# Real-Time Anomaly Detection with Subspace Periodic Clustering Approach
## 2 Related Works
In [28] the authors addressed the high dimensionality and proposed an unsupervised method for anomaly detection in such data. In [32], the authors presented a hybrid approach consisting of a semi-supervised approach for anomaly detection in high-dimensional data. In [33], the authors proposed a mixed approach consisting of rough set theory and a density-based clustering algorithm for anomaly detection in high-dimensional data. In [34], the authors addressed the issue of the temporality of anomalies and proposed a clustering-based system for real-time anomaly detection in streaming data. Most of the aforesaid methods tried to address high dimensionality efficiently but the periodicity of clusters or anomalies was not discussed. Rough set theory as a tool to deal with the ambiguity and uncertainty occurring in any real system was proposed by [PERSON] [35]. In [36], the authors applied the rough set theory to produce nano topology. In [37], the authors applied the notion of nano topology for medical diagnosis. The same notion can be used for attribute reduction in high-dimensional data [33]. [PERSON] et al. [44], proposed a method using diverse meta-featuresfor identifying recurring concepts of drift in data streams. In [45], the authors put forward a two-layered classification model for the online anomaly detection of highly unreliable data. In [46], the authors presented a scheme for the online detection of anomalies in data streams. In [47], the authors proposed to evaluate cyber risk for operation technology systems. In [48], the authors discussed insider threat, which creates significant issues for the cyber security of industrial control systems. [PERSON] et al. [49] presented an online anomaly detection model based on a random forest method. [PERSON] et al. [50] proposed to introduce fuzzy in anomaly detection by proposing a fuzzy c-means-based technique. [PERSON] et al. [53] presented a fuzzy neural network-based approach for detecting anomalies in massive cyberattacks. In [54], the authors presented an effective clustering-based real-time anomaly detection system. [PERSON] et al. [55] proposed a calendar-based periodic pattern from supermarket datasets. In [56], the authors used an interval operation called interval superimposition to find the solution of a fuzzy linear equation. In [58], the authors proposed a lemma called the Glivenko-Cantelli lemma. Using the lemma on superimposed intervals [56], fuzzy intervals [57; 59] can be generated. In [60], the authors proposed a dominance relation on conditional attributes to generate set-valued ordered information systems which can be used for attribute reduction in the dataset. In most of the anomaly detection cases discussed above, the methods tried to propose effective ways to deal with either high-dimensionality or real-time issues. However, a few were able to deal with both effectively. Also, no algorithms have addressed the periodicity of clusters or anomalies in the datasets. However, the periodicity of the clusters or anomalies can be very useful in designing early warning systems. In this article, we propose to address all the aforesaid issues effectively and present a suitable solution for them.