Non-fungible tokens (NFTs) have become a significant digital asset class, each uniquely representing virtual entities such as artworks. These tokens are stored in collections within smart contracts and are actively traded across platforms on Ethereum, Bitcoin, and Solana blockchains. The value of NFTs is closely tied to their distinctive characteristics that define rarity, leading to a growing interest in quantifying rarity within both industry and academia. While there are existing rarity meters for assessing NFT rarity, comparing them can be challenging without direct access to the underlying collection data. The Rating over all Rarities (ROAR) benchmark addresses this challenge by providing a standardized framework for evaluating NFT rarity. This paper explores a dimension reduction approach to rarity design, introducing new performance measures and meters, and evaluates them using the ROAR benchmark. Our contributions to the rarity meter design issue include developing an optimal rarity meter design using non-metric weighted multidimensional scaling, introducing Dissimilarity in Trades (DIT) as a performance measure inspired by dimension reduction techniques, and unveiling the non-interpretable rarity meter DIT, which demonstrates superior performance compared to existing methods.

翻译：非同质化代币（NFT）已成为重要的数字资产类别，每个NFT唯一地代表艺术品等虚拟实体。这些代币存储在智能合约的集合中，并在以太坊、比特币和Solana区块链上的平台间进行活跃交易。NFT的价值与其定义稀有度的独特特征密切相关，这促使工业界和学术界对量化稀有度的兴趣日益增长。尽管现有稀有度度量方法可用于评估NFT稀有度，但在无法直接访问底层集合数据的情况下，比较这些方法仍具挑战性。全稀有度评级（ROAR）基准通过提供标准化评估框架应对这一挑战。本文探索基于降维的稀有度设计方法，引入新的性能度量指标与测量工具，并利用ROAR基准进行评估。我们对稀有度度量设计问题的贡献包括：使用非度量加权多维尺度法开发最优稀有度度量设计，基于降维技术提出交易相异性（DIT）作为性能度量指标，并揭示不可解释的稀有度度量方法DIT，该方法相较于现有方法展现出更优越的性能。