1.1 Our proposal

We propose the Dataset of Aligned Lyric Information, DALI, with synchronized audio, lyrics, and notes (Meseguer-Brocal et al., 2018). DALI aims to serve as a reference dataset for singing voice research. Our approach is motivated by Active Learning (Settles, 2008) and the Teacher-Student paradigm (Hinton et al., 2014). We establish a loop where we incrementally adapt and refine imperfect karaoke annotations while simultaneously improving the ML models used. During this constant interaction both annotations and models are improved.

1.2 Paper organization

First, we review previous work related to our problem in Section 2. Then, we describe and define the DALI dataset itself and how to use it in Section 3. In Section 4, we outline the methodology used to create it. Our system acquires lyrics and notes aligned in time from the Web (Section 4.1); finds a set of audio candidates (Section 4.2); and selects the correct one and adapts the annotations to it (Section 4.3). To this end, we propose a similarity measurement. This procedure highly depends on the precision of the Singing Voice Detection (SVD) method. In Section 5, we thus progressively improve the SVD quality using the teacher-student paradigm. This produces an enhanced DALI. We study the quality of the data and present strategies to correct global issues in Section 6. Finally, we discuss our research (Section 7).

2.1 Singing Voice Datasets

The lack of large and good quality datasets is a crucial factor that prevents the development of singing voice tasks. There are no widely used reference datasets as in other disciplines, e.g. MNIST (Le Cun et al., 1998), CIFAR (Krizhevsky, 2009), or ImageNet (Deng et al., 2009) for computer vision. This problem is common to other MIR tasks. Fortunately, many solutions have been proposed in the last years (Benzi et al., 2016; Fonseca et al., 2017; Donahue et al., 2018; Nieto et al., 2019; Maia et al., 2019; Yesiler et al., 2019).

There are some datasets with audio and lyrics aligned in time for commercial purposes (LyricFind, Musixmatch or Music-story). Yet, they are private, not accessible outside host applications, come without audio, have only aligned lines, and do not contain symbolic vocal melody annotations (notes).

Currently, researchers working on singing voice tasks use small datasets, designed following different methodologies (Fujihara and Goto, 2012). Large datasets remain private (Humphrey et al., 2017; Stoller et al., 2019) or are vocal-only captures of amateur singers recorded on mobile phones that involve complex preprossessing (Smith, 2013; Kruspe, 2016; Gupta et al., 2018). An overview of datasets of public lyrics aligned in time can be found in Table 1. Most of these datasets are created in the context of lyrics alignment i.e. assigning start and end times to every textual element.

Lyrics are inevitably language-dependent. Researchers have created datasets for different languages: English (Kan et al., 2008; Iskandar et al., 2006; Gupta et al., 2018), Chinese (Wong et al., 2007; Dzhambazov, 2017), Turkish (Dzhambazov, 2017), German (Müller et al., 2007) and Japanese (Fujihara et al., 2011). In theory, we can adapt models obtained in one language to others, but it has not been proven.

Most of the datasets contain polyphonic popular music. There also some with A Capella music (Kruspe, 2016). However, it is always difficult to migrate from monophonic methods to polyphonic (Mesaros and Virtanen, 2010). More recently, authors proposed to use Automatic Speech Recognition (ASR) on imperfect transcripts to align lyrics and A Capella singing signals in a semi-supervised way (Gupta et al., 2018). The authors also propose a method for transferring A Capella alignment to the polyphonic case (Gupta et al., 2019). Datasets do not always contain the full duration audio track but often a shorter version (Gupta et al., 2018; Dzhambazov, 2017; Mesaros and Virtanen, 2010; Wong et al., 2007). If the tracks are complete, respective datasets are typically small.

2.2 The Teacher-Student Paradigm

This paradigm has two agents: the teacher and the student. We train the teacher on well-known labeled ground truth datasets (often manually annotated). The teacher labels some unlabeled data, used to train the student(s). Thus, students indirectly acquire the desired knowledge by mimicking the teacher’s “behavior”. This paradigm was originally introduced as a model compression technique to transfer knowledge from larger architectures to smaller ones (Bucilua et al., 2006). Small models (the students) are trained on a larger dataset labeled by large models (the teachers). A general formalization of this knowledge distillation trains the student on both the teacher’s labels and the training data (Hinton et al., 2014). In the context of Deep Learning, teachers also remove layers of the student’s architecture, automating the compression process (Ashok et al., 2017).

The teacher-student paradigm is also used as a solution to overcome the problem of insufficient labeled data, for instance for speech recognition (Watanabe et al., 2017; Wu and Lerch, 2017) or multilingual models (Cui et al., 2017). Since manual labeling is time-consuming, teachers automatically label unlabeled data on larger datasets used for training the students. This paradigm is relatively undeveloped in MIR. Wu and Lerch (2017) provide one of the few examples, applying it to automatic drum transcription, in which the teacher labels the student dataset of drum recordings.

All of these works report that the students improve the performance of the teachers. Therefore, this learning paradigm meets our requirements.

3.1 The Annotations

In DALI, songs are defined as:

where each granularity level g with K_g elements is a sequence of aligned segments:

with $t_k^0$M3 \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ t_k^0 \] \end{document} and $t_k^1$M4 \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ t_k^1 \] \end{document} being a text segment’s start and end times (in seconds) with M5 \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ t_k^0 < \,t_k^1, {f_k} \] \end{document} a tuple (f_min, f_max) with the frequency range (in Hz) covered by all the notes in the segment (at the note level f_min = f_max, a vocal note), l_k the actual lyric’s information and i_k = j the index that links an annotation a_{k, g} with its corresponding upper granularity level annotation a_{j, g+1}. The text segment’s events for a song are ordered and non-overlapping – that is, $t_k^1\le t_{k+1}^0\forall k$M6 \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ t_k^1\, \le \,t_{k + 1}^0\,\forall k \] \end{document} . Note how the annotations define a unique connection in time between the musical and textual domains.

In this article, we present the second version (v2) of the DALI dataset with 7756 songs, augmenting the first version (v1) with 5358 songs (Meseguer-Brocal et al., 2018) by 2398 songs. DALI has a total of 344.9 (v1) and 488.1 (v2) hours of music, and 176.9 (v1) and 247.2 (v2) hours with vocals. There are also more than 3.6 (v1) and 8.7 (v2) million segments a_{k, g} and the average per song is 679 (v1) and 710 (v2). There are, on average, 2.36 (2.71) songs per artist and 119s (115s) with vocals per song, in DALI v1 (v2), cf. Table 3. As seen in Table 2, DALI has many artists, genres, languages, and decades. Most of the songs are from popular genres like Pop or Rock, from the 2000s and English is the most predominant language.

3.2 Tools for Working with DALI

The richness of DALI renders the data complex. Hence, it would be difficult to use in a format such as JSON or XML. To overcome this limitation, we have developed a specific Python package with all the necessary tools to access the dataset. Users can find it at https://github.com/gabolsgabs/DALI and install it with pip.¹

A song is represented as the Python class Annotations. Each instance has two attributes info and annotations. The attribute info contains the metadata, the link to the audio and the scores that indicate the quality of the annotations (Section 6.2).

The attribute annotations contains the aligned segments a_k,g. We can work in two modes, horizontal and vertical, and easily change from one to the other. The horizontal mode stores the granularity levels in isolation, providing access to all its segments a_k,g. The vertical mode connects levels vertically across the hierarchy. A segment at a given granularity contains all its deeper segments e.g. a line has links to all its words and notes, allowing the study of hierarchical relationships.

The package also includes additional tools for reading the dataset and automatically retrieving the audio from YouTube. We also provide tools for working with individual granularity levels, i.e., transforming the data into vectors or matrices with a given time resolution, manually correcting the alignment parameters, or re-computing the alignment process for different audio than the original one (Section 4.3). For a detailed explanation of how to use DALI, we refer to the tutorial: https://github.com/gabolsgabs/DALI.

Finally, using the correlation score that indicates the accuracy of the alignment (cf. Section 4.3), we propose to split DALI into 3 sets: train, validation, and test (Table 4). Other splits are possible depending on the task at hand (e.g. analyzing only English songs for lyrics alignment (Section 6.1)).

3.3 Distribution

Each DALI dataset version is a set of gzip files. Each file encloses an instance of the class Annotations. The different versions are distributed as open-source under an Academic Free License (AFL)² and can be found at https://zenodo.org/record/2577915 that provides a fingerprint (an MD5 checksum file (Rivest, 1992)) that verifies their integrity. We describe them following the MIR corpora description (Peeters and Fort, 2012).

DALI is also part of mirdata (Bittner et al., 2019), a standard framework for MIR datasets that provides a fingerprint (also an MD5 file) per Annotations instance and audio track that verifies their integrity.

3.4 Reproducibility

Our main problem is the restriction on sharing the audio tracks, which complicates the result comparison. This is common to other datasets with YouTube audio such as the Weimar Jazz Database (Balke et al., 2018). Using different audio may create misaligned annotations. We suggest three ways to overcome this issue:

1. to use our tools to retrieve the correct audio from YouTube. However, some links may be broken.
2. to use a different audio track and reproduce the alignment process (Section 4.3). We provide all the tools for this task and grant a model (second generation, Section 5.2) for computing the singing voice prediction vector needed.
3. to send us the feature extractor to be run on our audio. Users have to agree to distribute the new feature to other users (at zenodo) as we do with the f₀ representation computed in Section 6.2.

4.1 From raw annotations to structured MIR data

Karaoke users create annotations and exchange them in text files that contain:

• the song_title and artist_name.
• a sequence of tuples {time, musical-note, text} with the actual annotations, Figure 1.
• the offset_time (start of the sequence) and the frame rate (annotation time-grid).

Table 5 defines the terms used in this article. We transform the raw annotation into useful data obtaining the time in seconds and the note’s frequency (raw annotations express notes as intervals), and creating the four levels of granularity: notes (textual information underlying a note), words, lines and paragraphs. The first three levels are encoded in the retrieved files. We deduce the paragraph level as follows.

The paragraph level. Using the song_title and artist_name, we connect each raw annotation file to Wasabi, a semantic database of song metadata collected from various music databases (Meseguer-Brocal et al., 2017). Wasabi provides lyrics grouped in lines and paragraphs, in a text-only form. We create the paragraph level merging the two representations (melodic note-based annotations from karaoke annotations and text only from Wasabi) in a text to text alignment form. Let l^m be our existing raw lines and p^m the paragraph we want to obtain. Similarly, p^t represents the target paragraphs in Wasabi and l^t their lines. Our task is to progressively merge a set of l^m such that the new p^m is maximally similar to an existing p^t. This is not trivial since l^m and l^t differ in some regards. l^m tends to be shorter, some lines might be missing in one domain, and p^t can be rearranged/scrambled. An example of merging is shown in Figure 2.

The phoneme information. The phonetic information is computed only for the word level. We use the Grapheme-to-Phoneme (G2P)³ system by CMU Sphinx⁴ at Carnegie Mellon University. This model uses a tensor2tensor transformer architecture that relies on global dependencies between input and output. This information is only available for DALI version two.

The metadata. Wasabi provides extra multi-modal information such as cover images, links to video clips, metadata, biography, and expert comments.

4.2 Retrieving audio candidates

The annotations are now ready to be used. Nevertheless, they come without audio. The same song_title and artist_name may have many different versions (studio, radio, edit, live or remix) and each one can have a different lyrics alignment. Hence, we need to find the right version used by the karaoke users. Given a song_title and an artist_name Wasabi provides many possible versions. With this information, we query YouTube to recover a set of audio candidates. This is similar to other works that used chroma features and diagonal matching to align jazz soli and audio candidates from YouTube (Balke et al., 2018).

To find the correct audio used by the karaoke-users we need to answer three questions:

1. Is the correct audio among the candidates?
2. If there are more than one correct audio, which one is the best?
3. Do annotations need to be adapted to the final audio to perfectly align with it?

Moreover, users are amateurs which may lead to errors. Depending on the amount of those, we may want to discard some files. This introduces a fourth question: are annotations good enough to be used?

4.3 Selecting the audio and adapting the annotation

To answer these questions, we measure the accuracy of aligned annotations to an audio candidate finding a common representation for both audio and text (Meseguer-Brocal et al., 2018).

We convert the audio into a singing-voice probability vector over time $\widehat{p}(t)$M13 \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ \hat p(t) \] \end{document} , with $\widehat{p}(t)\to 1$M14 \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ \hat p(t)\, \to \,1 \] \end{document} when there is voice and $\widehat{p}(t)\to 0$M15 \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ \hat p(t)\, \to \,0 \] \end{document} otherwise. We call these $\widehat{p}(t)$M16 \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ \hat p(t) \] \end{document} predictions. The Singing Voice Detection (SVD) system computes $\widehat{p}(t)$M17 \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ \hat p(t) \] \end{document} from the audio signal represented as a sequence of patches of 80 log-mel bands over 115 time frames (0.014s per frame). Our system is based on the Deep Convolutional Neural Network (CNN) proposed by (Schlüter and Grill, 2015). Figure 3 details the architecture of the network. The output of each patch corresponds to the $\widehat{p}(t)$M18 \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ \hat p(t) \] \end{document} of the central time frame.

Likewise, we transform the lyrics annotations into vas(t), an voice annotation sequence with value 1 when there is vocal and 0 otherwise. Although we can construct vas(t) at any level of granularity, we work only with the note level because it is the finest.

Our hypothesis is that, with a highly accurate SVD system and exact annotations, both vectors vas(t) and $\widehat{p}(t)$M19 \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ \hat p(t) \] \end{document} should be identical. Consequently, it should be reasonably easy to use them to find the correct audio.

At this stage, audio and annotation are described as vectors over time $\widehat{p}(t)\in [0,1]$M20 \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ \hat p(t)\, \epsilon [0, 1] \] \end{document} and vas_o,fr(t) ∊ {0,1}. We measure their similarity using the normalized cross-correlation (NCC). This similarity is not only important in recovering the right audio and finding the best alignment, but also in filtering imprecise annotations.

Since we are interested in global alignment we found this technique more precise than others such as Dynamic Time Warping (DTW). Indeed, DTW finds the minimal cost path for the alignment of two complete sequences. To do so, it can locally warp the annotations, this usually deforms them rather than correcting them. It is also costly to compute and its score is not directly normalized, which prevents us from selecting the right candidate.

The vas(t) depends on the parameters offset_time (o) and the frame rate (fr), vas_{o, fr}(t). Hence, the alignment between p̂ and vas depends on their correctness. While o defines the beginning of the annotations, fr controls the time grid size. When changing fr, the grid size is modified by a constant value that compresses or stretches the annotations as a whole respecting the global structure. Our NCC formula is as follows:

For a particular fr value, NCC(o, fr) can be used to estimate the best ô to align both sequences. We obtain the optimal $\widehat{f}r$M22 \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ \hat fr \] \end{document} using a brute force search in an interval α⁵ of values around fr:

This automatically obtains the ô and $\widehat{f}r$M24 \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ \hat fr \] \end{document} values that best align $\widehat{p}(t)$M25 \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ \hat p(t) \] \end{document} and vas_{o, fr}(t) and yields a similarity value between 0 and 1. Given an annotation vas_{o, fr}, we compute $\mathit{\text{NCC}}(\widehat{o},\widehat{f}r)$M26 \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ NCC(\hat o,\,\hat fr) \] \end{document} for all its audio candidates. Using it, we can find the best candidate (highest score) and establish if the final audio-annotation pair is good enough to keep. To this end, we set a threshold $\mathit{\text{NCC}}(\widehat{o},\widehat{f}r)\ge T_{\mathit{\text{corr}}}$M27 \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ NCC(\hat o,\,\hat fr)\, \ge \,{T_{corr}} \] \end{document} to filter the audio-annotations, storing only the accurate pairs and discarding those for which the correct audio could not be found or those with insufficiently accurate annotations.

We establish the threshold (T_corr = 0.8) to ensure well-aligned audio-annotation pairs. This strategy is similar to active learning, where instead of labeling and using all possible data, we find ways of selecting the accurate data. The process is summarized in Figure 4.

5.1 First generation

Datasets. Three ground-truth datasets are used to train the first teachers: Jamendo (Ramona et al., 2008), MedleyDB(Bittner et al., 2014) and a third that merges both, J+M. They are accurately labeled but small. Each dataset is split into a train, validation and test part using an artist filter.⁶ We keep the test set of Jamendo and MedleyDB for evaluating the different SVD systems.

Teachers. We train three teachers using the training part of each ground-truth set. The teachers select the audio and align the annotations as described in Section 4.3. This creates three new datasets (DALI v0) with 2440, 2673 and 1596 audio-annotation pairs for the teacher: J+M, Jamendo and MedleyDB respectively.

Students. We train three different students. Among the possible target values: p̂ given by the teacher (as is common in the teacher-student paradigm), vas after being aligned using NCC, or a combination of both; we use vas. We found this vector more accurate than p̂. In our approach, the teacher ‘filters’ and ‘corrects’ the source of knowledge from which the student learns. Each student is trained with different data since each teacher may find different audio-annotation pairs or alignments (each one gets a different p̂ which leads to different $\widehat{f}r,ô$M36 \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ \hat fr,\,\hat o \] \end{document} values).

We hypothesize that if we have a more accurate p̂, we can create a better DALI. In Tables 6 and 7, we observe how the students outperform the teachers in both the singing voice detection task and the alignment experiment. Thus, students compute better p̂. Furthermore, we assume that if we use these SVD systems, we will retrieve better audio and have a more accurate alignment. For this reason, we use the student with highest results (based on J+M) to create DALI v1 with 5358 songs (Meseguer-Brocal et al., 2018).

5.2 Second generation

We now use as a teacher the best student of the first iteration, the student J+M. We repeat again the process described in Section 4.3. In this case, the teacher is not trained on any ground truth but on DALI v1, using as target the aligned vas(t). We split DALI v1 (5358 tracks) into 5253 for training, 100 for validation (the ones with higher NCC) and 105 for testing. We manually annotated the test set finding the optimal $\widehat{f}r$M37 \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ \hat fr \] \end{document} and ô. This is our ground-truth for future experiments.⁷

The new SVD (student of the second generation) obtains even better results in the singing voice detection task. Hence, we assume that another repetition of the process will output a better DALI. This is indeed the DALI v2 with 7756 audio-annotation pairs.

This experiment proves that students work much better in the cross-dataset scenario (real generalization) when the train-set and test-set are from different datasets. It is important to note that the accuracy of the student networks is higher than that of the teachers, even if they have been trained on imperfect data.

6.1 On alignment

We hypothesize that a more accurate prediction p̂ leads to a better DALI. To prove this, we measure the precision of the $\widehat{f}r$M38 \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ \hat fr \] \end{document} and ô of each SVD system. To this end, we define a ground-truth dataset by manually annotating 105 songs of DALI v1, i.e. finding the $\widehat{f}r$M39 \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ \hat fr \] \end{document} and ô values that give the best global alignment. We measure then how far the estimated $\widehat{f}r$M40 \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ \hat fr \] \end{document} and ô are from the manually annotated ones. We name these deviations offset_d and fr_d.

Results are indicated in Table 7. We estimate the average offset_d, fr_d and the mean rank. For instance, four systems a, b, c and d with offset deviations 0.057, 0.049, 0.057 and 0.063 seconds are ranked as: b = 1st, a = 2nd, c = 2nd and d = 3rd, respectively. The mean rank per model is the average of all individual ranks per song.

Baseline SVD. The main motivation to improve p̂ is that the alignment observed with the baseline SVD systems is not sufficiently precise. This experiment quantifies this judgment. The T_M_Train and T_J+M_Train are ranked last in finding both the correct offset and frame rate. Their values are considerably different to the ground-truth and produce unacceptable alignments. Remarkably, the T_J_Train is much better and its results are comparable to the student networks.

First students. Each student exceeds its teacher with consistently higher rank and lower deviations. S[T_J+M_Train] is the best student. This is surprising because it is not trained with particularly well-aligned data (its teacher T_J+M_Train is placed 5th and 6th for offset and fr). Yet it scores almost as well as the S[T_J_Train], which was trained with better aligned data (its teacher is the best teacher). We presume an error tolerance in the singing voice detection task, which is not critical below an unknown value, but crucial above it: S[T_M_Train] (trained with the most misaligned data) is worse than the other students.

Second iteration. The Second Generation has the lowest deviations and the best results, being placed first for both rankings. However, the increase is moderate. We presume we are reaching the limit of the alignment precision that we can achieve with the NCC.

These results, together with those in Table 6 prove that DALI is improving at each iteration.

6.2 Quality of the annotations

We can only guarantee that each new DALI version has better audio-annotation pairs with a more accurate global alignment. But there is still the recurring question: how good are the annotations?. After manually analyzing the errors we can group them into two types.

Global errors. They affect the song as a whole and are the least frequent issues. We define two groups.

• Time: The most common global time errors are those with misaligned sections despite the audio-annotation pair having a high NCC and good o and fr values. In these cases, each section has a different offset. Moreover, there are songs with one or more missed sections. This is likely to occur when several vocalists sing at the same time or when a chorus is repeated at the end but not its lyrics.
• Frequency: Raw annotations store the notes as interval differences with respect to an unknown reference. Most songs use C4. But, some use a different reference.

To solve the global frequency errors, we perform a correlation in frequency between the note level $(a_k{}_{,\mathit{\text{notes}}}){}_{k=0}^k={(t_k^0,t_k^1,f_{\mathit{\text{min}}},f_{\mathit{\text{max}}},l_k,i_k)}_{\mathit{\text{notes}}}\to {(t_k^0,t_k^1,f_{\mathit{\text{min}}})}_{\mathit{\text{notes}}}$M41 \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ ({a_k}_{,\,notes})\,_{k = 0}^{{K_{notes}}}\,\, = \,\,\,{(t_k^0,t_k^1,\,{f_k},{l_k},{i_k})_{notes}} \to \,\,\,{(t_k^0,t_k^1,\,{f_k})_{notes}} \] \end{document} and the extracted fundamental note frequency (f₀) (Doras et al., 2019). The f₀ is a matrix over time where each frame stores the note likelihoods obtained directly from the original audio. We compress the original f₀ to 6 octaves, 1 bin per semitone and a time resolution of 0.058s. Similar to the process done in Section 4.3, we transform the annotations (a_{k, notes}) into a matrix. Unlike the previous correlation, we measure correlation along the frequency axis and not the time axis. We then simply transpose all the f_k in the a_{k, notes} by the same value. The transposition values covers all the frequency range in the f₀. We find the frequency scaling factor that maximizes the energy between the annotated frequencies a_{k, notes} and the estimated f₀. This defines the correct global frequency position of the annotations.

Moreover, we calculate the new “flexible” versions of the melody metrics Overall Accuracy, Raw Pitch Accuracy, Raw Chroma Accuracy, Voicing Recall, Voicing False Alarm (Bittner and Bosch, 2019). These metrics add new extra knowledge for understanding the quality of the annotations. Together with the NCC, they can guide us to know which annotations are good and which ones are of lesser quality. We can assume that a high Raw Pitch Accuracy suggests a good alignment. However and since the f₀ has errors, low metrics do not necessarily indicate bad alignment.

Local errors. These errors (Figure 7) occur because users are non-professionals. They cover local segment alignments, text misspellings and single note errors:

• Time: Errors in the positions of the start or end $t_k^0$M42 \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ t_k^0 \] \end{document} and $t_k^1$M43 \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ t_k^1 \] \end{document} . Notes are placed in the wrong position in time or have the wrong duration.
• Frequency: Errors in f_k. These errors are quite arbitrary and include octave, semitone and other harmonic interval errors such as major third, perfect fourth or perfect fifth.
• Text: Misspellings in l_k. Moreover, there are also errors in the phoneme level due to the automatic process employed.
• Missing: Occasional missing notes during humming, “oh”s or similar parts.

To quantify such local issues, it would be necessary to manually review the annotations one by one. This is demanding and time-consuming. Indeed, this is what we aim to avoid. Although solving these errors remains for future work, we can try to infer where they occurred using the time evolution of the f₀ correlation. This vector can filter the annotations, selecting only those segments with high correlation. The f₀ representation and the correlation vector are jointly accessible with the annotations.