weird
Overview
The weird package contains functions and data used in the book That’s Weird: Anomaly Detection Using R by Rob J Hyndman. It also loads several packages needed to do the analysis described in the book.
Installation
You can install the development version of weird from GitHub with:
# install.packages("devtools")
devtools::install_github("robjhyndman/weird-package")Usage
library(weird) will load the following packages:
- dplyr, for data manipulation.
- ggplot2, for data visualisation.
- ks, for fitting models and producing forecasts.
You also get a condensed summary of conflicts with other packages you have loaded:
library(weird)
#> ── Attaching packages ────────────────────────────────────── weird 0.0.0.9000 ──
#> ✔ dplyr 1.1.4 ✔ ks 1.14.1
#> ✔ ggplot2 3.4.4
#> ── Conflicts ──────────────────────────────────────────────── weird_conflicts ──
#> ✖ dplyr::filter() masks stats::filter()
#> ✖ dplyr::lag() masks stats::lag()Example: Old Faithful Geyser data
The oldfaithful data set contains eruption data from the Old Faithful
Geyser in Yellowstone National Park, Wyoming, USA, from 1 January 2015
to 1 October 2021. The data were obtained from the
geysertimes.org website. Recordings are
incomplete, especially during the winter months when observers may not
be present. There also appear to be some recording errors. The data set
contains 2261 observations of 3 variables: time giving the time at
which each eruption began, duration giving the length of the eruption
in seconds, and waiting giving the time to the next eruption in
seconds. In the analysis below, we omit the eruption with duration
greater than 1 hour as this is likely to be a recording error. Some of
the long waiting values are probably due to omitted eruptions, and so
we also omit eruptions with waiting greater than 2 hours.
oldfaithful
#> # A tibble: 2,261 × 3
#> time duration waiting
#> <dttm> <dbl> <dbl>
#> 1 2015-01-02 14:53:00 271 5040
#> 2 2015-01-09 23:55:00 247 6060
#> 3 2015-02-07 00:49:00 203 5460
#> 4 2015-02-14 01:09:00 195 5221
#> 5 2015-02-21 01:12:00 210 5401
#> 6 2015-02-28 01:11:00 185 5520
#> 7 2015-03-07 00:50:00 160 5281
#> 8 2015-03-13 21:57:00 226 6000
#> 9 2015-03-13 23:37:00 190 5341
#> 10 2015-03-20 22:26:00 102 3961
#> # ℹ 2,251 more rowsKernel density estimates
The package provides the kde_bandwidth() function for estimating the
bandwidth of a kernel density estimate, and an autoplot() method for
plotting the resulting density. The figure below shows the kernel
density estimate of the duration variable obtained using these
functions. The rug plot shows the actual data values.
of <- oldfaithful |>
filter(duration < 3600, waiting < 7200)
of_density <- kde(of$duration, h=kde_bandwidth(of$duration))
of_density |>
autoplot() +
geom_rug(aes(x=duration), of) +
labs(x = "Duration (seconds)")The kde_bandwidth() function can also be used to estimate the
bandwidth for a bivariate kernel density estimate. The figure below
shows the kernel density estimate of the duration and waiting
variables using the bandwidth selected by the kde_bandwidth()
function. The rug plot shows the actual data values.
of_density <- of |>
select(duration, waiting) |>
kde(H = kde_bandwidth(of[,c("duration","waiting")]))
of_density |>
autoplot() +
geom_point(aes(duration, waiting), data = of, alpha=0.15) +
labs(x = "Duration (seconds)", y = "Waiting time (seconds)")Statistical tests
Some old methods of anomaly detection used statistical tests. While these are not recommended, they are still widely used, and are provided in the package for comparison purposes.
of |> filter(peirce_anomalies(duration))
#> # A tibble: 1 × 3
#> time duration waiting
#> <dttm> <dbl> <dbl>
#> 1 2018-04-25 19:08:00 1 5700
of |> filter(chauvenet_anomalies(duration))
#> # A tibble: 1 × 3
#> time duration waiting
#> <dttm> <dbl> <dbl>
#> 1 2018-04-25 19:08:00 1 5700
of |> filter(grubbs_anomalies(duration))
#> # A tibble: 1 × 3
#> time duration waiting
#> <dttm> <dbl> <dbl>
#> 1 2018-04-25 19:08:00 1 5700
of |> filter(dixon_anomalies(duration))
#> # A tibble: 1 × 3
#> time duration waiting
#> <dttm> <dbl> <dbl>
#> 1 2018-04-25 19:08:00 1 5700In this example, they only detect the tiny 1-second duration, which is almost certainly a recording error. An explanation of these tests is provided in Chapter 4 of the book
Boxplots
Boxplots are widely used for anomaly detection. Here are three
variations of boxplots applied to the duration variable.
of |>
ggplot(aes(x = duration)) +
geom_boxplot() +
scale_y_discrete() +
labs(y = "", x = "Duration (seconds)")of |> gg_hdrboxplot(duration) +
labs(x = "Duration (seconds)")of |> gg_hdrboxplot(duration, scatterplot = TRUE) +
labs(x = "Duration (seconds)")The latter two plots are HDR boxplots, which allow the bimodality of the data to be seen. The dark shaded region contains 50% of the observations, while the lighter shaded region contains 99% of the observations. The plots use vertical jittering to reduce overplotting, and highlight potential outliers in red using the lookout algorithm (described in Chapter 6 of the book). An explanation of these plots is provided in Chapter 5 of the book.
It is also possible to produce bivariate boxplots. Several variations are provided in the package. Here are two types of bagplot.
of |>
gg_bagplot(duration, waiting) +
labs(x = "Duration (seconds)", y = "Waiting time (seconds)")of |>
gg_bagplot(duration, waiting, scatterplot = TRUE) +
labs(x = "Duration (seconds)", y = "Waiting time (seconds)")And here are two types of HDR boxplot
of |>
gg_hdrboxplot(duration, waiting) +
labs(x = "Duration (seconds)", y = "Waiting time (seconds)") of |>
gg_hdrboxplot(duration, waiting, scatterplot = TRUE) +
labs(x = "Duration (seconds)", y = "Waiting time (seconds)") The latter two plots show likely outliers in red, using the lookout algorithm.
Scoring functions
Several functions are provided for providing anomaly scores for all observations.
- The
density_scores()function uses either a fitted statistical model, or a kernel density estimate, to compute density scores. - The
stray_scores()function uses the stray algorithm to compute anomaly scores. - The
lof_scores()function uses local outlier factors to compute anomaly scores. - The
glosh_scores()function uses the Global-Local Outlier Score from Hierarchies algorithm to compute anomaly scores. - The
lookout()function uses the lookout algorithm to compute anomaly probabilities
Here are the top 0.02% most anomalous observations identified by each of the first four methods, along with the observations having lookout probability less than 0.05.
of |>
mutate(
denscore = density_scores(cbind(duration, waiting)),
strayscore = stray_scores(cbind(duration, waiting)),
lofscore = lof_scores(cbind(duration, waiting), k = 150),
gloshscore = glosh_scores(cbind(duration, waiting)),
lookout = lookout(cbind(duration, waiting))
) |>
filter(
denscore > quantile(denscore, prob=0.998) |
strayscore > quantile(strayscore, prob=0.998) |
lofscore > quantile(lofscore, prob=0.998) |
gloshscore > quantile(gloshscore, prob=0.998) |
lookout < 0.05
) |>
arrange(lookout)
#> # A tibble: 11 × 8
#> time duration waiting denscore strayscore lofscore gloshscore
#> <dttm> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 2018-04-25 19:08:00 1 5700 17.5 0.380 3.78 1
#> 2 2020-06-01 21:04:00 120 6060 17.5 0.132 1.88 1
#> 3 2021-01-22 18:35:00 170 3600 16.8 0.0606 1.09 0.860
#> 4 2020-08-31 09:56:00 170 3840 16.7 0.0606 1.01 0.816
#> 5 2015-11-21 20:27:00 150 3420 16.7 0.0772 1.27 1
#> 6 2017-05-03 06:19:00 90 4740 16.4 0.0495 1.68 1
#> 7 2020-10-15 17:11:00 220 7080 15.7 0.0429 2.42 1
#> 8 2017-09-22 18:51:00 281 7140 15.5 0.0333 2.64 1
#> 9 2017-08-12 13:14:00 120 4920 15.2 0.0690 1.53 1
#> 10 2020-05-18 21:21:00 272 7080 14.9 0.0333 2.42 1
#> 11 2018-09-22 16:37:00 253 7140 14.7 0.0200 2.63 1
#> # ℹ 1 more variable: lookout <dbl>Robust multivariate scaling
Some anomaly detection methods require the data to be scaled first, so
all observations are on the same scale. However, many scaling methods
are not robust to anomalies. The mvscale() function provides a
multivariate robust scaling method, that optionally takes account of the
relationships betwen variables, and uses robust estimates of center,
scale and covariance by default. The centers are removed using medians,
the scale function is the IQR, and the covariance matrix is estimated
using a robust OGK estimate. The data are scaled using the Cholesky
decomposition of the inverse covariance. Then the scaled data are
returned. The scaled variables are rotated to be orthogonal, so are
renamed as z1, z2, etc. Non-rotated scaling is possible by setting
cov = NULL.
mvscale(of)
#> Warning in mvscale(of): Ignoring non-numeric columns: time
#> # A tibble: 2,197 × 3
#> time z1 z2
#> <dttm> <dbl> <dbl>
#> 1 2015-01-02 14:53:00 2.06 -1.47
#> 2 2015-01-09 23:55:00 0.130 0.801
#> 3 2015-02-07 00:49:00 -1.78 -0.534
#> 4 2015-02-14 01:09:00 -2.04 -1.07
#> 5 2015-02-21 01:12:00 -1.38 -0.665
#> 6 2015-02-28 01:11:00 -2.76 -0.401
#> 7 2015-03-07 00:50:00 -3.92 -0.932
#> 8 2015-03-13 21:57:00 -0.932 0.668
#> 9 2015-03-13 23:37:00 -2.38 -0.799
#> 10 2015-03-20 22:26:00 -6.09 -3.87
#> # ℹ 2,187 more rows
mvscale(of, cov = NULL)
#> Warning in mvscale(of, cov = NULL): Ignoring non-numeric columns: time
#> # A tibble: 2,197 × 3
#> time duration waiting
#> <dttm> <dbl> <dbl>
#> 1 2015-01-02 14:53:00 1.61 -1.48
#> 2 2015-01-09 23:55:00 0.363 0.809
#> 3 2015-02-07 00:49:00 -1.92 -0.540
#> 4 2015-02-14 01:09:00 -2.33 -1.08
#> 5 2015-02-21 01:12:00 -1.56 -0.672
#> 6 2015-02-28 01:11:00 -2.85 -0.405
#> 7 2015-03-07 00:50:00 -4.15 -0.942
#> 8 2015-03-13 21:57:00 -0.726 0.674
#> 9 2015-03-13 23:37:00 -2.59 -0.807
#> 10 2015-03-20 22:26:00 -7.16 -3.91
#> # ℹ 2,187 more rows