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Has anyone attempted Principal component analysis on time series and acceleration data(ie. data from accelerometer and sensors) and tried compressing it as well as regenerating back the data with minimum error?

I wanted to know if this is possible using PCA. Kindly suggest alternate methods available to compress and regenrate my data.

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PCA doesn't really make sense for a time series if it is left as a time series:

There are times when its useful to aggregate time series data into a rectangular representation in order to gain insight into interesting aspects of the data. This is a feature engineering where the time series provides lots of the features. For instance, you can create features for 'minute of hour', 'hour of day', 'morning', 'afternoon','evening', 'day of week', 'day of month', 'week of month', 'week of year', 'season', ... You can even join this data with other data, like historical weather data or economic index, to see how daily temperature or economics affect your phenomenon. In these cases you could do all of this feature engineeting and then use PCA to find the most important features (radar plot) or simply to select the most important orthogonal features from the post PCA mashup (linear transformation).

Time Series Smothing:

There are a bunch of different methods to smooth and down-sample time series data. In this case, you are turning the quantized stochastic events and either turning them into regularly spaced data, or taking your already regularly spaced data and downsampling and smoothing it. Smoothing algorithms include Exponentially weighted moving average (EWMA) or Holt-Winters smoothing. Connor Johnson has a nice blog write-up on the these.

ARIMA is a more complete algorithm that includes smoothing, de-seasoning, and forecasting. It is very powerful, but takes some time to master.

Hope this helps!

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