# Random Subspace Ensembles of Fully Convolutional Network for Time Series Classification
## 1 Introduction  
Time series classification (TSC) has attracted great attention, for it exists in a wide variety of fields [1], such as recognition and diagnosis problems in many industries, such as finance and medicine. Meanwhile, it is deemed as a challenging problem of data mining [2], due to its high dimensionality and nonalignment. These two drawbacks make it difficult to find distinctive features from time series. To tackle this issue, hundreds of novel methods are proposed, including distance-based [3], feature-based, deep-learning-based [4] and ensemble-based. Wherein, methods based on deep learning shows impressive performance, as they have certain tolerance for the unaligned time series and be able to perceive the features benefiting for classification task automatically. An intuitional example is: [PERSON] [5], who evaluates some simple end-to-end deep learning benchmarks, which are Multilayer Perceptions (MLP), Residual Network (ResNet) and Fully Convolutional Network (FCN). The comparisons of experiment results show that FCN and ResNet outperform several complicated non-deep-learning TSC methods. The two winners, FCN and ResNet, are two specific forms of a Convolutional Neural Network (CNN). CNN is indeed the most highly regarded deep learning model in TSC field [4], and FCN is one of its common application forms. [PERSON] et al. [6] are attracted by the robustness and good performance of FCN, so that use it as the classifier to execute transfer learning experiments among datasets in UCR archive. [PERSON] et al. [7] employ FCN to perceive spatial features of time series curves, and augment it by adding LSTM module to extract time features simultaneously. Their proposed LSTM-FCN actually achieved the state-of-the-art performance at that time, whileElsayed [PERSON] et al. [8] use GRU module to realize the extraction of time-related features, and the GRU-FCN shows accurate results, as well. In fact, RNN modules like LSTM and GRU is not suitable for solving TSC problems alone [9], such superior results are mainly based on the contribution of FCN. Moreover, MFCN [10] is the proposed on the basis of FCN to learn multi-scale features of time series, and it also achieve improved performance. The successes of above models have repeatedly demonstrated the excellence of FCN for TSC problem. Ensemble learning is an approach to achieve further improve the accuracy when basic model reaches its bottleneck. COTE [11] and PROP [12] are the representative in TSC field. One uses a total of 35 weak classifiers which trained by information from four domain to construct a strong one, the other integrates 11 kinds of classifiers which evaluates similarity by different distance measures. Except methods like those above, which combine different existing TSC techniques, classical ensemble learning ideas which provide heuristic rules for constructing diversity individual classifiers with given dataset are also employed. [PERSON] et al. [13] propose an XG-SF based on XGBoost algorithm and Shapelet features. [PERSON] et al. [14] construct ensemble classifiers called EnRS-Bagging and EnRS-Boosting in a classical Boosting and Bagging manner, respectively. As we all know, the basic individual classifiers within ensemble model should be fine and diverse, whereas most of the mentioned methods employed the inferior decision tree or distance-based models, so that they cannot compete with state-of-the-art results, though achieve some improvements in accuracy. Furthermore, there is no method focuses on constructing deep neural network ensembles, until NNE [15] is proposed in 2019. NNE compose an ensemble of total 60 different neural networks that are generated by 6 kinds of models and 10 initial weights of each kind. It does pay attention to the diversity of individual classifiers but is not wise to involve the ones with more complex structure but less accurate judgment than FCN, such as Time-CNN [16] and MCD-CNN [17]. Which leads the achieved improvements not deserve the devoted efforts.