Properties of Algorithmic Information Distance
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912509025320960 |
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| author | Hutter, Marcus |
| author_facet | Hutter, Marcus |
| contents | The domain-independent universal Normalized Information Distance based on Kolmogorov complexity has been (in approximate form) successfully applied to a variety of difficult clustering problems. In this paper we investigate theoretical properties of the un-normalized algorithmic information distance $d_K$. The main question we are asking in this work is what properties this curious distance has, besides being a metric. We show that many (in)finite-dimensional spaces can(not) be isometrically scale-embedded into the space of finite strings with metric $d_K$. We also show that $d_K$ is not an Euclidean distance, but any finite set of points in Euclidean space can be scale-embedded into $(\{0,1\}^*,d_K)$. A major contribution is the development of the necessary framework and tools for finding more (interesting) properties of $d_K$ in future, and to state several open problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_21988 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Properties of Algorithmic Information Distance Hutter, Marcus Information Theory Metric Geometry The domain-independent universal Normalized Information Distance based on Kolmogorov complexity has been (in approximate form) successfully applied to a variety of difficult clustering problems. In this paper we investigate theoretical properties of the un-normalized algorithmic information distance $d_K$. The main question we are asking in this work is what properties this curious distance has, besides being a metric. We show that many (in)finite-dimensional spaces can(not) be isometrically scale-embedded into the space of finite strings with metric $d_K$. We also show that $d_K$ is not an Euclidean distance, but any finite set of points in Euclidean space can be scale-embedded into $(\{0,1\}^*,d_K)$. A major contribution is the development of the necessary framework and tools for finding more (interesting) properties of $d_K$ in future, and to state several open problems. |
| title | Properties of Algorithmic Information Distance |
| topic | Information Theory Metric Geometry |
| url | https://arxiv.org/abs/2507.21988 |