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p:subsmp1 [2020/04/01 05:43] – cjjp:subsmp1 [2020/04/01 07:53] (current) – [Principal component analysis] cjj
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 Random subsets of the neurons are chosen for analysis. The results are compared to original system and among different sub-sample sizes. Random subsets of the neurons are chosen for analysis. The results are compared to original system and among different sub-sample sizes.
 =====Principal component analysis===== =====Principal component analysis=====
-{{:p:subsmp1:subsamples_0425-3t1_pca.svg?380|}} +| {{  :p:subsmp1:subsamples_0425-3t1_pca.svg?380  |}} | {{  :p:subsmp1:subsamples_bialek_pca.svg?380  |}} | 
-{{:p:subsmp1:subsamples_bialek_pca.svg?380|}} +The errorbars are calculated from the standard deviation of 8 random subsets for each given size. It's seems power law scaling $\lambda_k \propto k^{-\alpha}$ with $\alpha \approx 0.5$ is more accurate for a sub-sampled system of smaller size.
-The errorbars are calculated from the standard deviation of 8 random subsets for each given size.+
 =====Thermodynamics of subsamples===== =====Thermodynamics of subsamples=====
 Boltzmann learning is performed for each random sub sample for the model parameters, $h_i$ and $J_{i,j}$. The specific heat curves of the resulted models are calculated and as shown below. Boltzmann learning is performed for each random sub sample for the model parameters, $h_i$ and $J_{i,j}$. The specific heat curves of the resulted models are calculated and as shown below.
 {{ :p:subsmp1:subsamples_0425-3t1.svg |}} {{ :p:subsmp1:subsamples_0425-3t1.svg |}}
 +The criticality condition ($T\approx 1.0$) appears pretty robust to sub sampling where only a portion of the neurons from a large network is observed.