Shift Invariance Property of a Non-Negative Matrix Factorization
Summary :
We consider a property about a result of non-negative matrix factorization under a parallel moving of data points. The shape of a cloud of original data points and that of data points moving parallel to a vector are identical. Thus it is sometimes required that the coefficients to basis vectors of both data points are also identical from the viewpoint of classification. We show a necessary and sufficient condition for such an invariance property under a translation of the data points.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E103-A No.2 pp.580-581
- Publication Date
- 2020/02/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.2019EAL2121
- Type of Manuscript
- LETTER
- Category
- General Fundamentals and Boundaries
Authors
Hideyuki IMAI
Hokkaido University
Keyword
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Hideyuki IMAI, "Shift Invariance Property of a Non-Negative Matrix Factorization" in IEICE TRANSACTIONS on Fundamentals,
vol. E103-A, no. 2, pp. 580-581, February 2020, doi: 10.1587/transfun.2019EAL2121.
Abstract: We consider a property about a result of non-negative matrix factorization under a parallel moving of data points. The shape of a cloud of original data points and that of data points moving parallel to a vector are identical. Thus it is sometimes required that the coefficients to basis vectors of both data points are also identical from the viewpoint of classification. We show a necessary and sufficient condition for such an invariance property under a translation of the data points.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2019EAL2121/_p
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@ARTICLE{e103-a_2_580,
author={Hideyuki IMAI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Shift Invariance Property of a Non-Negative Matrix Factorization},
year={2020},
volume={E103-A},
number={2},
pages={580-581},
abstract={We consider a property about a result of non-negative matrix factorization under a parallel moving of data points. The shape of a cloud of original data points and that of data points moving parallel to a vector are identical. Thus it is sometimes required that the coefficients to basis vectors of both data points are also identical from the viewpoint of classification. We show a necessary and sufficient condition for such an invariance property under a translation of the data points.},
keywords={},
doi={10.1587/transfun.2019EAL2121},
ISSN={1745-1337},
month={February},}
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TY - JOUR
TI - Shift Invariance Property of a Non-Negative Matrix Factorization
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 580
EP - 581
AU - Hideyuki IMAI
PY - 2020
DO - 10.1587/transfun.2019EAL2121
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E103-A
IS - 2
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - February 2020
AB - We consider a property about a result of non-negative matrix factorization under a parallel moving of data points. The shape of a cloud of original data points and that of data points moving parallel to a vector are identical. Thus it is sometimes required that the coefficients to basis vectors of both data points are also identical from the viewpoint of classification. We show a necessary and sufficient condition for such an invariance property under a translation of the data points.
ER -
English
