  The measure between heterogeneous data is still an open problem. Many
research works have been developed to learn a common subspace where the
similarity between different modalities can be calculated directly. However,
most of existing works focus on learning a latent subspace but the semantically
structural information is not well preserved. Thus, these approaches cannot get
desired results. In this paper, we propose a novel framework, termed
Cross-modal subspace learning via Kernel correlation maximization and
Discriminative structure-preserving (CKD), to solve this problem in two
aspects. Firstly, we construct a shared semantic graph to make each modality
data preserve the neighbor relationship semantically. Secondly, we introduce
the Hilbert-Schmidt Independence Criteria (HSIC) to ensure the consistency
between feature-similarity and semantic-similarity of samples. Our model not
only considers the inter-modality correlation by maximizing the kernel
correlation but also preserves the semantically structural information within
each modality. The extensive experiments are performed to evaluate the proposed
framework on the three public datasets. The experimental results demonstrated
that the proposed CKD is competitive compared with the classic subspace
learning methods.
