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The generation and collection of big data series are becoming an integral part of many emerging applications in sciences, IoT, finance, and web applications among several others. The terabyte-scale of data series has motivated recent efforts to design fully distributed techniques for supporting operations such as approximate kNN similarity search, which is a building block operation in most analytics services on data series. Unfortunately, these techniques are heavily geared towards achieving scalability at the cost of sacrificing the results' accuracy. State-of-the-art systems report accuracy below 10% and 40%, respectively, which is not practical for many real-world applications. In this paper, we investigate the root problems in these existing techniques that limit their ability to achieve better a trade-off between scalability and accuracy. Then, we propose a framework, called CLIMBER, that encompasses a novel feature extraction mechanism, indexing scheme, and query processing algorithms for supporting approximate similarity search in big data series. For CLIMBER, we propose a new loss-resistant dual representation composed of rank-sensitive and ranking-insensitive signatures capturing data series objects. Based on this representation, we devise a distributed two-level index structure supported by an efficient data partitioning scheme. Our similarity metrics tailored for this dual representation enables meaningful comparison and distance evaluation between the rank-sensitive and ranking-insensitive signatures. Finally, we propose two efficient query processing algorithms, CLIMBER-kNN and CLIMBER-kNN-Adaptive, for answering approximate kNN similarity queries. Our experimental study on real-world and benchmark datasets demonstrates that CLIMBER, unlike existing techniques, features results' accuracy above 80% while retaining the desired scalability to terabytes of data., Comment: 16 pages, 14 figures, 1 table