Sampling from a Data Stream (Data Stream Operator)

Extracts a sample form a data stream using Reservoir Sampling.

Usage

DSAggregate_Sample(k = 100, biased = FALSE)

Arguments

k

the number of points to be sampled from the stream.

biased

if FALSE then a regular (unbiased) reservoir sampling is used. If true then the sample is biased towards keeping more recent data points (see Details section).

Value

An object of class DSAggregate_Sample (subclass of DSAggregate).

Details

If biased = FALSE then the reservoir sampling algorithm by McLeod and Bellhouse (1983) is used. This sampling makes sure that each data point has the same chance to be sampled. All sampled points will have a weight of 1. Note that this might not be ideal for an evolving stream since very old data points have the same chance to be in the sample as newer points.

If bias = TRUE then sampling prefers newer points using the modified reservoir sampling algorithm 2.1 by Aggarwal (2006). New points are always added. They replace a random point in thre reservoir with a probability of reservoir size over k. This an exponential bias function of \(2^{-lambda}\) with \(lambda = 1 / k\).

References

Vitter, J. S. (1985): Random sampling with a reservoir. ACM Transactions on Mathematical Software, 11(1), 37-57.

McLeod, A.I., Bellhouse, D.R. (1983): A Convenient Algorithm for Drawing a Simple Random Sample. Applied Statistics, 32(2), 182-184.

Aggarwal C. (2006) On Biased Reservoir Sampling in the Presence of Stream Evolution. International Conference on Very Large Databases (VLDB'06). 607-618.

See also

Other DSAggregate: DSAggregate(), DSAggregate_Window()

Author

Michael Hahsler

Examples

set.seed(1500)

stream <- DSD_Gaussians(k = 3, noise = 0.05)

sample <- DSAggregate_Sample(k = 50)
update(sample, stream, 500)
sample
#> Reservoir samplingClass: DSAggregate_Sample, DSAggregate, DST 

head(get_points(sample))
#>             X1        X2 .class
#> 109 0.83291183 0.2829034      1
#> 474 0.03873609 0.7770021     NA
#> 499 0.90968289 0.4887009      2
#> 324 0.83677629 0.2078957      1
#> 297 0.94807296 0.5136577      2
#> 108 0.86037990 0.5448045      2

# apply k-means clustering to the sample (data without info columns)
km <- kmeans(get_points(sample, info = FALSE), centers = 3)
plot(get_points(sample, info = FALSE))
points(km$centers, col = "red", pch = 3, cex = 2)