# One-hot code[1]

Also known as One-vs-all (OVA) code, One-against-all (1AA) code, One-vs-rest (OvR) code, \(1\)-in-\(n\) code.

## Description

A length-\(n\) binary code whose codewords are those with Hamming weight one. The reverse of this code, where all codewords have Hamming weight \(n-1\) is called a one-cold code.

## Realizations

The bi-quinary code, a combination of one-hot 1-in-2 and 1-in-5 one-hot codes to encode decimal digits, was used in several early computers ([2], Ch. 27).Marking the state of a finite automaton [3].

## Parents

## Cousins

- Pulse-position modulation (PPM) code — The PPM code is an continuous analogue of the one-hot code.
- PPM c-q code — The PPM c-q code is an continuous analogue of the one-hot code designed for transmission through quantum channels.
- Error-correcting output code (ECOC) — One-hot codes are the primary codes used in multiclass classification [4–7].
- One-hot quantum code — The one-hot quantum code is the quantum version of the one-hot code.

## References

- [1]
- Nilsson, Nils J. "Learning machines." (1965).
- [2]
- Encyclopedia of Computer Science and Technology, Second Edition Volume I (CRC Press, 2017) DOI
- [3]
- S. Devadas and A. R. Newton, “Decomposition and factorization of sequential finite state machines”, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 8, 1206 (1989) DOI
- [4]
- L. Rokach, Pattern Classification Using Ensemble Methods (WORLD SCIENTIFIC, 2009) DOI
- [5]
- G. Anthony, H. Gregg, and M. Tshilidzi, “Image Classification Using SVMs: One-against-One Vs One-against-All”, (2007) arXiv:0711.2914
- [6]
- K. Potdar, T. S., and C. D., “A Comparative Study of Categorical Variable Encoding Techniques for Neural Network Classifiers”, International Journal of Computer Applications 175, 7 (2017) DOI
- [7]
- W. Utschick and W. Weichselberger, “Stochastic Organization of Output Codes in Multiclass Learning Problems”, Neural Computation 13, 1065 (2001) DOI

## Page edit log

- Victor V. Albert (2022-07-14) — most recent

## Cite as:

“One-hot code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/one_hot

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/bits/easy/one_hot.yml.