# Distributed Online Multi-Label Learning with Privacy Protection in Internet of Things
## 1 Introduction  
Label classification is a general task in machine learning, and multi-label classification builds on this by allowing each instance to be able to belong to a collection of multiple categories. Many mature multi-label classification algorithms have been developed, with numerous experiments demonstrating their performance. However, these approaches cannot be applied straightforwardly in real-world application scenarios due to various issues. For example, in the era of big data, where the Internet of Things (IoT) devices are widespread, privacy protection and big data communication cost need to be addressed by specialized technologies. Then, online multi-label classification (OMLC) learning algorithms are proposed to tackle these challenges by directly processing and discarding the incoming data. Because of the efficiency and fast processing of data by these algorithms, such algorithms are widely used in real-world applications, such as Twitter, Facebook, Instagram postings and RDF Site Summary (RSS) feeds [1]. Although OMLC algorithms can handle most real-life scenarios very well, in recent years, data generation has changed with the era of big data. In real-world applications, a large amount and variety of data are generated by a wide range of computing devices, such as home appliances, surveillance cameras, monitoring sensors, actuators, displays, vehicles and so on [2]. However, traditional online multi-label learning algorithms [3; 4; 5] can only process online data and train models independently at each computing node, which isincompatible with the data generation approach, and the additional communication costs are inevitable. In addition, unnecessary transfer steps inevitably increase the chance of being attacked. For example, multiple channels, such as WiFi, could easily attack user data, thus affecting its performance [6]. Moreover, avoiding user data leakage is also very important. Many technologies such as Privacy Enhancing Technologies or private synthetic data generators have been proposed and applied to protect users' data [7]. This type of security risk can be completely avoided if it is possible to avoid redundant raw data transfers. Current mainstream online learning is devoted to solving performance problems caused by, for example, concept drift, missing features, missing labels and data imbalance [8]. Extending online learning to distributed contexts has not received sufficient attention. Moreover, research on multi-label classification problems in the distributed domain lacks consideration of online data use, and there is no practical distributed online multi-label learning method. We propose a novel distributed approach for the OMLC problem (DOML), which updates the local model by allowing each node in the network to self-coordinate by transmitting only parameters. With this approach, each node can achieve the performance of a centralized multi-label classification algorithm by having data interact with its neighbours only and inferring the global model without exposing local data. In our proposed algorithm, the interaction of the metric models and the self-renewal process of each node are parallel, so the efficiency gains from the distributed algorithm are guaranteed. We compared our proposed algorithm with traditional batched learning algorithms and online learning algorithms using a classical dataset. We confirmed that our proposed algorithm has a performance that does not lose out to traditional centralised algorithms in a distributed scenario where the source data are not transferred. The remainder of the article is organized as follows. The next section discusses the current state of the multi-label classification problem and introduces the distributed least squares iterative method. This is followed by an explanation of the method for transforming real-world IoT networks into an abstract graph representation. The subsequent section shows the mathematical derivation of the distributed constrained optimization problem and gives an iterative update method.