wavethresh (version 4.7.3)

makewpstDO: Help page for a function

Description

Takes two time series: one a real-valued discrete-time time series, timeseries, the other, groups, a time series containing factor levels. This function performs a discriminant analysis of groups on a subset of the best-correlating nondecimated wavelet packets of timeseries

Usage

makewpstDO(timeseries, groups, filter.number=10, family="DaubExPhase",
	mincor=0.69999999999999996)

Value

An object of class wpstDO. This is a list containing the following components.

BPd

Object returned from the BMdiscr function. Contains the reduced matrix and the discriminant object

BP

Object returned from the Best1DCols function, essentially the reduced matrix and the groups variable.

filter

The details of the wavelet filter used. This is used if the other components are used to perform discrimination on new data one needs to know what wavelet was used to perform the original nondecimated wavelet packet transform.

Arguments

timeseries

The time series which is the `dependent variable', ie discrimination will be performed on the variables extracted from the non-decimated wavelet packet transform of this time series

groups

The factor levels as a time series

filter.number

The smoothness of the wavelet involved in the nondecimated wavelet packet transform. See filter.select

family

The wavelet family, see filter.select

mincor

Variables from the nondecimated wavelet packet transform with correlations less than this argument will be discarded in the first pass, and not considered as possible useful discriminants

Author

G P Nason

Details

This function implements the `discrimination' version of the "Wavelet packet transfer function modelling of nonstationary series" by Guy Nason and Theofanis Sapatinas, Statistics and Computing, 12, 45-56.

The function first takes the non-decimated wavelet packet transform of timeseries using the wpst function. Then the set of nondecimated wavelet packets is put into matrix form using the wpst2discr function. The Best1DCols function selects those variables from the matrix whose correlation with the groups time series is greater than mincor. The selected variables are put into a reduced matrix.

The next step, BMdiscr, performs a linear discriminant analysis of the groups values onto the reduced matrix. In principle, one could have carried out a discriminant analysis using the full matrix of all the packets, but the problem is not well-conditioned and computationally efficient. The strategy adopted by Nason and Sapatinas is to do a "first pass" to select a large number of "likely" variables that might contribute something to discrimination, and then carry out a "second pass" which performs a more detailed analysis to jointly determine which variables are the key ones for discrimination.

Note, using the discriminant model developed here, it is possible to use future values of timeseries and the model to predict future values of groups. See example below.

See Also

basisplot.BP, Best1DCols, BMdiscr, wpst, wpst2discr, wpstCLASS

Examples

#
# Use BabySS and BabyECG data for this example.
#
# Want to predict future values of BabySS from future values of BabyECG
#
# Build model on first 256 values of both
#
data(BabyECG)
data(BabySS)
BabyModel <- makewpstDO(timeseries=BabyECG[1:256], groups=BabySS[1:256],
	mincor=0.5)
#
# The results (ie print out answer)
#BabyModel
#Stationary wavelet packet discrimination object
#Composite object containing components:[1] "BPd"    "BP"     "filter"
#Fisher's discrimination: done
#BP component has the following information
#BP class object. Contains "best basis" information
#Components of object:[1] "nlevelsWT"     "BasisMatrix" "level"       "pkt"         "basiscoef"
#[6] "groups"
#Number of levels  8
#List of "best" packets
#Level id Packet id Basis coef
#[1,]        4         0  0.7340580
#[2,]        5         0  0.6811251
#[3,]        6         0  0.6443167
#[4,]        3         0  0.6193434
#[5,]        7         0  0.5967620
#[6,]        0         3  0.5473777
#[7,]        1        53  0.5082849
#
# You can plot the select basis graphically using
#
if (FALSE) basisplot(BabyModel$BP)
#
# An interesting thing are the final "best" packets, these form the
# "reduced" matrix, and the final discrimination is done on this
# In this case 7 wavelet packets were identified as being good for
# univariate high correlation.
#
# In the second pass lda analysis, using the reduced matrix, the following
# turns up as the best linear discriminant vectors
#
# The discriminant variables can be obtained by typing
#BabyModel$BPd$dm$scaling
#LD1        LD2
#[1,] 5.17130434  1.8961807
#[2,] 1.56487144 -3.5025251
#[3,] 1.69328553  1.1585477
#[4,] 3.63362324  8.4543247
#[5,] 0.15202947 -0.4530523
#[6,] 0.35659009 -0.3850318
#[7,] 0.09429836 -0.1281240
#
#
# Now, suppose we get some new data for the BabyECG time series.
# For the purposes of this example, this is just the continuing example
# ie BabyECG[257:512]. We can use our new discriminant model to predict
# new values of BabySS
#
BabySSpred <- wpstCLASS(newTS=BabyECG[257:512], BabyModel)
#
# Let's look at the first 10 (eg) values of this prediction
#
#BabySSpred$class[1:10]
#[1] 4 4 4 4 4 4 4 4 4 4
#Good. Now let's look at what the "truth" was:
#BabySS[257:267]
#[1] 4 4 4 4 4 4 4 4 4 4
#Good. However, the don't agree everywhere, let's do a cross classification
#between the prediction and the truth.
#
#> table(tmp2$class, BabySS[257:512])
#
#      1   2   3   4
#  1   4   1   1   0
#  2 116   0  23   3
#  4   2  12   0  94
#
#So class 3 and 4 agree pretty much, but class 1 has been mispredicted at class
#2 a lot.