## 1 Introduction  
Large amounts of digitally available music data require efficient retrieval strategies. In recent decades, many systems for music retrieval based on the query-by-example paradigm have been suggested. Given a fragment of a music representation as a query, the task is to automatically retrieve documents from a music database containing parts or aspects that are similar to the query [1; 2; 3]. One such retrieval scenario is known as audio identification or fingerprinting [4; 5; 6; 7], where the user specifies a query using an excerpt of an audio recording, and the task is to identify the particular audio recording that is the source of the query. A more challenging scenario is cross-version retrieval, including tasks such as audio matching, version identification, or cover song retrieval [8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30]. Here, given an excerpt of an audio recording as a query, the goal is to automatically retrieve all recordings in a database that correspond to the same piece of music as the query. Relevant documents may include various interpretations, arrangements, and cover songs of the piece underlying the recording of the query fragment. We focus on such a retrieval scenario in the context of Western classical music, where one typically has many different performances (referred to as versions) of the same piece of music. For example, given a 10 to 30 s fragment of a recording of [PERSON]'s Fifth Symphony performed by the Berlin Philharmonic conducted by [PERSON], the task is to identify all versions of this symphony in a database, including an interpretation by the New York Philharmonic conducted by [PERSON] and an interpretation by the Vienna Philharmonic conducted by [PERSON]. Figure 1 illustrates a typical retrieval procedure, where query and database recordings are compared employing chroma-based audio representations [7] (Chapter 3), resulting in a ranked list of database documents. For comparison, a temporal alignment procedure (e.g., subsequence dynamic time warping [7] (Chapter 7)) is often used to compensate for non-linear tempo differences between the query and relevant database documents [24; 31]. However, for huge data collections, the resulting runtime of such approaches is prohibitive. As a more efficient alternative, previous work [1; 9; 12] introduced shingling approaches, where short feature sequences are used for indexing. In this paper, we build on a study presented by [PERSON] and [PERSON] [12], who approached this task using chroma-based audio shingles (see the left part of Figure 1 for a visualization of such a shingle). Retrieval was performed via locality-sensitive hashing (LSH) applied to entire shingles. LSH is a random indexing technique for approximate nearest neighbor search [32]. The authors investigated the feature design, the length of the shingles, and the effect of dimensionality reduction applied to _individual_ feature vectors. In this paper, we propose approaches to increase the efficiency of the retrieval even more. We concentrate on the aspect of dimensionality reduction applied to _entire_ shingles so that standard tree-based indexing techniques for nearest neighbor search can be used for retrieval. As one contribution of this paper, we first use an approach based on principal component analysis (PCA) applied to entire shingles, rather than to individual chroma vectors as in previous work [12]. As another contribution, we then adapt convolutional neural networks with triplet loss [33] to further reduce the shingles' dimensionality without losing their discriminative power. We conduct basic experiments with a medium-sized collection of music recordings to study the benefits and limitations of the dimensionality reduction methods. As our main result, we show that the shingle dimension can be reduced from 240 to below 8 with only a moderate loss in retrieval quality.