Title: TailorPiece: Tailoring Linear Models for Joint Representation
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
Keywords: Piecewise Linear Approximation (PLA), lossy compression, time series, TailorPiece, compression ratio

Abstract: The need to represent a long data series using a sequence of line segments abiding by a maximum error threshold arises in various domains. This problem, known as Piecewise Linear Approximation (PLA), has a long history and has recently gained attention with the rise of applications dealing with time-stamped data. State-of-the-art PLA methods achieve space savings over lossless compression techniques with tolerable precision loss by quantizing starting points and representing similar line segments jointly. However, these methods do not tailor line segments for their eventual joint representation and do not minimize the number of segments either. In this paper, we present TailorPiece, a suite of algorithms for lossy PLA-based compression that explicitly tailor linear segments for both small sequence length and joint representation under a given error threshold and starting-value quantization. Our first algorithm, TailorPieceDP, optimizes a mergeability criterion of PLA segment descriptions; in a degenerate form, it reduces to an algorithm that represents the data series by the minimum number of PLA segments. Our second algorithm, TailorPieceGD, greedily selects the endpoint of each PLA segment within a tunable search space that allows the subsequent segment to extend farther, thereby balancing compression and runtime. Through experimentation, we show that TailorPieceDP achieves improvements of up to 34% over prior art in compression ratio and TailorPieceGD gains similar savings with a runtime reduced by two orders of magnitude.

TL;DR: We introduce algorithms for lossy PLA compression of time series that tailor segments for joint representation.