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.
You can install the stable version from CRAN with:
install.packages("weird")You can install the development version of weird from GitHub with:
# install.packages("pak")
pak::pak("robjhyndman/weird")library(weird) will load the following packages:
- dplyr, for data manipulation.
- ggplot2, for data visualisation.
- distributional, for handling probability distributions.
You also get a condensed summary of conflicts with other packages you have loaded:
library(weird)
#> ── Attaching packages ────────────────────────────────────────────────────────── weird 1.0.2.9000 ──
#> ✔ dplyr 1.1.4 ✔ distributional 0.5.0
#> ✔ ggplot2 4.0.1
#> ── Conflicts ──────────────────────────────────────────────────────────────────── weird_conflicts ──
#> ✖ dplyr::filter() masks stats::filter()
#> ✖ dplyr::lag() masks stats::lag()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 2097 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: 2,097 × 4
#> time recorded_duration duration waiting
#> <dttm> <chr> <dbl> <dbl>
#> 1 2017-01-14 00:06:00 3m 16s 196 5940
#> 2 2017-01-26 14:27:00 ~4m 240 5820
#> 3 2017-01-27 23:57:00 2m 1s 121 3900
#> 4 2017-01-30 15:09:00 ~4m 240 5280
#> 5 2017-01-31 13:27:00 ~3.5m 210 5580
#> 6 2017-01-31 15:00:00 ~4m 240 5760
#> 7 2017-02-03 23:13:00 3m 25s 205 5160
#> 8 2017-02-04 22:14:00 3m 34s 214 5400
#> 9 2017-02-05 17:19:00 4m 0s 240 6060
#> 10 2017-02-05 19:00:00 4m 2s 242 6060
#> # ℹ 2,087 more rowsThe package provides the kde_bandwidth() function for estimating the
bandwidth of a kernel density estimate, dist_kde() for constructing
the distribution, and gg_density() for plotting the resulting density.
The figure below shows the kernel density estimate of the duration
variable obtained using these functions.
of <- oldfaithful |>
filter(duration < 3600, waiting < 7200)
dist_kde(of$duration) |>
gg_density(show_points = TRUE, jitter = TRUE) +
labs(x = "Duration (seconds)")
The same functions also work with bivariate data. The figure below shows
the kernel density estimate of the duration and waiting variables.
of |>
select(duration, waiting) |>
dist_kde() |>
gg_density(show_points = TRUE, alpha = 0.15) +
labs(x = "Duration (seconds)", y = "Waiting time (seconds)")
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: 2 × 4
#> time recorded_duration duration waiting
#> <dttm> <chr> <dbl> <dbl>
#> 1 2018-04-25 19:08:00 1s 1 5700
#> 2 2022-12-07 17:19:00 ~4 30s 30 5220
of |> filter(chauvenet_anomalies(duration))
#> # A tibble: 2 × 4
#> time recorded_duration duration waiting
#> <dttm> <chr> <dbl> <dbl>
#> 1 2018-04-25 19:08:00 1s 1 5700
#> 2 2022-12-07 17:19:00 ~4 30s 30 5220
of |> filter(grubbs_anomalies(duration))
#> # A tibble: 1 × 4
#> time recorded_duration duration waiting
#> <dttm> <chr> <dbl> <dbl>
#> 1 2018-04-25 19:08:00 1s 1 5700
of |> filter(dixon_anomalies(duration))
#> # A tibble: 0 × 4
#> # ℹ 4 variables: time <dttm>, recorded_duration <chr>, duration <dbl>, waiting <dbl>In 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 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, show_points = TRUE) +
labs(x = "Duration (seconds)")
The latter two plots are highest density region (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 (those points lying outside the 99% HDR which have surprisal probability less than 0.0005). 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 possible outliers in black (again, defined as points outside the 99% HDR which have surprisal probability less than 0.0005).
Several functions are provided for providing anomaly scores for all observations.
- The
surprisals()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_prob()function uses the lookout algorithm of Kandanaarachchi & Hyndman (2022) to compute anomaly probabilities.
Here are the top 0.02% most anomalous observations identified by each of the methods.
of |>
mutate(
surprisal = surprisals(cbind(duration, waiting), probability = FALSE),
strayscore = stray_scores(cbind(duration, waiting)),
lofscore = lof_scores(cbind(duration, waiting), k = 150),
gloshscore = glosh_scores(cbind(duration, waiting)),
lookout = lookout_prob(cbind(duration, waiting))
) |>
filter(
surprisal > quantile(surprisal, prob = 0.998) |
strayscore > quantile(strayscore, prob = 0.998) |
lofscore > quantile(lofscore, prob = 0.998) |
gloshscore > quantile(gloshscore, prob = 0.998) |
lookout < 0.002
) |>
arrange(lookout)
#> # A tibble: 10 × 9
#> time recorded_duration duration waiting surprisal strayscore lofscore gloshscore
#> <dttm> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 2018-04-25 19:08:00 1s 1 5700 17.4 0.150 3.78 1
#> 2 2022-12-03 16:20:00 ~4m 240 3060 17.4 0.265 2.05 1
#> 3 2022-12-07 17:19:00 ~4 30s 30 5220 17.1 0.273 1.89 1
#> 4 2020-09-04 01:38:00 >1m 50s 110 6240 17.1 0.167 1.84 1
#> 5 2023-07-04 12:03:00 ~1 minute 55ish se… 60 4920 17.1 0.122 1.62 1
#> 6 2020-06-01 21:04:00 2 minutes 120 6060 16.8 0.132 2.01 1
#> 7 2023-05-26 00:53:00 4m45s 285 7140 15.2 0.0761 2.57 1
#> 8 2017-09-22 18:51:00 ~281s 281 7140 15.0 0.0683 2.57 1
#> 9 2023-08-09 20:52:00 4m39s 279 7140 14.9 0.0651 2.57 1
#> 10 2018-09-22 16:37:00 ~4m13s 253 7140 14.7 0.0194 2.57 1
#> # ℹ 1 more variable: lookout <dbl>The surprisals() function can also compute the probability of
obtaining surprisal values at least as extreme as those observed. In
fact, this is the default behaviour, obtained when probability = TRUE.
of |>
mutate(
surprisal = surprisals(cbind(duration, waiting), probability = FALSE),
prob = surprisals(cbind(duration, waiting))
) |>
arrange(prob)
#> # A tibble: 2,097 × 6
#> time recorded_duration duration waiting surprisal prob
#> <dttm> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 2018-04-25 19:08:00 1s 1 5700 17.4 0.000477
#> 2 2022-12-03 16:20:00 ~4m 240 3060 17.4 0.000954
#> 3 2023-07-04 12:03:00 ~1 minute 55ish seconds 60 4920 17.1 0.00143
#> 4 2022-12-07 17:19:00 ~4 30s 30 5220 17.1 0.00191
#> 5 2020-09-04 01:38:00 >1m 50s 110 6240 17.1 0.00238
#> 6 2020-06-01 21:04:00 2 minutes 120 6060 16.8 0.00286
#> 7 2021-01-22 18:35:00 2m50s 170 3600 16.7 0.00334
#> 8 2022-11-29 14:51:00 ~3m 180 3840 16.4 0.00381
#> 9 2020-08-31 09:56:00 ~2m50s 170 3840 16.4 0.00429
#> 10 2020-07-23 23:17:00 3m06s 186 4320 16.3 0.00477
#> # ℹ 2,087 more rowsSome 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, recorded_duration
#> # A tibble: 2,097 × 4
#> time recorded_duration z1 z2
#> <dttm> <chr> <dbl> <dbl>
#> 1 2017-01-14 00:06:00 3m 16s -2.20 0.332
#> 2 2017-01-26 14:27:00 ~4m -0.0431 0.111
#> 3 2017-01-27 23:57:00 2m 1s -4.27 -3.43
#> 4 2017-01-30 15:09:00 ~4m 0.345 -0.886
#> 5 2017-01-31 13:27:00 ~3.5m -1.28 -0.332
#> 6 2017-01-31 15:00:00 ~4m 0 0
#> 7 2017-02-03 23:13:00 3m 25s -1.22 -1.11
#> 8 2017-02-04 22:14:00 3m 34s -0.966 -0.665
#> 9 2017-02-05 17:19:00 4m 0s -0.215 0.554
#> 10 2017-02-05 19:00:00 4m 2s -0.121 0.554
#> # ℹ 2,087 more rows
mvscale(of, cov = NULL)
#> Warning in mvscale(of, cov = NULL): Ignoring non-numeric columns: time, recorded_duration
#> # A tibble: 2,097 × 4
#> time recorded_duration duration waiting
#> <dttm> <chr> <dbl> <dbl>
#> 1 2017-01-14 00:06:00 3m 16s -1.98 0.338
#> 2 2017-01-26 14:27:00 ~4m 0 0.113
#> 3 2017-01-27 23:57:00 2m 1s -5.37 -3.50
#> 4 2017-01-30 15:09:00 ~4m 0 -0.902
#> 5 2017-01-31 13:27:00 ~3.5m -1.35 -0.338
#> 6 2017-01-31 15:00:00 ~4m 0 0
#> 7 2017-02-03 23:13:00 3m 25s -1.58 -1.13
#> 8 2017-02-04 22:14:00 3m 34s -1.17 -0.676
#> 9 2017-02-05 17:19:00 4m 0s 0 0.564
#> 10 2017-02-05 19:00:00 4m 2s 0.0902 0.564
#> # ℹ 2,087 more rows