## 6 Extended Experiments
### Distance Analysis
Figure 8 shows such distributions for the brute-force approach, where the distributions of relevant document distances appear in orange color and the distributions of non-relevant document distances appear in blue color. The three rows show distributions for the composers that are part of both \(\mathbb{D}_{2}\) and \(\mathbb{D}_{3}\) ([PERSON], [PERSON], and [PERSON]); the three columns correspond to different evaluation settings. The left column refers to the smaller test set \(\mathbb{D}_{2}\) with \(\lambda=1\) (query length: 20 s), the middle column refers to the extended test set \(\mathbb{D}_{3}\) with \(\lambda=1\) (query length: 20 s), and the right column refers to the extended test set \(\mathbb{D}_{3}\) with \(\lambda=5\) (query length: 60 s). Considering [PERSON] in the left column, we see that the center of the orange distribution is much further to the left than the blue distribution. This means that the distances to the relevant documents are generally smaller than the distances to the non-relevant documents. We also see a small overlap between both distributions, which is caused by the fact that some distances to non-relevant documents are smaller than the greatest distances to relevant documents. However, since the distances that lead to the overlap could relate to different queries, we cannot conclude that this necessarily leads to confusion in the retrieval step. In general, since the overlap is small, the distributions indicate that the retrieval problem is well behaved for [PERSON]. For [PERSON] and [PERSON] (left column), there is more overlap. This suggests that the [PERSON] pieces are \"easier\" in the sense that they are more discriminative than other pieces. For the extended data set (middle column), we see similar tendencies for all three composers. The blue distributions come a bit closer to the orange ones with respect to their relation for the smaller data set (left column). The orange distributions are identical to the ones for the smaller data set because the distances to the relevant documents are the same. Only the distances to non-relevant documents decrease, because the extended data set contains more non-relevant documents with possibly smaller distances. When using a longer query length (\(\lambda=5\), right column), the orange and blue distributions are better separated for all three composers. The distances for the relevant documents only slightly increase because of the longer query length, but the distances to the non-relevant documents increase strongly, which leads to a better separation between the distributions. So far, we analyzed distributions for the brute-force approach to gain insights into the musical complexity of the retrieval task. In the following, we want to understand the effect of the embedding on the distributions. Figure 9 shows further distributions for the extended test set \(\mathbb{D}_{3}\) and five selected composers ([PERSON], [PERSON], [PERSON], [PERSON], and [PERSON]). The left column refers to the brute-force approach (\(K=240\)) with \(\lambda=1\) (query length: \(20\,\mathrm{s}\)), the middle column refers to the DNN embedding approach (\(K=12\)) with \(\lambda=1\) (query length: \(20\,\mathrm{s}\)), and the right column refers to the DNN embedding approach (\(K=12\)) with \(\lambda=5\) (query length: \(60\,\mathrm{s}\)). Note that the absolute distances between the different approaches are not comparable, but the relations between orange and blue distributions are meaningful. The distance measure is always the squared Euclidean distance, cf. Equation (5). However, for the brute-force approach, we have sequences of 20 non-negative \(\ell^{2}\)-normalized vectors of size 12, which are then flattened (distance range \([0,40]\)). For the DNN approach, we have real-valued \(\ell^{2}\)-normalized vectors of size 12 (distance range \([0,4]\)). For the brute-force approach (left column), the new composers of the extended data set ([PERSON], [PERSON]) behave similarly to the previous ones.