stream (version 1.1-1)

DSC_Sample: Extract a Fixed-size Sample from a Data Stream

Description

Extracts a sample form a data stream using Reservoir Sampling. The sample is stored as a set of micro-clusters to be compatible with other data DSC stream clustering algorithms.

Usage

DSC_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 DSC_Sample (subclass of DSC, DSC_R, DSC_Micro).

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

DSC, DSC_Micro

Examples

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

sample <- DSC_Sample(k=20)
update(sample, stream, 500)
sample

# plot micro-clusters
plot(sample, stream)

# reclustering (Kmeans is sufficient because DSC_Sample does not return weights)
kmeans <- DSC_Kmeans(3)
recluster(kmeans, sample)
plot(kmeans, stream, type="both")

# sample from an evolving stream
stream <- DSD_Benchmark(1)
sample <- DSC_Sample(k=100)
update(sample, stream, 2000)
plot(sample, stream)
# Note: the clusters move from left to right and the sample keeps many 
# outdated points
  
# use a biased sample to keep more recent data points 
stream <- DSD_Benchmark(1)
sample <- DSC_Sample(k=100, biased=TRUE)
update(sample, stream, 2000)
plot(sample, stream)