The truncated singular value decomposition is a widely used methodology in music recommendation for direct similar-item retrieval or embedding musical items for downstream tasks. This paper investigates a curious effect that we show naturally occurring on many recommendation datasets: spiking formations in the embedding space. We first propose a metric to quantify this spiking organization's strength, then mathematically prove its origin tied to underlying communities of items of varying internal popularity. With this new-found theoretical understanding, we finally open the topic with an industrial use case of estimating how music embeddings' top-k similar items will change over time under the addition of data.

翻译：截断奇异值分解是音乐推荐中广泛使用的方法，用于直接检索相似物品或为下游任务嵌入音乐物品。本文研究了一种在许多推荐数据集上自然出现的奇特现象：嵌入空间中的尖峰形成。我们首先提出一个指标来量化这种尖峰组织的强度，然后从数学上证明其起源与具有不同内部流行度的物品底层社区相关。基于这一新发现的理论理解，我们最终通过一个工业应用案例展开讨论，该案例用于估计在数据增加的情况下，音乐嵌入的前k个相似物品将如何随时间变化。