## 6 Extended Experiments
### Distance Analysis  
In the previous section, we addressed issues of scalability and generalizability in relation to the query length. Now we want to gain further insights into the challenges that occur in the retrieval scenario. For example, beyond rank-based evaluation measures, we want to find out whether particular compositions are easier or harder for retrieval than others, e.g., due to harmonic or melodic characteristics. Recall from Section 3 that the ranks are computed on the basis of the distances that appear between queries and documents. The retrieval problem is well behaved if the distances between queries and documents of the same piece of music (relevant documents) are substantially smaller than the distances between queries and documents of different pieces (non-relevant documents). To understand how well behaved our problem is, we now analyze the distances that appear in the nearest neighbor search. \begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline  & \multirow{2}{*}{**Queries**} & \multicolumn{4}{c}{**Brute Force**} & \multicolumn{4}{c}{**PCA (\(K=12\))**} & \multicolumn{4}{c}{**DNN (\(K=12\))**} \\  & & **P@1** & **P\({}_{R}\)** & **MAP** & **P@1** & **P\({}_{R}\)** & **MAP** & **P@1** & **P\({}_{R}\)** & **MAP** \\ \hline [PERSON] & 160 & 0.956 & 0.921 & 0.941 & 0.800 & 0.598 & 0.666 & 0.838 & 0.633 & 0.698 \\ [PERSON] & 2930 & 0.997 & 0.943 & 0.974 & 0.973 & 0.727 & 0.813 & 0.979 & 0.886 & 0.937 \\ [PERSON] & 210 & 1.000 & 0.986 & 0.996 & 0.971 & 0.864 & 0.918 & 0.976 & 0.864 & 0.925 \\ \hline [PERSON] & 240 & 1.000 & 0.998 & 0.999 & 0.996 & 0.912 & 0.950 & 0.992 & 0.943 & 0.967 \\ [PERSON] & 200 & 0.985 & 0.976 & 0.982 & 0.960 & 0.900 & 0.935 & 0.935 & 0.846 & 0.891 \\ [PERSON] & 200 & 1.000 & 0.966 & 0.980 & 0.935 & 0.639 & 0.704 & 0.880 & 0.600 & 0.670 \\ [PERSON] & 660 & 0.992 & 0.937 & 0.960 & 0.933 & 0.703 & 0.773 & 0.865 & 0.697 & 0.756 \\ [PERSON] & 150 & 0.993 & 0.977 & 0.983 & 0.800 & 0.630 & 0.681 & 0.920 & 0.780 & 0.840 \\ [PERSON] & 420 & 0.998 & 0.984 & 0.990 & 0.952 & 0.776 & 0.839 & 0.929 & 0.788 & 0.838 \\ [PERSON] & 180 & 1.000 & 0.956 & 0.975 & 0.978 & 0.884 & 0.922 & 0.989 & 0.904 & 0.940 \\ \hline \(\diameter\) over queries & 0.995 & 0.953 & 0.976 & 0.956 & 0.744 & 0.816 & 0.951 & 0.835 & 0.886 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Composer-wise evaluation results using the extended data set \(\mathbb{D}_{3}\) for \(\lambda=5\) (query length: 60 s). Recall that we have \(R\in\mathbb{N}\) relevant documents for a given query. We want to compare the distances to the relevant documents with the distances to the non-relevant documents. Since most of the non-relevant documents should be easily distinguishable from the relevant ones, we restrict our analysis to the most difficult non-relevant documents for the task. To balance the numbers of relevant and non-relevant documents, we only consider the \(R\) non-relevant documents with the smallest distances to the given query. Small distances mean that these non-relevant documents have the greatest confusion potential with the relevant documents. In the following, we analyze the relation of the distributions of distances for relevant documents and non-relevant documents, respectively. The relation between these distributions indicates how difficult the retrieval problem is. However, the analysis of the relation between the distributions has to be taken with care, because versions with different difficulties are included in a single distribution. For that reason, a strong separation of the distributions is a sufficient condition for perfect retrieval results, but not a necessary condition. In other words, even if the overlap between the distributions is large, the retrieval may still give excellent results. In this sense, we regard the distributions only as weak indicators and only evaluate them by visual inspection in the following. For a more statistically rigorous analysis of such distributions, we refer to the study by [PERSON] et al. [9].