# Detecting IoT Anomalies Using Fuzzy Subspace Clustering Algorithms
## 1 Introduction  
There are huge applications comprising sensors providing critical data that evolve mostly as a result of the development of the IoT [1] along with their sources of real data generation. As a result, a rapid surge in streaming and time-series data availability is witnessed. Analyzing such data can yield insightful information. The uncovering of anomalies from IoT data has substantial real-world applications across various activities such as pre-emptive maintenance, prevention of fraud, fault finding, and monitoring. Therefore, detecting anomalies can provide actionable information in the circumstances, where no trustworthy answers exist. A reliable answer to the problems is put forwarded here. High dimensionality typically makes difficult-to-discover anomalies in an IoT dataset. Data sparsity is a result of the fact that as the features or attributes grow, more dataare necessary for the generalization of the detection system. These extra variables, or a significant quantity of noise from numerous insignificant features hiding the genuine outliers, are the cause of the data sparsity. The \"curse of dimensionality\" [2; 3] is a famous term coined for the problem. Therefore, several conventional anomaly detection techniques like \(k\)-means, \(k\)-medoids, and DBSCAN [4; 5; 6] were found to be unsuitable for such data as they fail to retain their efficacy. Efficient anomaly detection of high-dimensional IoT data is an interesting problem of research. In [7], the authors introduced a new concept called rough set theory, for dealing with uncertainty or vagueness existing in any real-life problem. In [8], a classification algorithm based on a neighborhood rough set was proposed for the anomaly detection in mixed-attribute datasets. In [9], the authors defined the nano topological space of a subset \(X\) of universe \(U\) using both of the approximations of \(X\). In [10], the authors proposed to generate CORE (a subset of attribute sets) of the conditional attribute set for medical diagnosis. The method in [9] can be used to address the \"curse of dimensionality\" problem that exists in high-dimensional IoT data. Clustering is a data mining technique used to unearth the distribution of data and the patterns in any dataset. Clustering has been widely applied in anomaly detection. In [11], the authors used the \(k\)-means algorithm for anomaly detection in a network-traffic dataset. A fuzzy \(c\)-means clustering-based technique for anomaly detection in mixed data had been put out by the authors in [12]. In [13], the authors put forwarded a hierarchical clustering method for mixed-data anomaly detection. For detecting anomalies in mixed data, in [14], a hybrid clustering strategy was proposed that combines both partitioning and hierarchical techniques. In [15], a method of finding anomalies in high-dimensional and categorical data was proposed. Analogous research was presented in [16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29]. The authors of [30] addressed the insider threat, which poses serious problems for the industrial control systems' cyber security. The authors of [31] presented an online random forest-based anomaly detection method. In [32; 33; 34], fuzzy techniques for real-time anomaly detections were covered. For the purpose of identifying anomalies in significant cyberattacks, the authors of [35] presented a neural network-based fuzzy approach. The majority of the aforementioned algorithms have some limitations. Some, for instance, are ineffective in finding anomalies in high-dimensional data, while others lose detection accuracy with the increase in dimensions. In [36], the authors put forwarded a mixed algorithm consisting of a partitioning and a hierarchical approach for real-time anomaly detection which produces stable clusters along their fuzzy lifetimes. However, this approach loses efficacy when the dimension of the dataset increases.