We propose an approximation algorithm for efficient correlation search in time series data. In our method, we use Fourier transform and neural network to embed time series into a low-dimensional Euclidean space. The given space is learned such that time series correlation can be effectively approximated from Euclidean distance between corresponding embedded vectors. Therefore, search for correlated time series can be done using an index in the embedding space for efficient nearest neighbor search. Our theoretical analysis illustrates that our method's accuracy can be guaranteed under certain regularity conditions. We further conduct experiments on real-world datasets and the results show that our method indeed outperforms the baseline solution. In particular, for approximation of correlation, our method reduces the approximation loss by a half in most test cases compared to the baseline solution. For top- @math highest correlation search, our method improves the precision from 5 to 20 while the query time is similar to the baseline approach query time.
There are also more neural-network-based methods in time series related problems. Cui @cite_41 design an multi-scale convolution neural network for time series classification. Zheng @cite_14 apply convolution neural network for distance metric learning and classification. Both works show that the designed structures can achieve baseline performance when data is sufficiently large. However, in these works the networks are supervised to learn the mapping from time series to the given labels, while in this paper the network is developed for unsupervised dimension reduction and feature extraction of dataset structure.
@cite_41 @cite_14
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Time series classification has been around for decades in the data-mining and machine learning communities. In this paper, we investigate the use of convolutional neural networks (CNN) for time series classification. Such networks have been widely used in many domains like computer vision and speech recognition, but only a little for time series classification. We design a convolu-tional neural network that consists of two convolutional layers. One drawback with CNN is that they need a lot of training data to be efficient. We propose two ways to circumvent this problem: designing data-augmentation techniques and learning the network in a semi-supervised way using training time series from different datasets. These techniques are experimentally evaluated on a benchmark of time series datasets. textabstractForecasting financial time series using past observations has been a significant topic of interest. While temporal relationships in the data exist, they are difficult to analyze and predict accurately due to the non-linear trends and noise present in the series. We propose to learn these dependencies by a convolutional neural network. In particular the focus is on multivariate time series forecasting. Effectively, we use multiple financial time series as input in the neural network, thus conditioning the forecast of a time series x(t) on both its own history as well as that of a second (or third) time series y(t). Training a model on multiple stock series allows the network to exploit the correlation structure between these series so that the network can learn the market dynamics in shorter sequences of data. We show that long-term temporal dependencies in and between financial time series can be learned by means of a deep convolutional neural network based on the WaveNet model [2]. The network makes use of dilated convolutions applied to multiple time series so that the receptive field of the network is wide enough to learn both short and long-term dependencies. The architecture includes batch normalization and uses a 1 × k convolution with parametrized skip connections from the input time series as well as the time series we condition on, in this way learning long-term interdependencies in an efficient manner [1]. This improves the forecast, while at the same time limiting the requirement for a long historical price series and reducing the noise. Knowing the strong performance of CNNs on classification problems we show that they can be applied successfully to forecasting financial time series, without the need of large samples of data. We compare the performance of the WaveNet model to a state-of-the-art fully convolutional network (FCN), and an autoregressive model popular in econometrics and show that our model is much better able to learn important dependencies in between financial time series resulting in a more robust and accurate forecast. Deep learning methods such as convolutional neural networks (CNNs) can deliver highly accurate classification results when provided with large enough data sets and respective labels. However, using CNNs along with limited labeled data can be problematic, as this leads to extensive overfitting. In this letter, we propose a novel method by considering a pretrained CNN designed for tackling an entirely different classification problem, namely, the ImageNet challenge, and exploit it to extract an initial set of representations. The derived representations are then transferred into a supervised CNN classifier, along with their class labels, effectively training the system. Through this two-stage framework, we successfully deal with the limited-data problem in an end-to-end processing scheme. Comparative results over the UC Merced Land Use benchmark prove that our method significantly outperforms the previously best stated results, improving the overall accuracy from 83.1 up to 92.4 . Apart from statistical improvements, our method introduces a novel feature fusion algorithm that effectively tackles the large data dimensionality by using a simple and computationally efficient approach. Convolutional neural networks (CNNs) have shown great performance as general feature representations for object recognition applications. However, for multi-label images that contain multiple objects from different categories, scales and locations, global CNN features are not optimal. In this paper, we incorporate local information to enhance the feature discriminative power. In particular, we first extract object proposals from each image. With each image treated as a bag and object proposals extracted from it treated as instances, we transform the multi-label recognition problem into a multi-class multi-instance learning problem. Then, in addition to extracting the typical CNN feature representation from each proposal, we propose to make use of ground-truth bounding box annotations (strong labels) to add another level of local information by using nearest-neighbor relationships of local regions to form a multi-view pipeline. The proposed multi-view multiinstance framework utilizes both weak and strong labels effectively, and more importantly it has the generalization ability to even boost the performance of unseen categories by partial strong labels from other categories. Our framework is extensively compared with state-of-the-art handcrafted feature based methods and CNN based methods on two multi-label benchmark datasets. The experimental results validate the discriminative power and the generalization ability of the proposed framework. With strong labels, our framework is able to achieve state-of-the-art results in both datasets.