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p:subsmp1 [2020/04/01 07:49] – [Thermodynamics of subsamples] cjj | p:subsmp1 [2020/04/01 07:53] (current) – [Principal component analysis] cjj | ||
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=====Principal component analysis===== | =====Principal component analysis===== | ||
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- | The errorbars are calculated from the standard deviation of 8 random subsets for each given size. | + | 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 |
=====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. | ||
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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. | 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. |