Learning vector quantization: Difference between revisions

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==Algorithm==

SetThe up:algorithms are presented as in.<ref>{{Citation |last=Kohonen |first=Teuvo |title=Learning Vector Quantization |date=2001 |work=Self-Organizing Maps |volume=30 |pages=245–261 |url=http://link.springer.com/10.1007/978-3-642-56927-2_6 |access-date=2025-05-23 |place=Berlin, Heidelberg |publisher=Springer Berlin Heidelberg |doi=10.1007/978-3-642-56927-2_6 |isbn=978-3-540-67921-9|url-access=subscription }}</ref>

Set up:

* Let the data be denoted by <math>x_i \in \R^D</math>, and their corresponding labels by <math>y_i \in \{1, 2, \dots, C\}</math>.

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=== LVQ2 ===

LVQ2 is the same as LVQ3, but with this sentence removed: "If <math>w_j</math> and <math>w_k</math> and <math>x_i</math> have the same class, then <math>w_j \leftarrow w_j - \alpha_t(x_i - w_j)</math> and <math>w_k \leftarrow w_k + \alpha_t(x_i - w_k)</math>.". If <math>w_j</math> and <math>w_k</math> and <math>x_i</math> have the same class, then nothing happens.

=== LVQ3 ===

[[File:Apollonian_circles.svg|thumb|Some Apollonian circles. Every blue circle intersects every red circle at a right angle. Every red circle passes through the two points ''{{mvar|C, D}}'', and every blue circle separates the two points.]]

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

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#* If <math>w_j</math> and <math>x_i</math> have the same class, and <math>w_k</math> and <math>x_i</math> have different classes, then <math>w_j \leftarrow w_j + \alpha_t(x_i - w_j)</math> and <math>w_k \leftarrow w_k - \alpha_t(x_i - w_k)</math>.

#* If <math>w_k</math> and <math>x_i</math> have the same class, and <math>w_j</math> and <math>x_i</math> have different classes, then <math>w_j \leftarrow w_j - \alpha_t(x_i - w_j)</math> and <math>w_k \leftarrow w_k + \alpha_t(x_i - w_k)</math>.

#* If <math>w_j</math> and <math>w_k</math> and <math>x_i</math> have the same class, then <math>w_j \leftarrow w_j - \epsilon\alpha_t(x_i - w_j)</math> and <math>w_k \leftarrow w_k + \epsilon\alpha_t(x_i - w_k)</math>.

#* If <math>w_k</math> and <math>x_i</math> have different classes, and <math>w_j</math> and <math>x_i</math> have different classes, then the original paper simply does not explain what happens in this case, but presumably nothing happens in this case.

# Otherwise, skip.

Note that condition <math>\min \left(\frac{d_j}{d_k}, \frac{d_k}{d_j}\right)>s </math>, where <math>s=\frac{1-w}{1+w}</math>, precisely means that the point <math>x_i</math> falls between two [[Apollonian circles|Apollonian spheres]].

== References ==

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== Further reading ==

* {{cite journal |last1=Somervuo |first1=Panu |last2=Kohonen |first2=Teuvo |date=1999 |title=Self-organizing maps and learning vector quantization for feature sequences |journal=Neural Processing Letters |volume=10 |issue=2 |pages=151–159 |doi=10.1023/A:1018741720065}}

* [http://www.cis.hut.fi/panus/papers/dtwsom.pdf Self-Organizing Maps and Learning Vector Quantization for Feature Sequences, Somervuo and Kohonen. 2004] (pdf)

* {{Cite journal |last=Nova |first=David |last2=Estévez |first2=Pablo A. |date=2014-09-01 |title=A review of learning vector quantization classifiers |url=https://link.springer.com/article/10.1007/s00521-013-1535-3 |journal=Neural Computing and Applications |language=en |volume=25 |issue=3 |pages=511–524 |doi=10.1007/s00521-013-1535-3 |issn=1433-3058|arxiv=1509.07093 }}

== External links ==