Multi-level adaptive neuro-fuzzy inference system-based reconstruction of 1D ISOMAP representations

This paper addresses the inverse problem of isometric feature mapping (ISOMAP) via multi-level adaptive neuro-fuzzy inference system (ML-ANFIS). ISOMAP is a conventional nonlinear dimensionality reduction (NLDR) method, which prospects for low dimensional interior structure embedded in high dimensional data space. The inverse problem of ISOMAP reconstructs the original high dimensional data from the related low dimensional ISOMAP representations and holds promising applications in data representations, generation, compression and visualization. Because the reconstruction of 1D ISOMAP representations is ill-posed and undetermined, ML-ANFIS is wielded to augment the recovery quality of general ISOMAP reconstruction algorithm. By linearly combing inputs with nonlinear weights as output, ML-ANFIS can efficiently achieve the latent nonlinear relationship between the low-performance result of general ISOMAP reconstruction algorithm and its original data. The membership functions and fuzzy rules of ML-ANFIS can be automatically learned by gradient descent method as deep learning. It is demonstrated by the experimental results that, in the situation of 1D representations, the proposed method is superior to the state-of-the-art methods, such as nearest neighbor (NN), discrete cosine transformation (DCT), sparse representations (SR) and classical ANFIS algorithms, in the reconstruction performance of video data.