LORE：从序数数据中联合学习内在维度和相对相似性结构
LORE: Jointly Learning the Intrinsic Dimensionality and Relative Similarity Structure From Ordinal Data
AI总结：
LORE通过联合学习序数数据的内在维度和相似性结构，实现了高效且可解释的感知建模。
摘要：
从序数数据中学习主观感知空间（如味觉、嗅觉或审美）的内在维度性是一个具有挑战性的问题。我们介绍了LORE（低秩序数嵌入），一种可扩展的框架，该框架从噪声三元组比较（形式为“A比B比C更相似吗？”）中联合学习内在维度性和序数嵌入。与现有方法不同，LORE使用非凸的Schatten-p准范数正则化解，使能够自动联合恢复序数嵌入及其维度性。我们通过迭代加权算法优化此联合目标，并建立了收敛保证。在合成数据集、模拟感知空间和现实世界众包序数判断的大量实验中，LORE学习出紧凑、可解释且高度准确的低维嵌入，能够恢复主观感知的潜在几何结构。通过同时推断内在维度性和序数嵌入，LORE在心理学中实现了更具解释性和数据效率的感知建模，并为在机器学习中可扩展地发现低维结构从序数数据开辟了新方向。
英文摘要：
Learning the intrinsic dimensionality of subjective perceptual spaces such as taste, smell, or aesthetics from ordinal data is a challenging problem. We introduce LORE (Low Rank Ordinal Embedding), a scalable framework that jointly learns both the intrinsic dimensionality and an ordinal embedding from noisy triplet comparisons of the form, "Is A more similar to B than C?". Unlike existing methods that require the embedding dimension to be set apriori, LORE regularizes the solution using the nonconvex Schatten-$p$ quasi norm, enabling automatic joint recovery of both the ordinal embedding and its dimensionality. We optimize this joint objective via an iteratively reweighted algorithm and establish convergence guarantees. Extensive experiments on synthetic datasets, simulated perceptual spaces, and real world crowdsourced ordinal judgements show that LORE learns compact, interpretable and highly accurate low dimensional embeddings that recover the latent geometry of subjective percepts. By simultaneously inferring both the intrinsic dimensionality and ordinal embeddings, LORE enables more interpretable and data efficient perceptual modeling in psychophysics and opens new directions for scalable discovery of low dimensional structure from ordinal data in machine learning.
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