Hi,

Prior work in signal processing and machine learning for time series problems (including the accelerometer signals) has strongly emphasised on regularly sampled and equal length time series signals, resulting in fewer methods that exist specifically for analysing irregularly sampled and particularly, extremely very few methods for unequal in length signals.

Irregularly sampled time signals: For analysing the irregularly sampled time series directly, many techniques have already been proposed for example spectral analysis [3, 4] and kernel-based methods [5]. These techniques have already been used for extracting causal structures, statistics from data in fields such as from astronomy [6, 7], palaeontology [5] and economics [8]. On the other hand irregular time series data are transformed into regularly spaced data through some form of interpolation. For supervised learning tasks such as classification tasks, this has the added advantage of enabling the time series to be equalised to a given length by sampling from the interpolated function, thereby enabling standard classification algorithms to be used.

Unequal length time signals: To tackle the problem of unequal length time series problem, we recently proposed a new machine learning regression algorithm known as the probabilistic broken-stick model [1].  Using a set of locally linear line segments, our  novel algorithm can model any complex, non-linear function catering  for both short term interpretability and long term flexibility of any any irregularly sampled/ unequal in length time series simultaneously. This article is now freely available for over a month (until 1st Jan 2018) and if you are interested, please find it here https://lnkd.in/e3-Wd6Y . This paper is also available on arxiv: https://arxiv.org/pdf/1612.01409.pdf

In an another paper [2], we proposed Gaussian process regression to make the unequal length time series equal in length for the supervised learning i.e., classification which is published in Machine learning for signal processing. The paper is also available on arxiv: https://arxiv.org/pdf/1605.05142.pdf

From references [1,2], you may find citations to other researchers' works that you may find interesting.

All the best

Santosh

References:

[1] Norman Poh, Santosh Tirunagari, Nicholas Cole, Simon de Lusignan, Probabilistic broken-stick model: A regression algorithm for irregularly sampled and unequal length data with application to eGFR, In Journal of Biomedical Informatics, Volume 76, 2017, Pages 69-77, ISSN 1532-0464, https://doi.org/10.1016/j.jbi.2017.10.006.

[2] Tirunagari, Santosh, Simon Bull, and Norman Poh. "Automatic classification of irregularly sampled time series with unequal lengths: A case study on estimated glomerular filtration rate." In Machine Learning for Signal Processing (MLSP), 2016 IEEE 26th International Workshop on, pp. 1-6. IEEE, 2016.

[3] Michael Schulz and Karl Stattegger, “Spectrum: Spectral analysis of unevenly spaced paleoclimatic time series,” Computers & Geosciences, vol. 23, no. 9, pp. 929–945, 1997.

[4] Petre Stoica, Prabhu Babu, and Jian Li, “New method of sparse parameter estimation in separable models and its use for spectral analysis of irregularly sampled data,” Signal Processing, IEEE Transactions on, vol. 59, no. 1, pp. 35–47, 2011.

[5] Kira Rehfeld, Norbert Marwan, Jobst Heitzig, and Jurgen ¨ Kurths, “Comparison of correlation analysis techniques for irregularly sampled time series,” Nonlinear Processes in Geophysics, vol. 18, no. 3, pp. 389–404, 2011.

[6] Piet Broersen, “Time series models for spectral analysis of irregular data far beyond the mean data rate,” Measurement Science and Technology, vol. 19, no. 1, pp. 14, 2008.

[7] C. Thiebaut and S. Roques, “Time-scale and time-frequency analyses of irregularly sampled astronomical time series,” EURASIP J. Appl. Signal Process., vol. 2005, pp. 2486–2499, 2005.

[8] Ulrich Muller, “Specially weighted moving averages with re- ¨ peated application of the ema operator,” 2000.