Grubbs' test

We've now checked that the data are normal. Now let's apply Grubbs' outlier test!

Grubbs' test assesses whether the value that is farthest from the mean is an outlier - the value could be either the maximum or minimum value. The test is performed using the grubbs.test() function from the outliers package:

grubbs.test(x)

x is the input data as a numeric vector

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Introduction to Anomaly Detection in R

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Run the Grubbs' test on the nitrate concentrations.

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# Apply Grubbs' test to the river nitrate data
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Introduction to Anomaly Detection in R

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In this chapter, you'll learn how numerical and graphical summaries can be used to informally assess whether data contain unusual points. You'll use a statistical procedure called Grubbs' test to check whether a point is an outlier, and learn about the Seasonal-Hybrid ESD algorithm, which can help identify outliers when the data are a time series.

Exercise 1: What do we mean when we talk about anomalies?Exercise 2: Recognizing anomaly types Exercise 3: Exploring the river nitrate data Exercise 4: Testing the extremes with Grubbs' test Exercise 5: Visual check of normality Exercise 6: Grubbs' test

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Exercise 7: Hunting multiple outliers using Grubbs' test Exercise 8: Anomalies in time series Exercise 9: Visual assessment of seasonality Exercise 10: Seasonal Hybrid ESD algorithm Exercise 11: Interpreting Seasonal-Hybrid ESD output Exercise 12: Seasonal-Hybrid ESD versus Grubbs' test

In this chapter, you'll learn how to calculate the k-nearest neighbors distance and the local outlier factor, which are used to construct continuous anomaly scores for each data point when the data have multiple features. You'll learn the difference between local and global anomalies and how the two algorithms can help in each case.

Exercise 1: k-nearest neighbors distance score Exercise 2: Exploring wine Exercise 3: kNN distance matrix Exercise 4: kNN distance score Exercise 5: Visualizing kNN distance Exercise 6: Standardizing features Exercise 7: Appending the kNN score Exercise 8: Visualizing kNN distance score Exercise 9: Local outlier factor Exercise 10: LOF calculation Exercise 11: LOF visualization Exercise 12: LOF vs kNN

k-nearest neighbors distance and local outlier factor use the distance or relative density of the nearest neighbors to score each point. In this chapter, you'll explore an alternative tree-based approach called an isolation forest, which is a fast and robust method of detecting anomalies that measures how easily points can be separated by randomly splitting the data into smaller and smaller regions.

Exercise 1: Isolation trees Exercise 2: Fit and predict with an isolation tree Exercise 3: Score interpretation Exercise 4: Isolation forest Exercise 5: Fit an isolation forest Exercise 6: Checking convergence Exercise 7: Visualizing the isolation score Exercise 8: A grid of points Exercise 9: Prediction over a grid Exercise 10: Anomaly contours

You've now been introduced to a few different algorithms for anomaly scoring. In this final chapter, you'll learn to compare the detection performance of the algorithms in instances where labeled anomalies are available. You'll learn to calculate and interpret the precision and recall statistics for an anomaly score, and how to adapt the algorithms so they can accommodate data with categorical features.

Exercise 1: Labeled anomalies Exercise 2: Thyroid data Exercise 3: Visualizing thyroid disease Exercise 4: Anomaly score Exercise 5: Measuring performance Exercise 6: Binarized scores Exercise 7: Cross-tabulate binary scores Exercise 8: Thyroid precision and recall Exercise 9: Working with categorical features Exercise 10: Converting character to factor Exercise 11: Isolation forest with factors Exercise 12: LOF with factors Exercise 13: Wrap-up