Image representation using Laplacian regularized nonnegative tensor factorization

Tensor provides a better representation for image space by avoiding information loss in vectorization. Nonnegative tensor factorization (NTF), whose objective is to express an n-way tensor as a sum of k rank-1 tensors under nonnegative constraints, has recently attracted a lot of attentions for its efficient and meaningful representation. However, NTF only sees Euclidean structures in data space and is not optimized for image representation as image space is believed to be a sub-manifold embedded in high-dimensional ambient space. To avoid the limitation of NTF, we propose a novel Laplacian regularized nonnegative tensor factorization (LRNTF) method for image representation and clustering in this paper. In LRNTF, the image space is represented as a 3-way tensor and we explicitly consider the manifold structure of the image space in factorization. That is, two data points that are close to each other in the intrinsic geometry of image space shall also be close to each other under the factorized basis. To evaluate the performance of LRNTF in image representation and clustering, we compare our algorithm with NMF, NTF, NCut and GNMF methods on three standard image databases. Experimental results demonstrate that LRNTF achieves better image clustering performance, while being more insensitive to noise.