TRMF_seasonal: Add seasonal regularization model to a TRMF object In TRMF: Temporally Regularized Matrix Factorization

 TRMF_seasonal R Documentation

Add seasonal regularization model to a TRMF object

Description

Creates a regularization scheme that favors seasonally varying solutions and adds it to a TRMF object. In matrix optimization form, it adds the following term to the TRMF cost function: `R(x) = lambdaD^2||w(DX_s)||^2 + lambdaA^2||X_s||^2` where `X_s` is sub-set of the Xm matrix controlled by this model and D is a (with a lag of freq) finite difference matrix (or rolling sum matrix, see details).

Usage

``````TRMF_seasonal(obj,numTS = 1,freq = 12,sumFirst=FALSE,lambdaD=1,lambdaA=0.0001,weight=1)
``````

Arguments

 `obj` A TRMF object `numTS` number of latent time series in this model `lambdaD` regularization parameter for temporal constraint matrix `lambdaA` regularization parameter to apply simple L2 regularization to this time series model `weight` optional vector of weights to weight constraints, i.e. R(x) = lambdaD^2*||w*(D%*%X)||^2 `freq` The frequency of the seasonal time series model. `sumFirst` Minimize the rolling sum of length `freq` instead of a lagged finite difference.

Details

`TRMF_seasonal(freq=N)` fits a lag N random walk. For monthly data, use freq=12, for quarterly data, freq=4. If `sumFirst = TRUE`, (called this for legacy reasons), a different regularization matrix is used which minimizes a rolling sum of length `freq` in the latent time series. This can be useful to prevent drift and force the seasonal component to vary around a zero mean.

Value

Returns an updated object of class TRMF.

Note

Unlike `TRMF_columns()`, these lambdas are squared in the code.

References

Yu, Hsiang-Fu, Nikhil Rao, and Inderjit S. Dhillon. "High-dimensional time series prediction with missing values." arXiv preprint arXiv:1509.08333 (2015).

`create_TRMF`, `TRMF_columns`,`TRMF_simple`, `TRMF_trend`

Examples

``````# create test data
tm = 3*poly(x = (-20:20)/10,degree=3)
sm = diffinv(rnorm(29,0,.1),lag=12,xi=(-5:6)/6)
xm = cbind(sm,tm)
fm = matrix(runif(40),4,10)
Am = xm%*%fm+rnorm(410,0,.1)

# create model
obj = create_TRMF(Am)
obj = TRMF_columns(obj,reg_type ="interval")
obj = TRMF_trend(obj,numTS=3,order=2)