  In recent years, machine learning has been adopted to complex networks, but
most existing works concern about the structural properties. To use machine
learning to detect phase transitions and accurately identify the critical
transition point associated with dynamical processes on complex networks thus
stands out as an open and significant problem. Here we develop a framework
combining supervised and unsupervised learning, incorporating proper sampling
of training data set. In particular, using epidemic spreading dynamics on
complex networks as a paradigmatic setting, we start from supervised learning
alone and identify situations that degrade the performance. To overcome the
difficulties leads to the idea of exploiting confusion scheme, effectively a
combination of supervised and unsupervised learning. We demonstrate that the
scheme performs well for identifying phase transitions associated with
spreading dynamics on homogeneous networks, but the performance deteriorates
for heterogeneous networks. To strive to meet this challenge leads to the
realization that sampling the training data set is necessary for heterogeneous
networks, and we test two sampling methods: one based on the hub nodes together
with their neighbors and another based on k-core of the network. The end result
is a general machine learning framework for detecting phase transition and
accurately identifying the critical transition point, which is robust,
computationally efficient, and universally applicable to complex networks of
arbitrary size and topology. Extensive tests using synthetic and empirical
networks verify the virtues of the articulated framework, opening the door to
exploiting machine learning for understanding, detection, prediction, and
control of complex dynamical systems in general.
