Dimensionality Reduction on Neuronal Data

Data

Currently using data from hc-13

Filtered data consists of:

• data/N1.csv : spike timings from neuron 1(ms resolution)
• data/N4.csv : spike timings from neuron 4(ms resolution)
• data/pos.csv : timestamp, xpos, ypos

The above data is filtered for [Animal Q1] [Day 14] [Epoch 6] [Tetrode 27]. Below is few information on this session:

• startTime: 7946sec; endTime: 8882sec; Total: 936 secs
• Number of spikes in N1 : 11717
• Number of spikes in N4: 26161
• There were 5 other neurons but spikes were in order of 100, so were not considered for now
• The pos.csv is plotted below, showing the path taken by animal

DiffusionMap

Distance Matrix

1s_inf

• For each neuron N_i [startTime:endTime] is divided into 1sec intervals, giving 936 points. Distance between spike trains of 1sec interval are calucated using vanRossum metric with Tau=Infinity

1s_15ms

• For each neuron N_i [startTime:endTime] is divided into 1sec intervals, giving 936 points. Distance between spike trains of 1sec interval are calucated using vanRossum metric with Tau=15ms
• Current method takes ~45mins for 936 points

Final distance matrix d for both neurons combined is arrived by:

d_ij = sqrt( d1_ij^2 + d2_ij^2 )

where d1 is distance matrix for neuron1 and d2 is for neuron2

Laplacian and Eigen values

Eigen Values

#top 5 eigenValues for 1s_inf
1.480848230250900954e+00
1.453581974646489083e+00
1.414983182478089407e+00
1.379302645289375073e+00
1.366143674708713451e+00

#top 5 eigenValues for 1s_15s: neuron1
1.621338730825693908e+00
1.372961018632574248e+00
1.369770579632879404e+00
1.367424801952719982e+00
1.365294349138670649e+00

#top 5 eigenValues for 1s_15s: neuron1 & neuron4
1.379449029829036943e+00
1.372827343884797768e+00
1.370727056567152768e+00
1.369143754727786044e+00
1.366893634827345050e+00

Leading EigenVector

1s_inf

1s_15ms neuron1

1s_15ms both neurons

Distance Distributions

1s_15ms n1

1s_15ms n2

1s_15ms n1n2

1s_15ms pos

Results