Adaptive Heterogeneous Support Tensor Machine: An Extended STM for Object Recognition Using an Arbitrary Combination of Multisource Heterogeneous Remote Sensing Data

Multiple observation data from multisensor satellites lead to data with complex heterogeneous tensor structures, and the available object data are observed by the arbitrary combination of multisource satellites, which brings significant challenges to object recognition using typical deep learning methods, classical support vector machines (SVMs), and support tensor machines (STMs). To process multisource data represented as heterogeneous tensors effectively, the heterogeneous STM (HSTM) is proposed by integrating rank-
$R$
decomposition of multitensors with nu-STM to directly separate samples in heterogeneous tensor space. Furthermore, combining the shared projecting tensors used to mine related information for intercombinations and the auxiliary projecting tensors exploited to capture the individual information for intracombination, the HSTM is extended to Adaptive HSTM (AHSTM) to address the arbitrary combination of multisource data by only training once. To accelerate the training of AHSTM, the AHSTM-oriented decomposition method is proposed to use small sequential analytic optimizations instead of the original large numerical optimization. Using multiangle optical and synthetic aperture radar (SAR) satellite images, experimental results demonstrate that the proposed AHSTM obtains higher accuracy than typical SVM and STM methods for each combination of multisource data and reduces the time consumption by over 75% for the training set with different sizes compared with the typical interior-point method and the active-set method.