000 : 0.0605289936066
% 3 : HIST : 1 : 0.877053022385
% 0 : FANO : 1 : 0.000458002090454
% 3 : cPDF : 1 : 0.876579046249
% 0 : end : 1 : 0.00224089622498
% Total time : 25.2255859375
%
% \end{verbatim}
\textbf{Summary:}\\
Once per neuron:
\begin{itemize}
\item DATA: Data will be taken from simulation. No runtime needed for SpikeTrain creation...
\item MFR (mean firing rate): 2\% of total Statistics runtime. \\
Neurons: O(n)\\
Signal length: O(1)
\item IFR (instantaneous firing rate): 85\% of total Statistics runtime. \\
Neurons: O(n)\\
Signal length: O(n)
\item CV,ISIs: almost no runtime. \\
Neurons: O(n)\\
Signal length: O(1)
\end{itemize}
Once for all neurons:
\begin{itemize}
\item HIST: \textasciitilde O(n)
\item FANO: almost no runtime.
\item cPDF: \textasciitilde O(n)
\end{itemize}
\subsection{ASSET}
\label{subsec:asset}
\begin{figure}[tbhp]
\centering
\includegraphics[width=\linewidth]{graphics/runtime_asset_slen.png}
\caption[]{ASSET runtime with Signal length of 1 second and binsize of 5 ms.}
\label{fig:asset_neurons}
\end{figure}
\textbf{Runtime $>>$ Signal length}\\ %, \textasciitilde $O(n)$}\\
\renewcommand{\arraystretch}{1.5}
\begin{table}[h!]
\begin{tabular}{|c|c||c|c|}
\hline
& Signal length: 1s & & Num. neurons: 10 \\
\hline
\#Neurons & Runtime [s] & Sig.len [s] & Runtime [s] \\
\hline
5 & 189 & & \\ 10 & 209 & 1 & 209 \\
100 & 244 & 2 & 719 \\
1000 & 303 & 3 & 1542 \\
\hline
\end{tabular}
\end{table}
\renewcommand{\arraystretch}{1}
Number of Neurons: 5\\
Length of Signal: 1000ms
\begin{verbatim}
% : name : (count) : total time spend
==================================================
0 : start : 1 : 0.0
0 : generate data : 1 : 0.005774974823
0 : intersec mat : 1 : 0.0325310230255
0 : prob mat mc : 1 : 0.363873958588
0 : jmat_pmat_neighb : 1 : 0.0803229808807
0 : jmat_jsf_uni_init : 1 : 0.00139403343201
16 : jmat_jsf_uni_diff : 1395360 : 30.1089406013
7 : jmat_jsf_uni_reshape : 31878 : 12.6044211388
7 : jmat_jsf_uni_sum : 31878 : 14.2393944263
56 : jmat_jsf_uni_log : 31878 : 105.956119537
8 : jmat_jsf_uni_exp : 31878 : 14.9054570198
7 : jmat_jsf_uni_step : 1395360 : 12.4127993584
0 : jmat_jsf_uni : 1 : 5.96046447754e-06
0 : jmat : 1 : 0.000458002090454
0 : mask : 1 : 0.000148057937622
0 : cmat : 1 : 0.0209028720856
0 : extract_sse : 1 : 6.31809234619e-05
0 : end : 1 : 5.79357147217e-05
Total time : 190.732665062
\end{verbatim}
\textbf{Summary:}\\
Once for all neurons:
\begin{itemize}
\item 100\% of runtime for Joint Probability Matrix (jmat)
\item Almost no runtime for:
\begin{itemize}
\item Intersection Matrix (imat)
\item Probability Matrix, MonteCarlo (pmat)
\item Mask (from pmat and jmat)
\item Cluster Matrix
\item Extraxt SSE (synchronous spike events)
\end{itemize}
\end{itemize}
\subsection{SPADE}
\label{subsec:spade}
\textbf{Few Neurons: Runtime $<$ Signal length, \textasciitilde $O(n)$}\\
\textbf{Increasing Neurons: Runtime $>$ Signal length, \textasciitilde $O(n^2)$}\\
\textbf{Increasing Firing Rate: Runtime $>$ Signal length (>90\% from fast\_fca, \textasciitilde $O(n^2)$}\\
\renewcommand{\arraystretch}{1.5}
\begin{table}[h!]
\begin{tabular}{|c|c||c|c|}
\hline
& Runtime for: 10 Neurons & & Runtime for: 10 s \\
\hline
[s] & data mining / p-value spectrum & \#N & data mining / p-value spectrum \\
\hline 1 & 0.03 / 0.4 & 10 & 0.09 / 1.1 \\
10 & 0.09 / 1.1 & 20 & 0.18 / 3.1 \\
20 & 0.17 / 2.1 & 30 & 0.3 / 12 \\
30 & 0.24 / 3.8 & 40 & 0.48 / 150 \\
\hline
\end{tabular}
\end{table}
\renewcommand{\arraystretch}{1}
\newpage
10 Neurons, 10 seconds, 10 Hz
\begin{verbatim}
% : name : (count) : total time spend
==================================================
0 : import : 1 : 0.0
0 : data-gen : 1 : 0.0178639888763
0 : data mining : 1 : 0.000244140625
2 : pvalue: surr_init : 10 : 0.110061883926
6 : pvalue: con_mining_binning : 11 : 0.257157325745
29 : pvalue: con_mining_context : 11 : 1.34415078163
0 : pvalue: con_mining_max_spike : 11 : 0.00502347946167
0 : pvalue: con_mining_max_occ : 11 : 0.00521540641785
62 : pvalue: con_mining_fast_fca : 11 : 2.81482839584
0 : pvalue: step : 10 : 0.00246357917786
0 : spade end : 1 : 0.000770807266235
Total time : 4.55782604218
\end{verbatim}
10 Neurons, 10 seconds, 20 Hz
\begin{verbatim}
% : name : (count) : total time spend
==================================================
0 : data-gen : 1 : 0.023374080658
1 : pvalue: con_mining_binning : 11 : 0.258544206619
3 : pvalue: con_mining_context : 11 : 0.566279649734
0 : pvalue: con_mining_max_spike : 11 : 0.00187826156616
0 : pvalue: con_mining_max_occ : 11 : 0.00199890136719
1 : fast_fca_lattice_init : 11 : 0.24431180954
3 : fast_fca_lattice__compUpNeigh_init : 4616 : 0.638545274734
32 : fast_fca_lattice__compUpNeigh_intent_update : 4813666 : 6.31500482559
0 : fast_fca_lattice__compUpNeigh_else1 : 850 : 0.0161757469177
0 : fast_fca_lattice__compUpNeigh_else2 : 7213 : 0.0132088661194
25 : fast_fca_lattice__compUpNeigh_if1 : 4812816 : 4.93453645706
24 : fast_fca_lattice__compUpNeigh_if2 : 4806453 : 4.67416810989
2 : fast_fca_lattice__compUpNeigh_for2 : 7213 : 0.329411268234
1 : fast_fca_lattice_compUpNeigh : 4616 : 0.167640447617
6 : fast_fca_lattice_end : 11 : 1.15846991539
0 : pvalue: con_mining_fast_fca : 11 : 0.0549900531769
0 : data mining : 1 : 0.000248908996582
1 : pvalue: surr_init : 10 : 0.112371206284
0 : pvalue: step : 10 : 0.00310611724854
0 : pvalue spectrum : 1 : 3.69548797607e-05
0 : spade end : 1 : 0.000790119171143
Total time : 19.5150949955
\end{verbatim}
\subsection{Unitary Events (UE)}
\label{subsec:ue}
Parameters:
\begin{itemize}
\item spiketrains (number of trials, number of neurons, timestamps)
\item binsize \item winsize (size of window)
\item winstep (window step)
\item pattern hash
\end{itemize}
Test for runtime: \textbf{(TODO: finfish compelxity test)}
\begin{itemize}
\item number of trials \textbf{\textasciitilde $O(?)$}
\item number of neurons \textbf{\textasciitilde $O(?)$}
\item timestamps (firing rate,signal length) \textbf{\textasciitilde $O(?)$}
\item winsize, winstep \textbf{\textasciitilde $O(?)$}
\item hash?
\end{itemize}
\textbf{Example1:}\\
number of trials = 36\\
number of neurons: 2\\
firing rate = 10 Hz, signal length = 3s\\
winsize = 100ms, winstep = 10ms
\begin{verbatim}
% : name : (count) : total time spend
==================================================
0 : start : 1 : 0.0
12 : data_init : 1 : 0.250292062759
0 : init : 1 : 0.00165700912476
9 : binnedSpikeTrain_bool : 1 : 0.182360887527
0 : init_indices : 1 : 2.09808349609e-05
79 : _for_num_trials : 10476 : 1.64006233215
0 : for_win_pos : 291 : 0.000309705734253
0 : UE_end : 1 : 6.38961791992e-05
0 : end : 1 : 0.000160217285156
Total time : 2.0749270916
\end{verbatim}
\textbf{Example2:}\\
number of trials = 36\\
number of neurons: 64\\
firing rate = 10 Hz, signal length = 3s\\
winsize = 100ms, winstep = 10ms
\begin{verbatim}
% : name : (count) : total time spend
==================================================
0 : start : 1 : 0.0
52 : data_init : 1 : 6.45083498955
0 : init : 1 : 0.00162696838379
31 : binnedSpikeTrain_bool : 1 : 3.87675404549
0 : init_indices : 1 : 2.8133392334e-05
17 : _for_num_trials : 10476 : 2.19099497795
0 : for_win_pos : 291 : 0.000298976898193
0 : UE_end : 1 : 0.000151872634888
0 : end : 1 : 0.00414204597473
Total time : 12.5248320103
\end{verbatim}