The problem of time series prediction based on fuzzy cognitive maps (FCMs) is unresolved. Although many methods have been proposed to cope with this issue, the performance of these methods is far from satisfactory. Traditional FCM-based predictors have three limitations. First, current feature extraction operators are incapable of learning good representations of original time series. Second, current methods use just the output of FCMs to predict the next value; they do not directly utilize the important information of the latent features. Third, current FCM-based predictors optimize each component individually, thereby leading to low prediction accuracy. For example, these methods first optimize the feature extraction operator and then learn the FCMs from the latent features; they do not simultaneously optimize the whole prediction model. In this article, we develop a framework based on a sparse autoencoder (SAE) and a high-order FCM (HFCM) to address the time series prediction problem; we refer this framework as SAE-FCM. To overcome the first limitation of current methods, an SAE is employed to extract features from original time series. Unlike current FCM-based predictors, our method combines the output of both the SAE and the HFCM to calculate the predicted value, thereby overcoming the second limitation of traditional FCM-based predictors. In an application of the idea of “fine tuning” in deep learning, the weights of SAE-FCM can be updated by the batch gradient descent method if the prediction errors are great. Thus, we can optimize SAE-FCM as a whole and overcome the third limitation. We validate the performance of SAE-FCM on ten datasets. Compared with the experimental results obtained by using state-of-the-art methods, the experimental results obtained by using SAE-FCM demonstrate the effectiveness of our method. Extensive experiments also show that SAE-FCM can effectively overcome the above limitations.

中文翻译：

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使用稀疏自编码器和高阶模糊认知图的时间序列预测

基于模糊认知图 (FCM) 的时间序列预测问题尚未解决。尽管已经提出了许多方法来解决这个问题，但这些方法的性能远不能令人满意。传统的基于 FCM 的预测器具有三个局限性。首先，当前的特征提取算子无法学习原始时间序列的良好表示。其次，目前的方法只使用 FCM 的输出来预测下一个值；它们不直接利用潜在特征的重要信息。第三，当前基于 FCM 的预测器单独优化每个组件，从而导致预测精度低。例如，这些方法首先优化特征提取算子，然后从潜在特征中学习 FCM；它们不会同时优化整个预测模型。在本文中，我们开发了一个基于稀疏自编码器 (SAE) 和高阶 FCM (HFCM) 的框架来解决时间序列预测问题；我们将此框架称为 SAE-FCM。为了克服当前方法的第一个限制，使用 SAE 从原始时间序列中提取特征。与当前基于 FCM 的预测器不同，我们的方法结合了 SAE 和 HFCM 的输出来计算预测值，从而克服了传统基于 FCM 的预测器的第二个限制。在深度学习中“微调”思想的应用中，如果预测误差很大，可以通过批量梯度下降法更新 SAE-FCM 的权重。因此，我们可以整体优化 SAE-FCM 并克服第三个限制。我们在十个数据集上验证了 SAE-FCM 的性能。与使用最先进方法获得的实验结果相比，使用 SAE-FCM 获得的实验结果证明了我们方法的有效性。大量实验还表明，SAE-FCM 可以有效地克服上述限制。