  Homotopy model is an excellent tool exploited by diverse research works in
the field of machine learning. However, its flexibility is limited due to lack
of adaptiveness, i.e., manual fixing or tuning the appropriate homotopy
coefficients. To address the problem above, we propose a novel adaptive
homotopy framework (AH) in which the Maclaurin duality is employed, such that
the homotopy parameters can be adaptively obtained. Accordingly, the proposed
AH can be widely utilized to enhance the homotopy-based algorithm. In
particular, in this paper, we apply AH to contrastive learning (AHCL) such that
it can be effectively transferred from weak-supervised learning (given label
priori) to unsupervised learning, where soft labels of contrastive learning are
directly and adaptively learned. Accordingly, AHCL has the adaptive ability to
extract deep features without any sort of prior information. Consequently, the
affinity matrix formulated by the related adaptive labels can be constructed as
the deep Laplacian graph that incorporates the topology of deep representations
for the inputs. Eventually, extensive experiments on benchmark datasets
validate the superiority of our method.
