You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
In this work, we focus on distance-based outliers in a metric space, where the status of an entity as to whether it is an outlier is based on the number of other entities in its neighborhood. In recent years, several solutions have tackled the problem of distance-based outliers in data streams, where outliers must be mined continuously as new elements become available. An interesting research problem is to combine the streaming environment with massively parallel systems to provide scalable streambased algorithms. However, none of the previously proposed techniques refer to a massively parallel setting. Our proposal fills this gap and investigates the challenges in transferring state-of-the-art techniques to Apache Flink, a modern platform for intensive streaming analytics. We thoroughly present the technical challenges encountered and the alternatives that may be applied. We show speed-ups of up to 117 (resp. 2076) times over a naive parallel (resp. non-parallel) solution in Flink, by using just an ordinary four-core machine and a real-world dataset. When moving to a three-machine cluster, due to less contention, we manage to achieve both better scalability in terms of the window slide size and the data dimensionality, and even higher speed-ups, e.g., by a factor of 510. Overall, our results demonstrate that oulier mining can be achieved in an efficient and scalable manner. The resulting techniques have been made publicly available as open-source software.

Cited Abstract(s):
[1]: Anomaly detection is considered an important data mining task, aiming at the discovery of elements (known as outliers) that show significant diversion from the expected case. More specifically, given a set of objects the problem is to return the suspicious objects that deviate significantly from the typical behavior. As in the case of clustering, the application of different criteria leads to different definitions for an outlier. In this work, we focus on distance-based outliers: an object x is an outlier if there are less than k objects lying at distance at most R from x. The problem offers significant challenges when a stream-based environment is considered, where data arrive continuously and outliers must be detected on-the-fly. There are a few research works studying the problem of continuous outlier detection. However, none of these proposals meets the requirements of modern stream-based applications for the following reasons: (i) they demand a significant storage overhead, (ii) their efficiency is limited and (iii) they lack flexibility in the sense that they assume a single configuration of the k and R parameters. In this work, we propose new algorithms for continuous outlier monitoring in data streams, based on sliding windows. Our techniques are able to reduce the required storage overhead, are more efficient than previously proposed techniques and offer significant flexibility with regard to the input parameters. Experiments performed on real-life and synthetic data sets verify our theoretical study. HighlightsWe prove a linear space lower bound.A novel continuous algorithm is presented, which has two versions (COD).To support different views of outliers, we propose an extension (ACOD).We also propose algorithms based on micro-clusters (MCOD AMCOD).Performance evaluation results based on both real-life and synthetic data.

[2]: Real-time analytics of anomalous phenomena on streaming data typically relies on processing a large variety of continuous outlier detection requests, each configured with different parameter settings. The processing of such complex outlier analytics workloads is resource consuming due to the algorithmic complexity of the outlier mining process. In this work we propose a sharing-aware multi-query execution strategy for outlier detection on data streams called SOP. A key insight of SOP is to transform the problem of handling a multi-query outlier analytics workload into a single-query skyline computation problem. We prove that the output of the skyline computation process corresponds to the minimal information needed for determining the outlier status of any point in the stream. Based on this new formulation, we design a customized skyline algorithm called K-SKY that leverages the domination relationships among the streaming data points to minimize the number of data points that must be evaluated for supporting multi-query outlier detection. Based on this K-SKY algorithm, our SOP solution achieves minimal utilization of both computational and memory resources for the processing of these complex outlier analytics workload. Our experimental study demonstrates that SOP consistently outperforms the state-of-art solutions by three orders of magnitude in CPU time, while only consuming 5 of their memory footprint - a clear win-win. Furthermore, SOP is shown to scale to large workloads composed of thousands of parameterized queries.

[3]: Computing outliers and related statistical aggregation functions from large-scale big data sources is a critical operation in many cloud computing scenarios, e.g. service quality assurance, fraud detection, or novelty discovery. Such problems commonly have to be solved in a distributed environment where each node only has a local slice of the entirety of the data. To process a query on the global data, each node must transmit its local slice of data or an aggregated subset thereof to a global aggregator node, which can then compute the desired statistical aggregation function. In this context, reducing the total communication cost is often critical to the overall efficiency. In this paper, we show both theoretically and empirically that these communication costs can be significantly reduced for common distributed computing problems if we take advantage of the fact that production-level big data usually exhibits a form of sparse structure. Specifically, we devise a new aggregation paradigm for outlier detection and related queries. The paradigm leverages compressive sensing for data sketching in combination with outlier detection techniques. We further propose an algorithm that works even for non-sparse data that concentrates around an unknown value. In both cases, we show that the communication cost is reduced to the logarithm of the global data size. We incorporate our approach into Hadoop and evaluate it on real web-scale production data (distributed click-data logs). Our approach reduces data shuffling IO by up to 99 , and end-to-end job duration by up to 40 on many actual production queries.
A related yet different problem is examined in [3] . In a production distributed environment, a stream of data points may be split across multiple nodes, each holding part of the values of a data point. These parts will eventually need to be aggregated on a core node for outlier detection, but this incurs significant communication cost. The solution proposed is based on compressing local data into a sketch. Another related problem is that of supporting multiple outlier detection queries, i.e., combinations of @math and @math values. Examples include [1]0 and [1] . The latter presents multi-query extensions to MCOD and its approach is compatible with the our parallel pMCOD solution; here, we have examined single-query solutions only.