Package 'prim'

Patient Rule Induction Method (PRIM)

Description

PRIM for bump hunting for high-dimensional regression-type data.

Details

The data are $(\bold{X}_1, Y_1), \dots, (\bold{X}_n, Y_n)$ where $\bold{X}_i$ is d-dimensional and $Y_i$ is a scalar response. We wish to find the modal (and/or anti-modal) regions in the conditional expectation $m(\bold{x}) = \bold{E} (Y | \bold{x}).$ PRIM is a bump-hunting technique introduced by Friedman & Fisher (1999), taken from data mining. PRIM estimates are a sequence of nested hyper-rectangles (boxes).

For an overview of this package, see vignette("prim") for PRIM for bump hunting and estimating highest density difference regions.

Author(s)

Tarn Duong <[email protected]>

References

Friedman, J.H. & Fisher, N.I. (1999) Bump-hunting for high dimensional data. Statistics and Computing 9, 123–143.

Hyndman, R.J. (1996) Computing and graphing highest density regions. American Statistician 50, 120–126.

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PRIM plot for multivariate data

Description

PRIM plot for multivariate data.

Usage

## S3 method for class 'prim'
plot(x, splom=TRUE,  ...)

Arguments

x	object of class prim
splom	flag for plotting 3-d data as scatter plot matrix. Default is TRUE.
...	other graphics parameters

Details

The function headers are

  ## bivariate
  x, col, xlim, ylim, xlab, ylab, add=FALSE, add.legend=FALSE, cex.legend=1, 
  pos.legend, lwd=1, border, col.vec=c("blue", "orange"), alpha=1, ...)
  
  ## trivariate
  plot(x, xlim, ylim, zlim, xlab, ylab, zlab, col.vec=c("blue","orange"), 
  alpha=1, theta=30, phi=40, d=4, ...)
  
  ## d-variate
  plot(x, xmin, xmax, xlab, ylab, x.pt, m, col.vec=c("blue","orange"), 
  alpha=1, ...)

The arguments are

add.legend

flag for adding legend (2-d plot)

pos.legend

(x,y) co-ordinates for legend (2-d plot)

cex.legend

cex graphics parameter for legend (2-d plot)

col.vec

vector of plotting colours, one for each box

xlab,ylab,zlab,xlim,ylim,zlim,add,lwd,alpha,phi,theta,d

usual graphics parameters

xmin,xmax

vector of minimum and maximum axis plotting values for scatter plot matrix

x.pt

data set to plot (other than x)

Value

Plot of 2-dim PRIM is a set of nested rectangles. Plot of 3-dim PRIM is a scatter point cloud. Plot of d-dim PRIM is a scatter plot matrix. The scatter plots indicate which points belong to which box.

See Also

prim.box, predict.prim

Examples

## see ?prim.box for bivariate example
## trivariate example
data(quasiflow)
qf <- quasiflow[1:1000,1:3]
qf.label <- quasiflow[1:1000,4]
thr <- c(0.25, -0.3)
qf.prim <- prim.box(x=qf, y=qf.label, threshold=thr, threshold.type=0)
plot(qf.prim, splom=FALSE, colkey=FALSE, alpha=0.5, pch=16)

## high-dimensional example
data(Boston, package="MASS")
x <- Boston[,c(3,5:6,11,13)]
y <- Boston[,1]
boston.prim <- prim.box(x=x, y=y, threshold.type=1)
plot(boston.prim, x.pt=x, alpha=0.2, pch=16)

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S3 methods for PRIM for multivariate data

Description

S3 methods PRIM for multivariate data.

Usage

## S3 method for class 'prim'
predict(object, newdata, y.fun.flag=FALSE, ...)
## S3 method for class 'prim'
summary(object, ..., print.box=FALSE)

Arguments

object	object of class prim
newdata	data matrix
y.fun.flag	flag to return y value of PRIM box rather than box label. Default is FALSE.
print.box	flag to print out limits of all PRIM boxes. Default is FALSE.
...	other parameters

Details

–The predict method returns the value of PRIM box number in which newdata are located.

–The summary method displays a table with three columns: box-fun is the y value, box-mass is the mass of the box, threshold.type is the threshold direction indicator: 1 = ">= threshold", -1 = "<=threshold". Each box corresponds to a row. The second last row marked with an asterisk is the box which collates the remaining data points not belonging to a specific PRIM box. The final row is an overall summary, i.e. box-fun is the overall mean of y and box-mass is 1.

Examples

data(quasiflow)
qf <- quasiflow[1:1000,1:2]
qf.label <- quasiflow[1:1000,3]*quasiflow[1:1000,4]

qf.prim <- prim.box(x=qf, y=qf.label, threshold=c(0.3, -0.1), threshold.type=0)
summary(qf.prim)
predict(qf.prim, newdata=c(0.6,0.2))

## using median insted of mean for the response y
qf.prim2 <- prim.box(x=qf, y=qf.label, threshold=c(0.5, -0.2),
  threshold.type=0, y.fun=median)
summary(qf.prim2)
predict(qf.prim2, newdata=c(0.6,0.2))

---

PRIM for multivariate data

Description

PRIM for multivariate data.

Usage

prim.box(x, y, box.init=NULL, peel.alpha=0.05, paste.alpha=0.01,
     mass.min=0.05, threshold, pasting=TRUE, verbose=FALSE,
     threshold.type=0, y.fun=mean)

prim.hdr(prim, threshold, threshold.type, y.fun=mean)
prim.combine(prim1, prim2, y.fun=mean)

Arguments

x	matrix of data values
y	vector of response values
y.fun	function applied to response y. Default is mean.
box.init	initial covering box
peel.alpha	peeling quantile tuning parameter
paste.alpha	pasting quantile tuning parameter
mass.min	minimum mass tuning parameter
threshold	threshold tuning parameter(s)
threshold.type	threshold direction indicator: 1 = ">= threshold", -1 = "<= threshold", 0 = ">= threshold[1] & <= threshold[2]"
pasting	flag for pasting
verbose	flag for printing output during execution
prim, prim1, prim2	objects of type prim

Details

The data are $(\bold{X}_1, Y_1), \dots, (\bold{X}_n, Y_n)$ where $\bold{X}_i$ is d-dimensional and $Y_i$ is a scalar response. PRIM finds modal (and/or anti-modal) regions in the conditional expectation $m(\bold{x}) = \bold{E} (Y | \bold{x}).$

In general, $Y_i$ can be real-valued. See vignette("prim"). Here, we focus on the special case for binary $Y_i$. Let $Y_i$ = 1 when $\bold{X}_i \sim F^+$; and $Y_i$ = -1 when $\bold{X}_i \sim F^-$ where $F^+$ and $F^-$ are different distribution functions. In this set-up, PRIM finds the regions where $F^+$ and $F^-$ are most different.

The tuning parameters peel.alpha and paste.alpha control the ‘patience’ of PRIM. Smaller values involve more patience. Larger values less patience. The peeling steps remove data from a box till either the box mean is smaller than threshold or the box mass is less than mass.min. Pasting is optional, and is used to correct any possible over-peeling. The default values for peel.alpha, paste.alpha and mass.min are taken from Friedman & Fisher (1999).

The type of PRIM estimate is controlled threshold and threshold.type:

threshold.type=1

search for {$m(\bold{x}) \geq$ threshold}.

threshold.type=-1

search for {$m(\bold{x}) \leq$ threshold}.

threshold.type=0

search for both {$m(\bold{x}) \geq$ threshold[1]} and {$m(\bold{x}) \leq$ threshold[2]}.

There are two ways of using PRIM. One is prim.box with pre-specified threshold(s). This is appropriate when the threshold(s) are known to produce good estimates.

On the other hand, if the user doesn't provide threshold values then prim.box computes box sequences which cover the data range. These can then be pruned at a later stage. prim.hdr allows the user to specify many different threshold values in an efficient manner, without having to recomputing the entire PRIM box sequence. prim.combine can be used to join the regions computed from prim.hdr. See the examples below.

Value

– prim.box produces a PRIM estimate, an object of type prim, which is a list with 8 fields:

x	list of data matrices
y	list of response variable vectors
y.mean	list of vectors of box mean for y
box	list of matrices of box limits (first row = minima, second row = maxima)
mass	vector of box masses (proportion of points inside a box)
num.class	total number of PRIM boxes
num.hdr.class	total number of PRIM boxes which form the HDR
ind	threshold direction indicator: 1 = ">= threshold", -1 = "<=threshold"

The above lists have num.class fields, one for each box.

– prim.hdr takes a prim object and prunes it using different threshold values. Returns another prim object. This is much faster for experimenting with different threshold values than calling prim.box each time.

– prim.combine combines two prim objects into a single prim object. Usually used in conjunction with prim.hdr. See examples below.

Examples

data(quasiflow)
qf <- quasiflow[1:1000,1:2]
qf.label <- quasiflow[1:1000,4]

## using only one command
thr <- c(0.25, -0.3)
qf.prim1 <- prim.box(x=qf, y=qf.label, threshold=thr, threshold.type=0)

## alternative - requires more commands but allows more control
## in intermediate stages
qf.primp <- prim.box(x=qf, y=qf.label, threshold.type=1)
   ## default threshold too low, try higher one

qf.primp.hdr <- prim.hdr(prim=qf.primp, threshold=0.25, threshold.type=1)
qf.primn <- prim.box(x=qf, y=qf.label, threshold=-0.3, threshold.type=-1)
qf.prim2 <- prim.combine(qf.primp.hdr, qf.primn)

plot(qf.prim1, alpha=0.2)   ## orange=x1>x2, blue x2<x1

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Quasi flow cytometry data

Description

This data set is simulated data from two normal mixture distrbutions, mimicking a flow cytometry data set. It contains 10000 observations from an HIV+ patient and 10000 observations an HIV- patient.

Usage

data(quasiflow)

Format

quasiflow is a matrix with 6 columns and 20000 rows. Each row corresponds to measurements for one cell. The first 5 columns are flow cytometric measurements and the sixth column is a binary indicator, with 1 = HIV+ and -1 = HIV-.

Source

Generated by package author.

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