biology

Generalized Procrustes analysis

Generalized Procrustes analysis is a biology topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Generalized Procrustes analysis rather than just read about it. In short: Generalized Procrustes analysis (GPA) is a method of statistical analysis that can be used to compare the shapes of objects, or the results of surveys, interviews, or panels. It was developed for analysing the results of free-choice profiling, a survey technique which allows respondents (such as sensory panelists) to describe a range of products in their own words or language.

Key takeaways

Generalized Procrustes analysis belongs to biology; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Generalized Procrustes analysis to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Generalized Procrustes analysis from memory before moving on to harder problems.

Reference excerpt

Generalized Procrustes analysis (GPA) is a method of statistical analysis that can be used to compare the shapes of objects, or the results of surveys, interviews, or panels. It was developed for analysing the results of free-choice profiling, a survey technique which allows respondents (such as sensory panelists) to describe a range of products in their own words or language. GPA is one way to make sense of free-choice profiling data; other ways can be multiple factor analysis (MFA), or the STATIS method. The method was first published by J. C. Gower in 1975. Generalized Procrustes analysis estimates the scaling factor applied to respondent scale usage, generating a weighting factor that is used to compensate for individual scale usage differences. Unlike measures such as a principal component analysis, GPA uses individual level data and a measure of variance is utilized in the analysis. The Procrustes distance provides a metric to minimize in order to superimpose a pair of shape instances annotated by landmark points. GPA applies the Procrustes analysis method to superimpose a population of shapes instead of only two shape instances. The algorithm outline is the following:

arbitrarily choose a reference shape (typically by selecting it among the available instances) superimpose all instances to current reference shape compute the mean shape of the current set of superimposed shapes if the Procrustes distance between the mean shape and the reference is above a certain threshold, set the reference to mean shape and continue to step 2.

See also Procrustes analysis Orthogonal Procrustes problem

References

I.L. Dryden and K.V. Mardia (1998). Statistical Shape Analysis. John Wiley & Sons. ISBN 0-471-95816-6.

Worked examples

Example 1 — a first encounter with Generalized Procrustes analysis

Start with the simplest possible case. Write down what Generalized Procrustes analysis claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In biology, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Generalized Procrustes analysis before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Generalized Procrustes analysis ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Generalized Procrustes analysis

In research: Generalized Procrustes analysis appears in biology research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Generalized Procrustes analysis in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Generalized Procrustes analysis is common in secondary-school and first-year university syllabi. It links to neighbouring topics Biometrics, Euclidean symmetries, Multivariate statistics, so understanding it makes those chapters shorter.
In everyday life: Look for Generalized Procrustes analysis outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Generalized Procrustes analysis in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Generalized Procrustes analysis means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Generalized Procrustes analysis out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Generalized Procrustes analysis in simple terms?

Why does Generalized Procrustes analysis matter?

Because it connects several biology ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Generalized Procrustes analysis?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Generalized Procrustes analysis.