science

Tree kernel

Tree kernel is a science 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 Tree kernel rather than just read about it. In short: In machine learning, tree kernels are the application of the more general concept of positive-definite kernel to tree structures. They find applications in natural language processing, where they can be used for machine-learned parsing or classification of sentences.

Key takeaways

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

Reference excerpt

In machine learning, tree kernels are the application of the more general concept of positive-definite kernel to tree structures. They find applications in natural language processing, where they can be used for machine-learned parsing or classification of sentences.

Motivation In natural language processing, it is often necessary to compare tree structures (e.g. parse trees) for similarity. Such comparisons can be performed by computing dot products of vectors of features of the trees, but these vectors tend to be very large: NLP techniques have come to a point where a simple dependency relation over two words is encoded with a vector of several millions of features. It can be impractical to represent complex structures such as trees with features vectors. Well-designed kernels allow computing similarity over trees without explicitly computing the feature vectors of these trees. Moreover, kernel methods have been widely used in machine learning tasks (e.g. SVM), and thus plenty of algorithms are working natively with kernels, or have an extension that handles kernelization. An example application is classification of sentences, such as different types of questions.

Examples

Here are presented two examples of tree kernel applied to the constituency trees of the sentences "A cat eats a mouse." and "A mouse eats a cat.". In this example "A" and "a" are the same words, and in most of the NLP applications they would be represented with the same token. The interest of these two kernels is that they show very different granularity (the subset tree kernel being far more fine-grained than the subtree kernel), for the same computational complexity. Both can be computed recursively in time O(|T1|.|T2|).

Subtree kernel In the case of constituency tree, a subtree is defined as a node and all its children (e.g., [NP [D [A]] [N [mouse]]] is a subtree of the two trees). Terminals are not considered subtree (e.g. [a] is not a subtree). The subtree kernel count the number of common subtrees between two given trees. In this example, there are seven common subtrees:

[NP [D [a]] [N [cat]]], [NP [D [a]] [N [mouse]]], [N [mouse]], [N [cat]], [V [eats]], [D [a]] (counted twice as it appears twice).

Subset tree kernel A subset tree is a more general structure than a subtree. The basic definition is the same, but in the case of subset trees, leaves need not be terminals (e.g., [VP [V] [NP]] is a subset tree of both trees), but here two single nodes are not considered as trees. Because of this more general definition, there are more subset trees than subtrees, and more common subset trees than common subtrees. In this example, there are 54 common subset trees. The seven common subtrees plus among others:

[NP [D] [N]] (counted twice), [VP [V [eats]] [NP]]...

Illustrations

Worked examples

Example 1 — a first encounter with Tree kernel

Start with the simplest possible case. Write down what Tree kernel claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, 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 Tree kernel 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 Tree kernel 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 Tree kernel

In research: Tree kernel appears in science 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 Tree kernel 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: Tree kernel is common in secondary-school and first-year university syllabi. It links to neighbouring topics Hilbert spaces, Operator theory, so understanding it makes those chapters shorter.
In everyday life: Look for Tree kernel 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.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Tree kernel” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Tree kernel in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Tree kernel 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 Tree kernel out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Tree kernel in simple terms?

Why does Tree kernel matter?

Because it connects several science 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 Tree kernel?

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 Tree kernel.