ISSN 1671-3710
CN 11-4766/R

Humans represent visuo-spatial probability distribution as k-means clusters

Sun Jingwei; Li Jian; Zhang Hang

1. School of Psychological and Cognitive Sciences, Peking University, 52 Haidian Road, Haidian District, Beijing, China, 100082
PKU-IDG/McGovern Institute for Brain Research, Peking University, 52 Haidian Road, Haidian District, Beijing, China, 100082
Peking-Tsinghua Center for Life Science, Peking University, 5 Yiheyuan Road, Haidian District, Beijing, China, 100871
• Online:2016-12-31 Published:2016-12-31

Abstract:

PURPOSE: Many behavioral and neuroimaging studies have shown that human decisions are sensitive to the statistical moments (mean, variance, etc.) of reward distributions. However, little is known about how reward distributions—or, probability distributions in general—are represented in the human brain. When the possible values of a probability distribution is numerous (infinite for a continuous distribution), it would be unrealistic or at least cognitively costly to maintain the probability for each possible value. Here we explored potential heuristic representations of probability distributions and tested them on human subjects. In particular, we tested a recently developed hypothesis that human representations of probability distributions are mixtures of a small number of non-overlapping basis distributions.
METHODS: In two experiments, we constructed a variety of multimodal distributions of spatial positions. On each trial, 70 vertical lines—the horizontal coordinates of which were samples independently drawn from the distributions—were briefly presented, one at a time on the computer screen. Human subjects were asked to locate (on the axis where stimuli were presented) the mean and the mode of the samples. A total of 19 naive subjects participated and completed 144–162 trials each.
RESULTS: All subjects’ mean and mode responses were highly correlated with the true mean and mode of the samples. Interestingly, all subjects’ mean and mode responses had systematic deviations from the true means and modes. The deviation patterns could be well predicted by computational models that assume a division of samples into a small number of clusters following the k-means clustering algorithm. Only the centroid and the relative weight of each cluster were necessary for the further calculation of mean and mode responses.
CONCLUSIONS: Humans represent probability distribution as k-means clusters, and use the centroid and relative weight of each cluster to calculate concerned statistics of the distribution.