Anomaly detection for time-series data has been viewed widely in many practical applications and caused lots of research interests. A popular solution based on deep learning techniques is first building an anomaly detection model by offline learning on a specific training data and subsequently utilizing the model to detect anomalies in the online setting. On the one hand, previous works have introduced a plenty of learning methods for building anomaly detection models, but it is well known that no one can perform best in all settings. Therefore, there is usually high demand for collecting multiple detection models in practical applications. On the other hand, in view of the limited computing resources in many online anomaly detection applications, it is almost impossible to run multiple detection models simultaneously due to the high time cost. Then, a natural idea is to enhance the general anomaly detection procedure with an effective mechanism for selecting proper models to avoid the high cost caused by executing too many detection models. Previous works focusing on the recommendation either are time inefficient or usually show weak performance, suffering from the missing labels and heterogeneous data characteristics met in real applications. Therefore, it is highly needed to design effective recommendation methods for automatically choosing anomaly detection models. Motivated by the technical challenges, a novel recommendation method for anomaly detection models is proposed in this article. First, a model recommendation framework based on the concept of detectability is introduced, where the detectability of an anomaly detection model is defined using a fine-grained strategy for comparing data characteristics. Then, based on efficient techniques for computing detectability, an efficient model recommendation algorithm is designed. Finally, extensive experimental results are produced on real time series and typical anomaly detection methods, and show that the proposed method is both effective and efficient.

Range query is an important operation on big multi-dimensional data. This paper studies the problem of multi-dimensional range query filtering for speeding up the range query processing by avoiding reading the useless data. To solve the problem, a novel multi-dimensional range filter is proposed to filter the multi-dimensional range queries, while the existing one-dimensional range filters can not provide efficient filtering. Based on the multi-dimensional range filter, an efficient range query processing algorithm is presented. It can directly return the locations of the I/O units that contain the data in the query result without any access to the input dataset. The time complexity of the algorithm is$O(3^{m}h)$, where$h$is the number of I/O units partially overlapping with a range query, and$m$is the dimension number. Since$m$is usually$o(\sqrt{\log n})$, it is a sublinear time algorithm if$V=O(n)$, where$n$is the size of the input dataset,$V=\prod _{i=1}^{m}d_{i}$, and$d_{i}$is the number of distinct values on the$i$-th dimension of the dataset for$1\leq i\leq m$. Experimental results show that the multi-dimensional range filter has low false positive rate and good filtering efficiency. The proposed range query processing algorithm achieves at least 3$\sim$7 times improvement compared to the one-dimensional filter based algorithms on different datasets.

This article proposes algorithms for evaluating XPath queries over an XML tree that is partitioned horizontally and vertically, and is distributed across a number of sites. The key idea is based on partial evaluation: it is to send the whole query to each site that partially evaluates the query, in parallel, and sends the results as compact (Boolean) functions to a coordinator that combines these to obtain the result. This approach possesses the following performance guarantees. First, each site is visited at most twice for data-selecting XPath queries, and only once for Boolean XPath queries. Second, the network traffic is determined by the answer to the query, rather than the size of the tree. Third, the total computation is comparable to that of centralized algorithms on the tree stored in a single site, regardless of how the tree is fragmented and distributed. We also present a MapReduce algorithm for evaluating Boolean XPath queries, based on partial evaluation. In addition, we provide algorithms to evaluate XPath queries on very large XML trees, in a centralized setting. We show both analytically and empirically that our techniques are scalable with large trees and complex XPath queries. These results, we believe, illustrate the usefulness and potential of partial evaluation in distributed systems as well as centralized XML stores for evaluating XPath queries and beyond.