## 7 Conclusions  
In this paper, we proposed two dimensionality reduction methods for learning compact embeddings of audio shingles (short sequences of chroma vectors) for a cross-version retrieval scenario in the context of Western classical music. We showed that our strategy of reducing entire shingles results in better retrieval quality and faster speed compared to those of the previous approach of reducing individual chroma vectors [12]. In our experiments, we greatly reduced the dimensionality of shingles--from 240 to below 12--with only little loss in retrieval quality. Both PCA and neural networks with triplet loss turned out to be effective for this task. In particular, we found that neural networks are beneficial for small dimensionalities of between 6 and 12. Such small dimensions allow for indexing by simple nearest neighbor trees, which could be the foundation of fast content-based audio retrieval in large classical music databases where efficiency is an important issue. We also showed that the database size has a strong impact on the retrieval results, especially when using dimensionality reduction methods. Applying such techniques, one needs a longer query length to be discriminative enough on a larger data set. Increasing the query length from 20 to 60 s results in a high retrieval accuracy, even for low-dimensional embeddings. We also showed that our approaches generalize to composers of the common practice period of Western classical music which are not contained in the training set. Furthermore, we analyzed the distances that appear in the nearest neighbor search to gain insights into the challenges of the retrieval scenario. For example, we showed that the distance distributions for different composers can differ strongly and give the indication that certain composers or pieces are more difficult for retrieval than others. In future work, we will investigate whether training on larger data sets can make the embeddings more robust for shorter query  
Figure 9: Distance distributions for five composers ([PERSON], [PERSON], [PERSON], [PERSON], and [PERSON]) for the brute-force approach (\(K=240\)) with \(\lambda=1\) (left column), the deep neural network (DNN) approach (\(K=12\)) with \(\lambda=1\) (middle column), and the DNN approach (\(K=12\)) with \(\lambda=5\) (right column). All distributions are computed for the extended test set \(\mathbb{D}_{3}\). The orange color refers to distances for relevant documents and the blue color refers to distances for non-relevant documents.  
lengths. Furthermore, up to now, we used CENS features--which are state-of-the-art for the given task--as the input. We want to investigate if good embeddings can be learned from less specialized input features such as \"raw\" chroma features, spectrograms, or even waveforms.  
Both authors substantially contributed to this work, including the formalization of the problem, the development of the ideas, and the writing of the paper. [PERSON] implemented the approaches and conducted the experiments. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the German Research Foundation (DFG-MU 2686/11-1, DFG-MU 2686/12-1).  
The International Audio Laboratories Erlangen are a joint institution of the Friedrich-Alexander-Universitat Erlangen-Nurnberg (FAU) and Fraunhofer Institute for Integrated Circuits IIS. The authors gratefully acknowledge the computational resources and support provided by the Erlangen Regional Computing Center (RRZE).  
The authors declare no conflict of interest.