Computational studies have reported that a combination of spike-timing dependent plasticity (STDP) and a spiking neuron model can resolve the first principal component (PC1) of principal component analysis (PCA) [W. Gerstner & W.M. Kistler, 2002]. Recently, electrophysiological studies have reported dopaminergic modulation of the window function of STDP [J.C. Zhang et al., 2009]. Dopaminergic modulation of learning has frequently been discussed in the context of reinforcement learning; however, it has hardly been considered whether dopamine modulates the PCA of neurons. Here, using theoretical analyses and computer simulations, we have investigated whether the dopamine concentration modulates the accuracy of resolving the PC1.
We used a conventional leaky integrate-and-fire (LIF) model and a simple add-STDP model [S. Song et al., 2000], and assumed that the learning efficacy of the long-term depression (LTD) part of STDP was modulated by the dopamine concentration. From our analysis, we confirmed that the instantaneous firing rates of neurons represent the dynamics of PC1 after learning, while there was some bias in the estimated angle of a rotation matrix. We then found that, in the case with 2-dimensional input, by increasing the dopamine concentration, the preferred direction of the neuron shifted to θ = π/4, which indicates that both synaptic connections of the neuron attain a similar amplitude. These results suggest that with abnormal dopamine concentrations, neurons tend to regard their input as more highly correlated than it actually is. Moreover, only the ratio of long-term potentiation (LTP) and LTD, which was modulated by dopamine, affected the final state of the estimated angle, whereas averaged learning efficacy and constant input to neurons did not contribute. We also observed the dopaminergic modulation of PCA performed using STDP and LIF using computer simulation. Therefore, the faulty state of neural networks in which the networks fail to represent the outer world correctly can provide a computational model of hallucination and delusion, which are common positive symptoms of schizophrenia, and be utilized to consider an appropriate treatment for schizophrenia.