Similarity between Euclidean and cosine angle distance for nearest neighbor queries

Understanding the relationship among different distance measures is helpful in choosing a proper one for a particular application. In this paper, we compare two commonly used distance measures in vector models, namely, Euclidean distance (EUD) and cosine angle distance (CAD), for nearest neighbor (NN) queries in high dimensional data spaces. Using theoretical analysis and experimental results, we show that the retrieval results based on EUD are similar to those based on CAD when dimension is high. We have applied CAD for content based image retrieval (CBIR). Retrieval results show that CAD works no worse than EUD, which is a commonly used distance measure for CBIR, while providing other advantages, such as naturally normalized distance.