In this paper, we propose a method of improving Convolutional Neural Networks (CNN) by determining the optimal alignment of weights and inputs using dynamic programming. Conventional CNNs convolve learnable shared weights, or filters, across the input data. These filters use an inner product to linearly match the shared weights to a window of the input. However, it is possible that there exists a more optimal alignment of weights. Thus, we propose the use of Dynamic Time Warping (DTW) to dynamically align the weights to optimized input elements. This dynamic alignment is especially useful for time series recognition due to the complexities with temporal distortions, such as varying rates and sequence lengths. We demonstrate the effectiveness of the proposed architecture on the Unipen online handwritten digit and character datasets, the UCI Spoken Arabic Digit dataset, and the UCI Activities of Daily Life dataset.
TDNNs are classical feed-forward neural networks designed to address shift variance @cite_40 by introducing wider sliding window receptive fields to represent multiple points in time. These windows, or , are passed through learned filters to create subsequent feature map time series. CNNs continue the idea of learned filters permeated across a structural input to the domain of images. However, CNNs have been used for time series recognition by considering the time steps as a dimension for the convolutions. @cite_17 use CNNs with 1D subsequences created from multivariate time series. There also have been attempts @cite_13 @cite_22 @cite_27 @cite_49 to classify time series patterns by embedding them into 2D matrices for classification by CNN.
@cite_22 @cite_27 @cite_40 @cite_49 @cite_13 @cite_17
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Two architectures that generalize convolutional neural networks (CNNs) for the processing of signals supported on graphs are introduced. We start with the selection graph neural network (GNN), which replaces linear time invariant filters with linear shift invariant graph filters to generate convolutional features and reinterprets pooling as a possibly nonlinear subsampling stage where nearby nodes pool their information in a set of preselected sample nodes. A key component of the architecture is to remember the position of sampled nodes to permit computation of convolutional features at deeper layers. The second architecture, dubbed aggregation GNN, diffuses the signal through the graph and stores the sequence of diffused components observed by a designated node. This procedure effectively aggregates all components into a stream of information having temporal structure to which the convolution and pooling stages of regular CNNs can be applied. A multinode version of aggregation GNNs is further introduced for operation in large-scale graphs. An important property of selection and aggregation GNNs is that they reduce to conventional CNNs when particularized to time signals reinterpreted as graph signals in a circulant graph. Comparative numerical analyses are performed in a source localization application over synthetic and real-world networks. Performance is also evaluated for an authorship attribution problem and text category classification. Multinode aggregation GNNs are consistently the best-performing GNN architecture. In recent years, the convolutional neural network (CNN) has achieved great success in many computer vision tasks. Partially inspired by neuroscience, CNN shares many properties with the visual system of the brain. A prominent difference is that CNN is typically a feed-forward architecture while in the visual system recurrent connections are abundant. Inspired by this fact, we propose a recurrent CNN (RCNN) for object recognition by incorporating recurrent connections into each convolutional layer. Though the input is static, the activities of RCNN units evolve over time so that the activity of each unit is modulated by the activities of its neighboring units. This property enhances the ability of the model to integrate the context information, which is important for object recognition. Like other recurrent neural networks, unfolding the RCNN through time can result in an arbitrarily deep network with a fixed number of parameters. Furthermore, the unfolded network has multiple paths, which can facilitate the learning process. The model is tested on four benchmark object recognition datasets: CIFAR-10, CIFAR-100, MNIST and SVHN. With fewer trainable parameters, RCNN outperforms the state-of-the-art models on all of these datasets. Increasing the number of parameters leads to even better performance. These results demonstrate the advantage of the recurrent structure over purely feed-forward structure for object recognition. Convolutional Neural Networks (CNN) have been regarded as a powerful class of models for image recognition problems. Nevertheless, it is not trivial when utilizing a CNN for learning spatio-temporal video representation. A few studies have shown that performing 3D convolutions is a rewarding approach to capture both spatial and temporal dimensions in videos. However, the development of a very deep 3D CNN from scratch results in expensive computational cost and memory demand. A valid question is why not recycle off-the-shelf 2D networks for a 3D CNN. In this paper, we devise multiple variants of bottleneck building blocks in a residual learning framework by simulating @math convolutions with @math convolutional filters on spatial domain (equivalent to 2D CNN) plus @math convolutions to construct temporal connections on adjacent feature maps in time. Furthermore, we propose a new architecture, named Pseudo-3D Residual Net (P3D ResNet), that exploits all the variants of blocks but composes each in different placement of ResNet, following the philosophy that enhancing structural diversity with going deep could improve the power of neural networks. Our P3D ResNet achieves clear improvements on Sports-1M video classification dataset against 3D CNN and frame-based 2D CNN by 5.3 and 1.8 , respectively. We further examine the generalization performance of video representation produced by our pre-trained P3D ResNet on five different benchmarks and three different tasks, demonstrating superior performances over several state-of-the-art techniques. Convolutional neural networks (CNNs) are usually built by stacking convolutional operations layer-by-layer. Although CNN has shown strong capability to extract semantics from raw pixels, its capacity to capture spatial relationships of pixels across rows and columns of an image is not fully explored. These relationships are important to learn semantic objects with strong shape priors but weak appearance coherences, such as traffic lanes, which are often occluded or not even painted on the road surface as shown in Fig. 1 (a). In this paper, we propose Spatial CNN (SCNN), which generalizes traditional deep layer-by-layer convolutions to slice-byslice convolutions within feature maps, thus enabling message passings between pixels across rows and columns in a layer. Such SCNN is particular suitable for long continuous shape structure or large objects, with strong spatial relationship but less appearance clues, such as traffic lanes, poles, and wall. We apply SCNN on a newly released very challenging traffic lane detection dataset and Cityscapse dataset. The results show that SCNN could learn the spatial relationship for structure output and significantly improves the performance. We show that SCNN outperforms the recurrent neural network (RNN) based ReNet and MRF+CNN (MRFNet) in the lane detection dataset by 8.7 and 4.6 respectively. Moreover, our SCNN won the 1st place on the TuSimple Benchmark Lane Detection Challenge, with an accuracy of 96.53 .