#' Anomaly Detection Using Seasonal Hybrid ESD Test
#'
#' A technique for detecting anomalies in seasonal univariate time series where the input is a
#' series of <timestamp, count> pairs.
#' @name AnomalyDetectionTs
#' @param x Time series as a two column data frame where the first column consists of the
#' timestamps and the second column consists of the observations.
#' @param max_anoms Maximum number of anomalies that S-H-ESD will detect as a percentage of the
#' data.
#' @param direction Directionality of the anomalies to be detected. Options are:
#' \code{'pos' | 'neg' | 'both'}.
#' @param alpha The level of statistical significance with which to accept or reject anomalies.
#' @param only_last Find and report anomalies only within the last day or hr in the time series.
#' \code{NULL | 'day' | 'hr'}.
#' @param threshold Only report positive going anoms above the threshold specified. Options are:
#' \code{'None' | 'med_max' | 'p95' | 'p99'}.
#' @param e_value Add an additional column to the anoms output containing the expected value.
#' @param longterm Increase anom detection efficacy for time series that are greater than a month.
#' See Details below.
#' @param piecewise_median_period_weeks The piecewise median time window as described in Vallis, Hochenbaum, and Kejariwal (2014).
#' Defaults to 2.
#' @param plot A flag indicating if a plot with both the time series and the estimated anoms,
#' indicated by circles, should also be returned.
#' @param y_log Apply log scaling to the y-axis. This helps with viewing plots that have extremely
#' large positive anomalies relative to the rest of the data.
#' @param xlabel X-axis label to be added to the output plot.
#' @param ylabel Y-axis label to be added to the output plot.
#' @details
#' \code{longterm} This option should be set when the input time series is longer than a month.
#' The option enables the approach described in Vallis, Hochenbaum, and Kejariwal (2014).\cr\cr
#' \code{threshold} Filter all negative anomalies and those anomalies whose magnitude is smaller
#' than one of the specified thresholds which include: the median
#' of the daily max values (med_max), the 95th percentile of the daily max values (p95), and the
#' 99th percentile of the daily max values (p99).
#' @param title Title for the output plot.
#' @param verbose Enable debug messages.
#' @param na.rm Remove any NAs in timestamps.(default: FALSE)
#' @return The returned value is a list with the following components.
#' @return \item{anoms}{Data frame containing timestamps, values, and optionally expected values.}
#' @return \item{plot}{A graphical object if plotting was requested by the user. The plot contains
#' the estimated anomalies annotated on the input time series.}
#' @return One can save \code{anoms} to a file in the following fashion:
#' \code{write.csv(<return list name>[["anoms"]], file=<filename>)}
#' @return One can save \code{plot} to a file in the following fashion:
#' \code{ggsave(<filename>, plot=<return list name>[["plot"]])}
#' @references Vallis, O., Hochenbaum, J. and Kejariwal, A., (2014) "A Novel Technique for
#' Long-Term Anomaly Detection in the Cloud", 6th USENIX, Philadelphia, PA.
#' @references Rosner, B., (May 1983), "Percentage Points for a Generalized ESD Many-Outlier Procedure"
#' , Technometrics, 25(2), pp. 165-172.
#'
#' @docType data
#' @keywords datasets
#' @name raw_data
#'
#' @examples
#' data(raw_data)
#' AnomalyDetectionTs(raw_data, max_anoms=0.02, direction='both', plot=TRUE)
#' # To detect only the anomalies on the last day, run the following:
#' AnomalyDetectionTs(raw_data, max_anoms=0.02, direction='both', only_last="day", plot=TRUE)
#' @seealso \code{\link{AnomalyDetectionVec}}
#' @export
#'
AnomalyDetectionTs <- function(x, max_anoms = 0.10, direction = 'pos',
alpha = 0.05, only_last = NULL, threshold = 'None',
e_value = FALSE, longterm = FALSE, piecewise_median_period_weeks = 2, plot = FALSE,
y_log = FALSE, xlabel = '', ylabel = 'count',
title = NULL, verbose=FALSE, na.rm = FALSE){
# Check for supported inputs types
if(!is.data.frame(x)){
stop("data must be a single data frame.")
} else {
if(ncol(x) != 2 || !is.numeric(x[[2]])){
stop("data must be a 2 column data.frame, with the first column being a set of timestamps, and the second coloumn being numeric values.")
}
# Format timestamps if necessary
if (!(class(x[[1]])[1] == "POSIXlt")) {
x <- format_timestamp(x)
}
}
# Rename data frame columns if necessary
if (any((names(x) == c("timestamp", "count")) == FALSE)) {
colnames(x) <- c("timestamp", "count")
}
if(!is.logical(na.rm)){
stop("na.rm must be either TRUE (T) or FALSE (F)")
}
# Deal with NAs in timestamps
if(any(is.na(x$timestamp))){
if(na.rm){
x <- x[-which(is.na(x$timestamp)), ]
} else {
stop("timestamp contains NAs, please set na.rm to TRUE or remove the NAs manually.")
}
}
# Sanity check all input parameters
if(max_anoms > .49){
stop(paste("max_anoms must be less than 50% of the data points (max_anoms =", round(max_anoms*length(x[[2]]), 0), " data_points =", length(x[[2]]),")."))
} else if(max_anoms < 0){
stop("max_anoms must be positive.")
} else if(max_anoms == 0){
warning("0 max_anoms results in max_outliers being 0.")
}
if(!direction %in% c('pos', 'neg', 'both')){
stop("direction options are: pos | neg | both.")
}
if(!(0.01 <= alpha || alpha <= 0.1)){
if(verbose) message("Warning: alpha is the statistical signifigance, and is usually between 0.01 and 0.1")
}
if(!is.null(only_last) && !only_last %in% c('day','hr')){
stop("only_last must be either 'day' or 'hr'")
}
if(!threshold %in% c('None','med_max','p95','p99')){
stop("threshold options are: None | med_max | p95 | p99.")
}
if(!is.logical(e_value)){
stop("e_value must be either TRUE (T) or FALSE (F)")
}
if(!is.logical(longterm)){
stop("longterm must be either TRUE (T) or FALSE (F)")
}
if(piecewise_median_period_weeks < 2){
stop("piecewise_median_period_weeks must be at greater than 2 weeks")
}
if(!is.logical(plot)){
stop("plot must be either TRUE (T) or FALSE (F)")
}
if(!is.logical(y_log)){
stop("y_log must be either TRUE (T) or FALSE (F)")
}
if(!is.character(xlabel)){
stop("xlabel must be a string")
}
if(!is.character(ylabel)){
stop("ylabel must be a string")
}
if(!is.character(title) && !is.null(title)){
stop("title must be a string")
}
if(is.null(title)){
title <- ""
} else {
title <- paste(title, " : ", sep="")
}
# -- Main analysis: Perform S-H-ESD
# Derive number of observations in a single day.
# Although we derive this in S-H-ESD, we also need it to be minutley later on so we do it here first.
gran <- get_gran(x, 1)
if(gran == "day"){
num_days_per_line <- 7
if(is.character(only_last) && only_last == 'hr'){
only_last <- 'day'
}
} else {
num_days_per_line <- 1
}
# Aggregate data to minutely if secondly
if(gran == "sec"){
x <- format_timestamp(aggregate(x[2], format(x[1], "%Y-%m-%d %H:%M:00"), eval(parse(text="sum"))))
}
period = switch(gran,
min = 1440,
hr = 24,
# if the data is daily, then we need to bump the period to weekly to get multiple examples
day = 7)
num_obs <- length(x[[2]])
if(max_anoms < 1/num_obs){
max_anoms <- 1/num_obs
}
# -- Setup for longterm time series
# If longterm is enabled, break the data into subset data frames and store in all_data
if(longterm){
# Pre-allocate list with size equal to the number of piecewise_median_period_weeks chunks in x + any left over chunk
# handle edge cases for daily and single column data period lengths
if(gran == "day"){
# STL needs 2*period + 1 observations
num_obs_in_period <- period*piecewise_median_period_weeks + 1
num_days_in_period <- (7*piecewise_median_period_weeks) + 1
} else {
num_obs_in_period <- period*7*piecewise_median_period_weeks
num_days_in_period <- (7*piecewise_median_period_weeks)
}
# Store last date in time series
last_date <- x[[1]][num_obs]
all_data <- vector(mode="list", length=ceiling(length(x[[1]])/(num_obs_in_period)))
# Subset x into piecewise_median_period_weeks chunks
for(j in seq(1,length(x[[1]]), by=num_obs_in_period)){
start_date <- x[[1]][j]
end_date <- min(start_date + lubridate::days(num_days_in_period), x[[1]][length(x[[1]])])
# if there is at least 14 days left, subset it, otherwise subset last_date - 14days
if(difftime(end_date, start_date, units = "days") == as.difftime(num_days_in_period, units="days")){
all_data[[ceiling(j/(num_obs_in_period))]] <- subset(x, x[[1]] >= start_date & x[[1]] < end_date)
}else{
all_data[[ceiling(j/(num_obs_in_period))]] <- subset(x, x[[1]] > (last_date-lubridate::days(num_days_in_period)) & x[[1]] <= last_date)
}
}
}else{
# If longterm is not enabled, then just overwrite all_data list with x as the only item
all_data <- list(x)
}
# Create empty data frames to store all anoms and seasonal+trend component from decomposition
all_anoms <- data.frame(timestamp=numeric(0), count=numeric(0))
seasonal_plus_trend <- data.frame(timestamp=numeric(0), count=numeric(0))
# Detect anomalies on all data (either entire data in one-pass, or in 2 week blocks if longterm=TRUE)
for(i in 1:length(all_data)) {
anomaly_direction = switch(direction,
"pos" = data.frame(one_tail=TRUE, upper_tail=TRUE), # upper-tail only (positive going anomalies)
"neg" = data.frame(one_tail=TRUE, upper_tail=FALSE), # lower-tail only (negative going anomalies)
"both" = data.frame(one_tail=FALSE, upper_tail=TRUE)) # Both tails. Tail direction is not actually used.
# detect_anoms actually performs the anomaly detection and returns the results in a list containing the anomalies
# as well as the decomposed components of the time series for further analysis.
s_h_esd_timestamps <- detect_anoms(all_data[[i]], k=max_anoms, alpha=alpha, num_obs_per_period=period, use_decomp=TRUE, use_esd=FALSE,
one_tail=anomaly_direction$one_tail, upper_tail=anomaly_direction$upper_tail, verbose=verbose)
# store decomposed components in local variable and overwrite s_h_esd_timestamps to contain only the anom timestamps
data_decomp <- s_h_esd_timestamps$stl
s_h_esd_timestamps <- s_h_esd_timestamps$anoms
# -- Step 3: Use detected anomaly timestamps to extract the actual anomalies (timestamp and value) from the data
if(!is.null(s_h_esd_timestamps)){
anoms <- subset(all_data[[i]], (all_data[[i]][[1]] %in% s_h_esd_timestamps))
} else {
anoms <- data.frame(timestamp=numeric(0), count=numeric(0))
}
# Filter the anomalies using one of the thresholding functions if applicable
if(threshold != "None"){
# Calculate daily max values
periodic_maxs <- tapply(x[[2]],as.Date(x[[1]]),FUN=max)
# Calculate the threshold set by the user
if(threshold == 'med_max'){
thresh <- median(periodic_maxs)
}else if (threshold == 'p95'){
thresh <- quantile(periodic_maxs, .95)
}else if (threshold == 'p99'){
thresh <- quantile(periodic_maxs, .99)
}
# Remove any anoms below the threshold
anoms <- subset(anoms, anoms[[2]] >= thresh)
}
all_anoms <- rbind(all_anoms, anoms)
seasonal_plus_trend <- rbind(seasonal_plus_trend, data_decomp)
}
# Cleanup potential duplicates
all_anoms <- all_anoms[!duplicated(all_anoms[[1]]), ]
seasonal_plus_trend <- seasonal_plus_trend[!duplicated(seasonal_plus_trend[[1]]), ]
# -- If only_last was set by the user, create subset of the data that represent the most recent day
if(!is.null(only_last)){
start_date <- x[[1]][num_obs]-lubridate::days(7)
start_anoms <- x[[1]][num_obs]-lubridate::days(1)
if(gran == "day"){
#TODO: This might be better set up top at the gran check
breaks <- 3*12
num_days_per_line <- 7
} else {
if(only_last == 'day'){
breaks <- 12
}else{
# We need to change start_date and start_anoms for the hourly only_last option
start_date <- lubridate::floor_date(x[[1]][num_obs]-lubridate::days(2), "day")
start_anoms <- x[[1]][num_obs]-lubridate::hours(1)
breaks <- 3
}
}
# subset the last days worth of data
x_subset_single_day <- subset(x, (x[[1]] > start_anoms))
# When plotting anoms for the last day only we only show the previous weeks data
x_subset_week <- subset(x, ((x[[1]] <= start_anoms) & (x[[1]] > start_date)))
all_anoms <- subset(all_anoms, all_anoms[[1]] >= x_subset_single_day[[1]][1])
num_obs <- length(x_subset_single_day[[2]])
}
# Calculate number of anomalies as a percentage
anom_pct <- (length(all_anoms[[2]]) / num_obs) * 100
# If there are no anoms, then let's exit
if(anom_pct == 0){
if(verbose) message("No anomalies detected.")
return (list("anoms"=data.frame(), "plot"=plot.new()))
}
if(plot){
# -- Build title for plots utilizing parameters set by user
plot_title <- paste(title, round(anom_pct, digits=2), "% Anomalies (alpha=", alpha, ", direction=", direction,")", sep="")
if(longterm){
plot_title <- paste(plot_title, ", longterm=T", sep="")
}
# -- Plot raw time series data
color_name <- paste("\"", title, "\"", sep="")
alpha <- 0.8
if(!is.null(only_last)){
xgraph <- ggplot2::ggplot(x_subset_week, ggplot2::aes_string(x="timestamp", y="count")) + ggplot2::theme_bw() + ggplot2::theme(panel.grid.major = ggplot2::element_blank(), panel.grid.minor = ggplot2::element_blank(), text=ggplot2::element_text(size = 14))
xgraph <- xgraph + ggplot2::geom_line(data=x_subset_week, ggplot2::aes_string(colour=color_name), alpha=alpha*.33) + ggplot2::geom_line(data=x_subset_single_day, ggplot2::aes_string(color=color_name), alpha=alpha)
week_rng = get_range(x_subset_week, index=2, y_log=y_log)
day_rng = get_range(x_subset_single_day, index=2, y_log=y_log)
yrange = c(min(week_rng[1],day_rng[1]), max(week_rng[2],day_rng[2]))
xgraph <- add_day_labels_datetime(xgraph, breaks=breaks, start=as.POSIXlt(min(x_subset_week[[1]]), tz="UTC"), end=as.POSIXlt(max(x_subset_single_day[[1]]), tz="UTC"), days_per_line=num_days_per_line)
xgraph <- xgraph + ggplot2::labs(x=xlabel, y=ylabel, title=plot_title)
}else{
xgraph <- ggplot2::ggplot(x, ggplot2::aes_string(x="timestamp", y="count")) + ggplot2::theme_bw() + ggplot2::theme(panel.grid.major = ggplot2::element_line(colour = "gray60"), panel.grid.major.y = ggplot2::element_blank(), panel.grid.minor = ggplot2::element_blank(), text=ggplot2::element_text(size = 14))
xgraph <- xgraph + ggplot2::geom_line(data=x, ggplot2::aes_string(colour=color_name), alpha=alpha)
yrange <- get_range(x, index=2, y_log=y_log)
xgraph <- xgraph + ggplot2::scale_x_datetime(labels=function(x) ifelse(as.POSIXlt(x, tz="UTC")$hour != 0,strftime(x, format="%kh", tz="UTC"), strftime(x, format="%b %e", tz="UTC")),
expand=c(0,0))
xgraph <- xgraph + ggplot2::labs(x=xlabel, y=ylabel, title=plot_title)
}
# Add anoms to the plot as circles.
# We add zzz_ to the start of the name to ensure that the anoms are listed after the data sets.
xgraph <- xgraph + ggplot2::geom_point(data=all_anoms, ggplot2::aes_string(color=paste("\"zzz_",title,"\"",sep="")), size = 3, shape = 1)
# Hide legend
xgraph <- xgraph + ggplot2::theme(legend.position="none")
# Use log scaling if set by user
xgraph <- xgraph + add_formatted_y(yrange, y_log=y_log)
}
# Fix to make sure date-time is correct and that we retain hms at midnight
all_anoms[[1]] <- format(all_anoms[[1]], format="%Y-%m-%d %H:%M:%S")
# Store expected values if set by user
if(e_value) {
anoms <- data.frame(timestamp=all_anoms[[1]], anoms=all_anoms[[2]],
expected_value=subset(seasonal_plus_trend[[2]], as.POSIXlt(seasonal_plus_trend[[1]], tz="UTC") %in% all_anoms[[1]]),
stringsAsFactors=FALSE)
} else {
anoms <- data.frame(timestamp=all_anoms[[1]], anoms=all_anoms[[2]], stringsAsFactors=FALSE)
}
# Make sure we're still a valid POSIXlt datetime.
# TODO: Make sure we keep original datetime format and timezone.
anoms$timestamp <- as.POSIXlt(anoms$timestamp, tz="UTC")
# Lastly, return anoms and optionally the plot if requested by the user
if(plot){
return (list(anoms = anoms, plot = xgraph))
} else {
return (list(anoms = anoms, plot = plot.new()))
}
}
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.