D-Stream Data Stream Clustering Algorithm

Micro Clusterer with reclustering. Implements the grid-based D-Stream data stream clustering algorithm.

Usage

DSC_DStream(
  formula = NULL,
  gridsize,
  lambda = 0.001,
  gaptime = 1000L,
  Cm = 3,
  Cl = 0.8,
  attraction = FALSE,
  epsilon = 0.3,
  Cm2 = Cm,
  k = NULL,
  N = 0
)

get_attraction(x, relative = FALSE, grid_type = "dense", dist = FALSE)

# S3 method for class 'DSC_DStream'
plot(
  x,
  dsd = NULL,
  n = 500,
  type = c("auto", "micro", "macro", "both"),
  grid = FALSE,
  grid_type = "used",
  assignment = FALSE,
  ...
)

DSOutlier_DStream(
  formula = NULL,
  gridsize,
  lambda = 0.001,
  gaptime = 1000L,
  Cm = 3,
  Cl = 0.8,
  outlier_multiplier = 2
)

Arguments

formula: NULL to use all features in the stream or a model formula of the form ~ X1 + X2 to specify the features used for clustering. Only ., + and - are currently supported in the formula.
gridsize: a single number defining the size of grid cells in each dimension. For example for 3d data, the cells would be of size gridsize x gridsize x gridsize.
lambda: Fading constant used function to calculate the decay factor \(2^-lambda\). (Note: in the paper the authors use lamba to denote the decay factor and not the fading constant!)
gaptime: sporadic grids are removed every gaptime number of points.
Cm: density threshold used to detect dense grids as a proportion of the average expected density (Cm > 1). The average density is given by the total weight of the clustering over \(N\), the number of grid cells.
Cl: density threshold to detect sporadic grids (0 > Cl > Cm). Transitional grids have a density between Cl and Cm.
attraction: compute and store information about the attraction between adjacent grids. If TRUE then attraction is used to create macro-clusters, otherwise macro-clusters are created by merging adjacent dense grids.
epsilon: overlap parameter for attraction as a proportion of gridsize.
Cm2: threshold on attraction to join two dense grid cells (as a proportion on the average expected attraction). In the original algorithm Cm2 is equal to Cm.
k: alternative to Cm2 (not in the original algorithm). Create k clusters based on attraction. In case of more than k unconnected components, closer groups of MCs are joined.
N: Fix the number of grid cells used for the calculation of the density thresholds with Cl and Cm. If N is not given (0) then the algorithm tries to determine N from the data. Note that this means that N potentially increases over time and outliers might produce an extremely large value which will lead to a sudden creation of too many dense micro-clusters. The original paper assumed that N is known a priori.
x: DSC_DStream object to get attraction values from.
relative: calculates relative attraction (normalized by the cluster weight).
grid_type: the attraction between what grid types should be returned?
dist: make attraction symmetric and transform into a distance.
dsd: a DSD data stream object.
n: number of plots taken from dsd to plot.
type: Plot micro clusters (type = "micro"), macro clusters (type = "macro"), both micro and macro clusters (type = "both"), outliers(type = "outliers"), or everything together (type = "all"). type = "auto" leaves to the class of DSC to decide.
grid: logical; show the D-Stream grid instead of circles for micro-clusters.
assignment: logical; show assignment area of micro-clusters.
...: further argument are passed on.
outlier_multiplier: multiplier for assignment grid width to declare outliers.

Value

An object of class DSC_DStream (subclass of DSC, DSC_R, DSC_Micro).

Details

D-Stream creates an equally spaced grid and estimates the density in each grid cell using the count of points falling in the cells. Grid cells are classified based on density into dense, transitional and sporadic cells. The density is faded after every new point by a factor of \(2^{-lambda}\). Every gaptime number of points sporadic grid cells are removed.

For reclustering D-Stream (2007 version) merges adjacent dense grids to form macro-clusters and then assigns adjacent transitional grids to macro-clusters. This behavior is implemented as attraction = FALSE.

The 2009 version of the algorithm adds the concept of attraction between grids cells. If attraction = TRUE is used then the algorithm produces macro-clusters based on attraction between dense adjacent grids (uses Cm2 which in the original algorithm is equal to Cm).

For many functions (e.g., get_centers(), plot()), D-Stream adds a parameter grid_type with possible values of "dense", "transitional", "sparse", "all" and "used". This only returns the selected type of grid cells. "used" includes dense and adjacent transitional cells which are used in D-Stream for reclustering. For plot() D-Stream also provides extra parameters "grid" and "grid_type" to show micro-clusters as grid cells (density represented by gray values).

DSOutlier_DStream classifies points that do not fall into a dense grid cell as outlier/noise. Parameter outlier_multiplier specifies how far the point needs to be away from a dense cell to be classified as an outlier by multiplying the grid size.

Note that DSC_DStream currently cannot be saved to disk using save() or saveRDS(). This functionality will be added later!

References

Yixin Chen and Li Tu. 2007. Density-based clustering for real-time stream data. In Proceedings of the 13th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD '07). ACM, New York, NY, USA, 133-142.

Li Tu and Yixin Chen. 2009. Stream data clustering based on grid density and attraction. ACM Transactions on Knowledge Discovery from Data, 3(3), Article 12 (July 2009), 27 pages.

Author

Michael Hahsler

Examples

stream <- DSD_BarsAndGaussians(noise = .05)
plot(stream)


dstream1 <- DSC_DStream(gridsize = 1, Cm = 1.5)
update(dstream1, stream, 1000)
dstream1
#> D-Stream 
#> Class: DSC_DStream, DSC_Micro, DSC_R, DSC 
#> Number of micro-clusters: 45 
#> Number of macro-clusters: 5 

# micro-clusters (these are "used" grid cells)
nclusters(dstream1)
#> [1] 45
head(get_centers(dstream1))
#>      x    y
#> 1 -5.5  0.5
#> 2 -5.5  1.5
#> 3 -4.5 -1.5
#> 4 -4.5 -0.5
#> 5 -4.5  0.5
#> 6 -4.5  1.5

# plot (DStream provides additional grid visualization)
plot(dstream1, stream)

plot(dstream1, stream, grid = TRUE)


# look only at dense grids
nclusters(dstream1, grid_type = "dense")
#> [1] 32
plot(dstream1, stream, grid = TRUE, grid_type = "dense")


# look at transitional and sparse cells
plot(dstream1, stream, grid = TRUE, grid_type = "transitional")

plot(dstream1, stream, grid = TRUE, grid_type = "sparse")


### Macro-clusters
# standard D-Stream uses reachability
nclusters(dstream1, type = "macro")
#> [1] 5
get_centers(dstream1, type = "macro")
#>           x         y
#> 1 -2.834756  1.255131
#> 2 -4.192024 -1.186004
#> 3 -1.919891 -1.287899
#> 4  2.717368 -1.705919
#> 5  3.171841  1.941804
plot(dstream1, stream, type = "macro")

evaluate_static(dstream1, stream, measure = "crand", type = "macro")
#> Evaluation results for macro-clusters.
#> Points were assigned to micro-clusters.
#> 
#>     cRand 
#> 0.8633109 
#> attr(,"type")
#> [1] "macro"
#> attr(,"assign")
#> [1] "micro"

# use attraction for reclustering
dstream2 <- DSC_DStream(gridsize = 1, attraction = TRUE, Cm = 1.5)
update(dstream2, stream, 1000)
dstream2
#> D-Stream 
#> Class: DSC_DStream, DSC_Micro, DSC_R, DSC 
#> Number of micro-clusters: 51 
#> Number of macro-clusters: 2 

plot(dstream2, stream, grid = TRUE)

evaluate_static(dstream2, stream, measure = "crand", type = "macro")
#> Evaluation results for macro-clusters.
#> Points were assigned to micro-clusters.
#> 
#>     cRand 
#> 0.5783599 
#> attr(,"type")
#> [1] "macro"
#> attr(,"assign")
#> [1] "micro"