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

Description Usage Arguments Details Value Author(s) References See Also Examples

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.

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

`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. Minimize the differences of lag = `freq`
`sumFirst`	minimize the sum of first `freq` elements in time series

TRMF_seasonal(freq=N) fits a lag N random walk. For monthly data, use freq=12, for quarterly data, freq=4. If sumFirst = TRUE, the sum of the first freq elements in the latent time series are also minimized.This can be used to help force the seasonal component to vary around a zero mean.

Returns an updated object of class TRMF.

Chad Hammerquist

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

# 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)
obj = TRMF_seasonal(obj,numTS=1,freq=12,lambdaD=5)
out = train(obj)
plot(out)