  Wisdom of the crowd, the collective intelligence derived from responses of
multiple human or machine individuals to the same questions, can be more
accurate than each individual, and improve social decision-making and
prediction accuracy. This can also integrate multiple programs or datasets,
each as an individual, for the same predictive questions. Crowd wisdom
estimates each individual's independent error level arising from their limited
knowledge, and finds the crowd consensus that minimizes the overall error.
However, previous studies have merely built isolated, problem-specific models
with limited generalizability, and mainly for binary (yes/no) responses. Here
we show with simulation and real-world data that the crowd wisdom problem is
analogous to one-dimensional unsupervised dimension reduction in machine
learning. This provides a natural class of crowd wisdom solutions, such as
principal component analysis and Isomap, which can handle binary and also
continuous responses, like confidence levels, and consequently can be more
accurate than existing solutions. They can even outperform
supervised-learning-based collective intelligence that is calibrated on
historical performance of individuals, e.g. penalized linear regression and
random forest. This study unifies crowd wisdom and unsupervised dimension
reduction, and thereupon introduces a broad range of highly-performing and
widely-applicable crowd wisdom methods. As the costs for data acquisition and
processing rapidly decrease, this study will promote and guide crowd wisdom
applications in the social and natural sciences, including data fusion,
meta-analysis, crowd-sourcing, and committee decision making.
