# A Correlation-Change Based Feature Selection Method for IoT Equipment Anomaly Detection
## 1 Introduction  
In the era of the fourth industrial revolution, there is a growing trend to deploy sensors on industrial equipment, and analyze the industrial equipment's running status according to the sensor data. Thanks to the rapid development of IoT technologies [1], sensor data could be easily fetched from industrial equipment, and analyzed to produce further value for industrial control at the edge of the network or at data centers. Due to the considerable development of deep learning in recent years, a common practice of such analysis is to conduct deep learning [2; 3; 4]. Such methods select a subset of all fetched sensor data stream as the input features, and generate equipment predictions. As a result, the performance of the learning model was seriously impacted by the features selected, thus feature selection plays a critical role for such methods. To select an appropriate set of features for the learning model, researchers aim to select the most relevant features to the prediction model to improve the prediction performance, or to select the most informative features to conduct data reduction. Unfortunately, both kinds of methods have intrinsic drawbacks when applied in the online scenarios. The former kind of methods seriously depends on predefined evaluation criteria, such as feature relevance metrics [5] or a predefined learning model [6]. Thus, such method are limited to certain dataset, and are not suitable for online scenarios whichinvolve dynamical and unsupervised feature selection. The later kind of methods right fits in the online scenarios. However, data reduction mainly aims to improve the efficiency (but not accuracy) of the prediction model, which is not the most concerning factor of online industrial equipment status analysis. To relieve the dependency of predefined evaluation criteria, researchers switch to select the features which can indicate the online sensor data's characters, such as features which are smoothest on the graph [7], or the features with highest clusterability [8; 9]. In this paper, we focus on the features with correlation changes such as smoothness and clusterability, which are important characters for traditional pattern recognition fields like image processing and voice recognition [7; 8; 9]. We believe that correlation changes can significantly pinpoint status changes in industrial environment. As far as we know, this is the first work focusing on correlation changes for online feature selection. In practical industrial scenarios, sensors catch equipment indicators that reflect various types of running status of industrial equipment. Because of the intrinsic mechanism of the industrial equipment, there exist prevalent correlations among equipment indicators. Herein, the corresponding sensor data streams are correlated. For example, as shown in Figure 1 are two sensor data streams collected from a coal mill in a thermal power plant, which indicates the power and coal flow of the coal mill over time. As the coal flow increases, the coal mill needs more power to digest the growing amount of coal, leading to the coal mill's power increase. Accordingly, we can observe that the indicators of \"power\" and \"coal flow\" are correlated. Sensor data correlations indicate the normal running of a set of equipment intrinsic mechanisms under certain running status. When the running status changes, the conditions supporting the equipment intrinsic mechanisms may break, and the running status changes may be reflected by the corresponding sensor data correlations. Considering that dynamic data correlations among industrial equipment sensors prevalently exist [10; 11], we believe sensor data correlation change could be an effective metric for identifying the running status changes. Consequently, we propose to conduct online feature selection by selecting the sensors with data correlation changes. To capture the sensor data correlation changes, the challenges include two-folds. The first problem is that industrial sensor data are always correlated with time lags [12].