## 5 Basic Experiments
### Brute Force  
As a baseline, we performed a first retrieval experiment based on the original audio shingles without dimensionality reduction (see Section 4.1). Since no training was involved, we report the results in Table 3 (upper rows) for both the training set \(\mathbb{D}_{1}\) and the test set \(\mathbb{D}_{2}\). For example, in the case of the test set \(\mathbb{D}_{2}\), we achieved a P@1 value of 0.996, which means that only 13 of the 3300 queries did not yield a relevant document on the top rank. Furthermore, the MAP value of 0.972 indicates that almost all relevant documents appear at the beginning of the ranked list. The results for the training set are similar, indicating a comparable complexity of both data sets. The parameters and feature design of the shingles were chosen in such a way that the brute-force approach yielded close to perfect results for the given task. For a comparison, we also performed an experiment using a temporal alignment procedure, similar to the classical state-of-the-art approaches for cover song retrieval by [PERSON] et al. (2019, 2020, 2021). In essence, these approaches are based on the combination of enhanced chroma representations with non-linear temporal alignment procedures. In our experiments, we performed subsequence dynamic time warping (SDTW) (Chapter 7) to align the feature sequences of a query and a database document. The approaches of [PERSON] et al. (2019, 2021) used local alignment procedures that aligned subsequences of the query to subsequences of the database document (e.g., Smith-Waterman, or \(Q_{\text{max}}\) algorithm). This was motivated by the task of popular music cover song retrieval where the query is a complete recording. In this case, query and relevant database documents typically have a different structure. However, in our case, we are dealing with Western classical music, and the query is only a 20 s excerpt. Therefore, we can expect that the query is entirely represented as a musically corresponding subsequence in the relevant database documents. Under this assumption, SDTW is more or less equivalent to the Smith-Waterman algorithm. For SDTW, we used the Euclidean distance, the step size condition \(\{(2,1),(1,2),(1,1)\}\), and the weights \((2,1,1)\) for vertical, horizontal, and diagonal steps, respectively. As a result of SDTW, we obtained a matching function; the minimum of this matching function was used as a distance measure for ranking the documents. Table 3 (middle rows) shows the retrieval results for this experiment, using the CENS features described in Section 3. These results are very close to the results of the shingle-based brute-forceapproach. This confirms that in our music scenario, no alignment procedure is needed when using CENS processing. One main motivation for using CENS smoothing is to introduce robustness to local tempo variations. When an alignment procedure is used, such smoothing is not needed. Therefore, we also conducted an alignment experiment, using the original chroma features without CENS post-processing. In this setting, the feature rate was \(10\,\mathrm{Hz}\) instead of \(1\,\mathrm{Hz}\). Table 3 (lower rows) shows the retrieval results using these features. In the case of the test set \(\mathbb{D}_{2}\), we achieved a P@1-value of 0.999, which means that almost all queries yielded a relevant document on the top rank. In all evaluation measures, we see small improvements over the shingle-based brute-force approach. However, this goes along with a dramatic increase in runtime. The runtime for the overall retrieval experiment in our setting increased from about a minute for the shingle-based brute-force approach (\(1\,\mathrm{Hz}\) features) to several hours for the alignment-based approach using \(10\,\mathrm{Hz}\) features. We describe further aspects related to runtime in Section 5.7. In summary, we showed that we can get close-to-perfect results with the brute-force approaches.