Graphs provide a powerful means for representing complex interactions between entities. Recently, deep learning approaches are emerging for representing and modeling graph-structured data, although the conventional deep learning methods (such as convolutional neural networks and recurrent neural networks) have mainly focused on grid-structured inputs (image and audio). Leveraged by the capability of representation learning, deep learning based techniques are reporting promising results for graph applications by detecting structural characteristics of graphs in an automated fashion. In this paper, we attempt to advance deep learning for graph-structured data by incorporating another component, transfer learning. By transferring the intrinsic geometric information learned in the source domain, our approach can help us to construct a model for a new but related task in the target domain without collecting new data and without training a new model from scratch. We thoroughly test our approach with large-scale real corpora and confirm the effectiveness of the proposed transfer learning framework for deep learning on graphs. According to our experiments, transfer learning is most effective when the source and target domains bear a high level of structural similarity in their graph representations.
Particularly relevant to our approach is the localized SCNN model @cite_3 , which is a deep learning approach that can extract the properties of deformable shapes. The generalized SCNN model @cite_23 @cite_10 , a key component of our framework, borrowed the Fourier transform concept from the signal processing field in order to apply CNNs in a grid domain to a graph-structured domain. In this model, the convolutional operation was re-defined for graphs.
@cite_10 @cite_23 @cite_3
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In this paper, we propose a generalization of convolutional neural networks (CNN) to non-Euclidean domains for the analysis of deformable shapes. Our construction is based on localized frequency analysis (a generalization of the windowed Fourier transform to manifolds) that is used to extract the local behavior of some dense intrinsic descriptor, roughly acting as an analogy to patches in images. The resulting local frequency representations are then passed through a bank of filters whose coefficient are determined by a learning procedure minimizing a task-specific cost. Our approach generalizes several previous methods such as HKS, WKS, spectral CNN, and GPS embeddings. Experimental results show that the proposed approach allows learning class-specific shape descriptors significantly outperforming recent state-of-the-art methods on standard benchmarks. Convolutional neural networks (CNNs) have demonstrated their ability object detection of very high resolution remote sensing images. However, CNNs have obvious limitations for modeling geometric variations in remote sensing targets. In this paper, we introduced a CNN structure, namely deformable ConvNet, to address geometric modeling in object recognition. By adding offsets to the convolution layers, feature mapping of CNN can be applied to unfixed locations, enhancing CNNs’ visual appearance understanding. In our work, a deformable region-based fully convolutional networks (R-FCN) was constructed by substituting the regular convolution layer with a deformable convolution layer. To efficiently use this deformable convolutional neural network (ConvNet), a training mechanism is developed in our work. We first set the pre-trained R-FCN natural image model as the default network parameters in deformable R-FCN. Then, this deformable ConvNet was fine-tuned on very high resolution (VHR) remote sensing images. To remedy the increase in lines like false region proposals, we developed aspect ratio constrained non maximum suppression (arcNMS). The precision of deformable ConvNet for detecting objects was then improved. An end-to-end approach was then developed by combining deformable R-FCN, a smart fine-tuning strategy and aspect ratio constrained NMS. The developed method was better than a state-of-the-art benchmark in object detection without data augmentation. The Fourier domain is used in computer vision and machine learning as image analysis tasks in the Fourier domain are analogous to spatial domain methods but are achieved using different operations. Convolutional Neural Networks (CNNs) use machine learning to achieve state-of-the-art results with respect to many computer vision tasks. One of the main limiting aspects of CNNs is the computational cost of updating a large number of convolution parameters. Further, in the spatial domain, larger images take exponentially longer than smaller image to train on CNNs due to the operations involved in convolution methods. Consequently, CNNs are often not a viable solution for large image computer vision tasks. In this paper a Fourier Convolution Neural Network (FCNN) is proposed whereby training is conducted entirely within the Fourier domain. The advantage offered is that there is a significant speed up in training time without loss of effectiveness. Using the proposed approach larger images can therefore be processed within viable computation time. The FCNN is fully described and evaluated. The evaluation was conducted using the benchmark Cifar10 and MNIST datasets, and a bespoke fundus retina image dataset. The results demonstrate that convolution in the Fourier domain gives a significant speed up without adversely affecting accuracy. For simplicity the proposed FCNN concept is presented in the context of a basic CNN architecture, however, the FCNN concept has the potential to improve the speed of any neural network system involving convolution. Convolutional neural networks (CNNs) are inherently limited to model geometric transformations due to the fixed geometric structures in their building modules. In this work, we introduce two new modules to enhance the transformation modeling capability of CNNs, namely, deformable convolution and deformable RoI pooling. Both are based on the idea of augmenting the spatial sampling locations in the modules with additional offsets and learning the offsets from the target tasks, without additional supervision. The new modules can readily replace their plain counterparts in existing CNNs and can be easily trained end-to-end by standard back-propagation, giving rise to deformable convolutional networks. Extensive experiments validate the performance of our approach. For the first time, we show that learning dense spatial transformation in deep CNNs is effective for sophisticated vision tasks such as object detection and semantic segmentation. The code is released at https: github.com msracver Deformable-ConvNets.