cep.lda: Discriminant Analysis of Time Series in the Presence of...

In CepLDA: Discriminant Analysis of Time Series in the Presence of Within-Group Spectral Variability

Description

The main program.

Usage

cep.lda(y,x,xNew,L,mcep,nw,k,cv,tol)

Arguments

y	n-vector indicating group membership of training time series.
x	N by n matrix containing n training time series each with length N.
xNew	N by nNew matrix, containing nNew time series whose memberships are predicted.
L	Number of cepstral coefficients used in the lda. If FALSE, cross-validation is used for the data driven selection of L. Default is FALSE.
mcep	Maximum number of cepstral coefficients considerd. Default is set to 10.
nw	Width of tapers used in multitaper spectral estimation. Default is set to 4.
k	Number of tapers used in multitaper spectral estimation. Default is set to 7.
cv	If TRUE, returns results (classes and posterior probabilities) for leave-one-out cross-validation. Note that, if the prior is estimated, the proportions in the whole dataset are used. As with the standard lda function, if used, prediction on a test data set cannot be done and weight functions are not produced (simular to the predict.lda). Default is FALSE.
tol	Tolerance to decide if a matrix is singular; it will reject variables and linear combinations of unit-variance variables whose variance is less than tol^2.

Value

List with 5 elements

C.lda	lda output on the cepstral scale. Similar to output of lda(MASS) function.
cep.data	Data frame containing cepstral coefficients and group information from training data.
Lopt	Number of cepstral coefficients used.
lspec	Estimated log-spectral weight functions.
predict	Results of classification. If external data xNew is supplied, these data are classified. If not, biased classification of the training data x is returned. For unbiased leave-out-one cross-validated classification of training data, use cv=TRUE.

Author(s)

Zeda Li <[e-mail]>; Robert Krafty <[e-mail]>

References

Krafty, RT (2016) Discriminant Analysis of Time Series in the Presence of Within-Group Spectral Variability. Journal of Time Series Analysis

See Also

predict.ceplda, plot.ceplda, print.ceplda, Lopt.get

Examples

## Simulate training data
nj = 50  #number of series in training data
N = 500  #length of time series
traindata1 <- r.cond.ar2(N=N,nj=nj,r.phi1=c(.01,.7),r.phi2=c(-.12,-.06),r.sig2=c(.3,3))
traindata2 <- r.cond.ar2(N=N,nj=nj,r.phi1=c(.5,1.2),r.phi2=c(-.36,-.25),r.sig2=c(.3,3))
traindata3 <- r.cond.ar2(N=N,nj=nj,r.phi1=c(.9,1.5),r.phi2=c(-.56,-.75),r.sig2=c(.3,3))
train <- cbind(traindata1$X,traindata2$X,traindata3$X)
y <- c(rep(1,nj),rep(2,nj),rep(3,nj))

## Fit the discriminant analysis
fit <- cep.lda(y,train)
fit  #displays group means and cepstral weight functions

## Discriminant plot
plot(fit)

## Plot log-spectral weights
par(mfrow=c(1,2))
plot(fit$lspec$frq, fit$lspec$dsc[,1],type='l',xlab="frequency", ylab="log-spectral weights")
plot(fit$lspec$frq, fit$lspec$dsc[,2],type='l',xlab="frequency", ylab="log-spectral weights")

## Bias classification of training data
mean(fit$predict$class == y) #classifictaion rate
table(y,fit$predict$class)

## Fit the discriminant analysis while classifing training data via cross-validation
fit.cv <- cep.lda(y,train, cv=TRUE)
mean(fit.cv$predict$class == y) #classifictaion rate
table(y,fit.cv$predict$class)

## Simulate test data
testdata1 <- r.cond.ar2(N=N,nj=nj,r.phi1=c(.01,.7),r.phi2=c(-.12,-.06),r.sig2=c(.3,3))
testdata2 <- r.cond.ar2(N=N,nj=nj,r.phi1=c(.5,1.2),r.phi2=c(-.36,-.25),r.sig2=c(.3,3))
testdata3 <- r.cond.ar2(N=N,nj=nj,r.phi1=c(.9,1.5),r.phi2=c(-.56,-.75),r.sig2=c(.3,3))
test <- cbind(testdata1$X,testdata2$X,testdata3$X)
yTest <- c(rep(1,nj),rep(2,nj),rep(3,nj))

## Fit discriminant analysis and classify new data
fit.pre <- cep.lda(y,train,test)
mean(fit.pre$predict$class == y)
table(yTest,fit.pre$predict$class)

Example output

Loading required package: astsa
Loading required package: MASS
Loading required package: class
Loading required package: multitaper
Optimal L selected: 
[1] 7

Linear Discriminat Analysis results: 
Call:
lda(b, data = D.hat0, CV = FALSE, tol = tol)

Prior probabilities of groups:
        1         2         3 
0.3333333 0.3333333 0.3333333 

Group means:
         C0        C1           C2           C3           C4           C5
1 0.3423284 0.4795663 -0.022610659 -0.005007833 -0.012871940 -0.004088972
2 0.1570039 1.2373639  0.113795715 -0.047083614 -0.005310349  0.003602583
3 0.2711212 1.7417336 -0.006678723 -0.408506567 -0.350204275 -0.163858097
             C6           C7
1  0.0007526505 -0.005135245
2 -0.0095896052 -0.007464212
3 -0.0095181663  0.058085390

Coefficients of linear discriminants:
           LD1       LD2
C0  0.03330297  0.138069
C1  4.61036968 -4.056601
C2 -1.81696548  4.503829
C3 -6.88861108 -1.830867
C4 -3.79847338 -8.748704
C5 -1.11768995 -4.602806
C6 -1.63522831  3.158840
C7  0.76658152  3.080357

Proportion of trace:
   LD1    LD2 
0.9345 0.0655 
[1] 0.9866667
   
y    1  2  3
  1 48  2  0
  2  0 50  0
  3  0  0 50
[1] 0.9866667
   
y    1  2  3
  1 48  2  0
  2  0 50  0
  3  0  0 50
[1] 0.98
     
yTest  1  2  3
    1 47  3  0
    2  0 50  0
    3  0  0 50

CepLDA documentation built on May 1, 2019, 6:50 p.m.