computer science

Learning vector quantization

Learning vector quantization is a computer 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 Learning vector quantization rather than just read about it. In short: In computer science, learning vector quantization (LVQ) is a prototype-based supervised classification algorithm. LVQ is the supervised counterpart of vector quantization systems.

Key takeaways

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

Reference excerpt

In computer science, learning vector quantization (LVQ) is a prototype-based supervised classification algorithm. LVQ is the supervised counterpart of vector quantization systems. LVQ can be understood as a special case of an artificial neural network, more precisely, it applies a winner-take-all Hebbian learning-based approach. It is a precursor to self-organizing maps (SOM) and related to neural gas and the k-nearest neighbor algorithm (k-NN). LVQ was invented by Teuvo Kohonen.

Definition An LVQ system is represented by prototypes W = ( w ( i ) , . . . , w ( n ) ) {\displaystyle W=(w(i),...,w(n))} which are defined in the feature space of observed data. In winner-take-all training algorithms one determines, for each data point, the prototype which is closest to the input according to a given distance measure. The position of this so-called winner prototype is then adapted, i.e. the winner is moved closer if it correctly classifies the data point or moved away if it classifies the data point incorrectly. An advantage of LVQ is that it creates prototypes that are easy to interpret for experts in the respective application domain. LVQ systems can be applied to multi-class classification problems in a natural way. A key issue in LVQ is the choice of an appropriate measure of distance or similarity for training and classification. Recently, techniques have been developed which adapt a parameterized distance measure in the course of training the system, see e.g. (Schneider, Biehl, and Hammer, 2009) and references therein. LVQ can be a valuable aid in classifying text documents.

Algorithm The algorithms are presented as in. Set up:

Let the data be denoted by x i ∈ R D {\displaystyle x_{i}\in \mathbb {R} ^{D}} , and their corresponding labels by y i ∈ { 1 , 2 , … , C } {\displaystyle y_{i}\in \{1,2,\dots ,C\}} . The complete dataset is { ( x i , y i ) } i = 1 N {\displaystyle \{(x_{i},y_{i})\}_{i=1}^{N}} . The set of code vectors is w j ∈ R D {\displaystyle w_{j}\in \mathbb {R} ^{D}} . The learning rate at iteration step t {\displaystyle t} is denoted by α t {\displaystyle \alpha _{t}} . The hyperparameters w {\displaystyle w} and ϵ {\displaystyle \epsilon } are used by LVQ2 and LVQ3. The original paper suggests ϵ ∈ [ 0.1 , 0.5 ] {\displaystyle \epsilon \in [0.1,0.5]} and w ∈ [ 0.2 , 0.3 ] {\displaystyle w\in [0.2,0.3]} .

LVQ1 Initialize several code vectors per label. Iterate until convergence criteria is reached.

Sample a datum x i {\displaystyle x_{i}} , and find out the code vector w j {\displaystyle w_{j}} , such that x i {\displaystyle x_{i}} falls within the Voronoi cell of w j {\displaystyle w_{j}} . If its label y i {\displaystyle y_{i}} is the same as that of w j {\displaystyle w_{j}} , then w j ← w j + α t ( x i − w j ) {\displaystyle w_{j}\leftarrow w_{j}+\alpha _{t}(x_{i}-w_{j})} , otherwise, w j ← w j − α t ( x i − w j ) {\displaystyle w_{j}\leftarrow w_{j}-\alpha _{t}(x_{i}-w_{j})} .

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Learning vector quantization

Start with the simplest possible case. Write down what Learning vector quantization claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer 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 Learning vector quantization 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 Learning vector quantization 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 Learning vector quantization

In research: Learning vector quantization appears in computer 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 Learning vector quantization 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: Learning vector quantization is common in secondary-school and first-year university syllabi. It links to neighbouring topics Artificial neural networks, Classification algorithms, Machine learning algorithms, so understanding it makes those chapters shorter.
In everyday life: Look for Learning vector quantization 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 Learning vector quantization in 20 minutes

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

Frequently asked questions

What is Learning vector quantization in simple terms?

In computer science, learning vector quantization (LVQ) is a prototype-based supervised classification algorithm. LVQ is the supervised counterpart of vector quantization systems.

Why does Learning vector quantization matter?

Because it connects several computer 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 Learning vector quantization?

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 Learning vector quantization.