Scalable similarity search in metric spaces relies on using the mathematical properties of the space in order to allow efficient querying. Most important in this context is the triangle inequality property, which can allow the majority of individual similarity comparisons to be avoided for a given query.

However many important metric spaces, typically those with high dimensionality, are not amenable to such techniques. In the past convex transforms have been studied as a pragmatic mechanism which can overcome this effect; however the problem with this approach is that the metric properties may be lost, leading to loss of accuracy.

Here, we study the underlying properties of such transforms and their effect on metric indexing mechanisms. We show there are some spaces where certain transforms may be applied without loss of accuracy, and further spaces where we can understand the engineering tradeoffs between accuracy and efficiency. We back these observations with experimental analysis. To highlight the value of the approach, we show three large spaces deriving from practical domains whose dimensionality prevents normal indexing techniques, but where the transforms applied give scalable access with a relatively small loss of accuracy.

度量空间中的可伸缩相似性搜索依赖于使用空间的数学属性，以便进行有效查询。在这种情况下，最重要的是三角形不等式属性，它可以避免给定查询的大多数个体相似性比较。

但是，许多重要的度量空间（通常是具有高维的度量空间）不适合此类技术。在过去，凸变换作为一种可以克服这种影响的实用机制而被研究。但是，这种方法的问题在于度量标准属性可能会丢失，从而导致准确性下降。

在这里，我们研究了此类转换的基本属性及其对度量索引机制的影响。我们显示了可以在不损失准确性的情况下应用某些变换的一些空间，以及可以了解准确性和效率之间的工程折衷的其他空间。我们通过实验分析来支持这些观察。为了强调该方法的价值，我们展示了三个来自于实际域的大空间，这些空间的维数阻止了常规索引技术的发展，但是所应用的变换所提供的空间却带来了可伸缩的访问，而精度损失却相对较小。