multiview_embedding: Multiview Embedding
In luke-a-rogers/pbsedm: An R package to implement some of the methods of empirical dynamic modelling

multiview_embedding

R Documentation

Multiview Embedding

Description

Take a multivariate data set containing variables through time, a response variable (the variable we care about, such as population number), and a set of lags that we wish to consider. Based on Ye and Sugihara (2016)'s description.

Usage

multiview_embedding(data, response, lags)

Arguments

`data`	[tibble()] or [data.frame()] with named [numeric()] columns
`response`	[character()] column name of the response variable in `data`
`lags`	[list()] of a named vector of lags for each explanatory variable.

Details

For all allowed lags, this function builds every possible state space reconstruction (Figure 1C in Ye and Sugihara), of all possible dimensions. So variable 1 with 0 lag, variable 1 with 0 lag and variable 2 with 0 lag, variable 1 with 0 lag and variable 2 with 1 lag, etc. up to variable 1 with all lag allowed from 'lags' and variable 2 with all lags allowed from 'lags'. TODO I feel that some combinations should be duplicated, in the sense that variable 1 with lag 1 and variable 2 with lag 2 is the same as variable 1 with lag 0 and variable 2 with lag 1 (i.e. if you have nothing with lag of 0 then you can shift everything), but this will reduce the data a little – look into as may end up keeping state space reconstructions that are essentially the same, just shifted in time. If there are $N$ total variable-lag combinations, then there should be $2^N - 1$ possible reconstructions (each one is either in or out, minus them all being out), but this may get reduced with what is described above.

This function calls 'single_view_embedding_for_sve()' (the 'for_sve' was just to distinguish from earlier functions), which creates the state space reconstruction, calculates the distances between points, makes predictions for all allowable focal times $t^*$ taking into account which neighbours should be candidates for nearest neighbours - predictions are just from the single nearest neighbour (as per Y&S, rather than full Simplex), calculate predicted values of the response variable both scaled and unscaled. Here we will calculate metrics of the fit, based on just the response variable (as that is what we are interested in), and pick the best performing ones - the square root of the total number of reconstructions, as per Y&S. Then use the average of those to make the actual forecast for the time step after the data.

Returns **