CpPewma function

Classic Processing Probabilistic-EWMA (PEWMA).

CpPewma calculates the anomalies of a dataset using classical processing based on the PEWMA algorithm. This algorithm is a probabilistic method of EWMA which dynamically adjusts the parameterization based on the probability of the given observation. This method produces dynamic, data-driven anomaly thresholds which are robust to abrupt transient changes, yet quickly adjust to long-term distributional shifts. See also OcpPewma, the optimized and faster function of the this function.

CpPewma(data, n.train = 5, alpha0 = 0.8, beta = 0.3, l = 3)

Arguments

• data: Numerical vector with training and test dataset.
• n.train: Number of points of the dataset that correspond to the training set.
• alpha0: Maximal weighting parameter.
• beta: Weight placed on the probability of the given observation.
• l: Control limit multiplier.

Returns

dataset conformed by the following columns:

• is.anomaly: 1 if the value is anomalous 0, otherwise.

• ucl: Upper control limit.

• lcl: Lower control limit.

Details

data must be a numerical vector without NA values. alpha0 must be a numeric value where 0 < alpha0 < 1. If a faster adjustment to the initial shift is desirable, simply lowering alpha0 will suffice. beta is the weight placed on the probability of the given observation. It must be a numeric value where 0 <= beta <= 1. Note that if beta equals 0, PEWMA converges to a standard EWMA. Finally l is the parameter that determines the control limits. By default, 3 is used.

Examples

## Generate data
set.seed(100)
n <- 180
x <- sample(1:100, n, replace = TRUE)
x[70:90] <- sample(110:115, 21, replace = TRUE)
x[25] <- 200
x[150] <- 170
df <- data.frame(timestamp = 1:n, value = x)

## Calculate anomalies
result <- CpPewma(
  data = df$value,
  n.train = 5,
  alpha0 = 0.8,
  beta = 0.1,
  l = 3
)

## Plot results
res <- cbind(df, result)
PlotDetections(res, title = "PEWMA ANOMALY DETECTOR")

References

M. Carter, Kevin y W. Streilein. Probabilistic reasoning for streaming anomaly detection. 2012 IEEE Statistical Signal Processing Workshop (SSP), pp. 377-380, Aug 2012.