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# Interactive singing melody extraction based on active adaptation
††thanks: This work was supported by grant no. PB/EE/2021128B from Prasar
Bharti.

Kavya Ranjan Saxena, Vipul Arora,
<EMAIL_ADDRESS><EMAIL_ADDRESS>
Department of Electrical Engineering
Indian Institute of Technology Kanpur, India

###### Abstract

Extraction of predominant pitch from polyphonic audio is one of the
fundamental tasks in the field of music information retrieval and
computational musicology. To accomplish this task using machine learning, a
large amount of labeled audio data is required to train the model. However, a
classical model pre-trained on data from one domain (source), e.g., songs of a
particular singer or genre, may not perform comparatively well in extracting
melody from other domains (target). The performance of such models can be
boosted by adapting the model using very little annotated data from the target
domain. In this work, we propose an efficient interactive melody adaptation
method. Our method selects the regions in the target audio that require human
annotation using a confidence criterion based on normalized true class
probability. The annotations are used by the model to adapt itself to the
target domain using meta-learning. Our method also provides a novel meta-
learning approach that handles class imbalance, i.e., a few representative
samples from a few classes are available for adaptation in the target domain.
Experimental results show that the proposed method outperforms other adaptive
melody extraction baselines. The proposed method is model-agnostic and hence
can be applied to other non-adaptive melody extraction models to boost their
performance. Also, we released a Hindustani Alankaar and Raga (HAR) dataset
containing 523 audio files of about 6.86 hours of duration intended for
singing melody extraction tasks.

###### Index Terms:

melody extraction, domain adaptation, model agnostic meta-learning, active-
learning

##  I Introduction

Extracting sining melody from polyphonic audio is a fundamental and important
task in the music information retrieval field. The aim is to extract the pitch
of the dominant singing voice from polyphonic audio. There are many downstream
applications of melody extraction, including music recommendation [1], cover
song identification [2], music generation [3], and voice separation [4].

Machine learning methods generally use supervised learning that involves
training a model on source domain data and testing/deploying on target domain
data. These models provide excellent performance when sufficiently large
annotated data is available in the source domain and the data distribution of
the target domain is approximately same as that of source domain. But the
performance degrades when these models are applied to different target domains
which may vary in data distribution as compared to that of source domain [5].
This is called domain shift. For example, a model trained on songs of a
particular singer or genre (source domain), may not perform comparatively well
in extracting melody for a different singer or genre (target domain). In this
paper, we study the effect of domain shift on melody extraction and propose
methods to tackle this problem. The performance degradation by domain shift
can be avoided by adapting on a very little annotated data in the target
domain. This is referred to as domain adaptation[6]. In this paper, we propose
a novel model-agnostic active-meta-learning-based domain adaptation technique
that is a combination of active-learning [7] and meta-learning [8]. Given a
spectrogram of an audio in the target domain, the model uses active-learning
to select those frames of the spectrogram where it is least confident and
marks those frames for the human annotator to annotate. Once the human
annotator provides the melody annotations for those frames, the model uses
meta-learning to adapt its parameters. In this way, the model adapts to the
target domain. One major application of the proposed domain adaptation
technique is to obtain precise melody annotations for a large corpus of
unlabelled audio with minimum human effort.

In this paper, melody extraction is treated as a classification problem, where
the pitch values are binned into a fixed number of pitch classes. This leads
to high class imbalance in the data and the trained model would be severely
biased to the majority classes. Generally meta-learning algorithm [8] is used
for domain adaptation in few-shot learning [9] setting where each class is
represented with small number of examples, but in case of melody extraction we
do not have representative samples for each class. Hence we modify the vanilla
meta-learning approach to handle the severe class imbalance seen in the task
at hand. In this paper we follow optimization-based meta-learning algorithm
which is robust in its ability to quickly adapt to a few samples from a new
target domain.

The main contributions of this work are:

  * •

A comprehensive study on the problem of domain shift in polyphonic melody
extraction.

  * •

A novel meta-learning-based adaptation approach to handle severe class
imbalance in classification.

  * •

A novel interactive domain adaptation method that combines active-learning
with meta-learning.

  * •

We apply the above methods to effectively tackle the problem of domain shift
in melody extraction. To the best of our knowledge, no work on domain
adaptation for singing melody extraction has been done in the past.

  * •

We release a new dataset named Hindustani Alankaar and Raga (HAR) dataset for
singing melody extraction task. The dataset will be accessible using the link
https://zenodo.org/record/8252222

##  II Related Works

###  II-A Existing works on melody extraction

An earlier attempt at extracting melody from polyphonic audio is inclined
toward signal processing methods[10]. Due to the presence of accompaniments in
polyphonic audio, often the first harmonic gets distorted. So, instead of
conventional methods, which tracked pitch values, a robust harmonic comb
tracking approach[11] is proposed that focuses on the strong higher harmonics.
This method extracts the melody in real time, which has applications in query-
based music search. In [12], many other non-deep learning approaches such as
salience-based and source separation based approaches are summarized along
with various applications and challenges in the field of polyphonic melody
extraction. With the advances in the field of deep learning, various neural
network-based methods have been proposed to extract melody from polyphonic
audios. One such work by Lu et al. [13] uses a deep convolutional neural
network (DCNN) with dilated convolution as the semantic segmentation tool. The
candidate pitch contours on the time-frequency image are enhanced by combining
the spectrogram and cepstral-based features. Another work by Bittner et
al.[14] describes a fully convolutional neural network for learning salience
representations for estimating fundamental frequencies. Another proposed
encoder-decoder architecture by Hsieh et al.[15] is used to estimate the
presence of melody line and improve the performance by independently
recognizing the voiced and unvoiced frames. To improve the performance of
these networks, varied musical and structural context is required. For
example, classification tasks[16] are used to jointly detect the voiced and
unvoiced frames. Attention networks[17] are used to further capture the
relationship between frequencies.

All the above deep-learning based methods employ a standard supervised
learning approach for melody extraction from polyphonic audio involving
training a model on source domain data and testing on target domain data. The
models are not adapted to annotated data in the target domain. In this paper,
we propose a novel domain adaptation algorithm that is model-agnostic and can
be applied to the non-adaptive models to improve their performance.

###  II-B Existing domain adaptation techniques

Domain adaptation techniques are used to minimize the domain shift between the
source and target domain by adapting on a few annotated data from the target
domain. Such type of adaptation is called supervised domain adaptation (SDA).
The other types of domain adaptation techniques are unsupervised [18] and
semi-supervised[19] domain adaptation. In this paper, we focus only on SDA.
Tzeng et al. [20] introduced an auxiliary adversarial task of domain
classification to learn domain invariant embeddings. Additionally, they match
the softmax output for a sample of a particular class from target domain with
the mean softmax output for all samples of that class in the source domain.
Motiian et al. [21] suggested to use contrastive loss to minimize the distance
between the samples of same class from source and target domains and
simultaneously penalize the distance of samples from different classes from
source and target domain. This idea is further extended in neural embedding
matching [22] that adds a constraint, encoded using using graph-embedding
techniques to preserve the local geometry of data across domains. Xu et al.
[23] proposed to use stochastic neighbourhood embedding that uses modified-
Hausdorff distance for supervised domain adaptation.

###  II-C Existing works on Meta-learning

The most popular definition of meta-learning is learning to learn, that
focuses on improving the learning algorithm over multiple learning episodes.
In meta-learning, an inner learning algorithm solves a task such as image
classification [24] that is defined by a dataset and objective. Further, the
outer learning algorithm updates inner learning algorithm to improve the outer
objective that can be either generalization or learning speed of the inner
learning algorithm. The existing works on meta-learning are divided into three
categories, namely, metric-based [9], model-based [25] and optimization-based
[26] learning. Optimization-based methods include approaches where the inner-
level task is explicitly formulated as an optimization problem. These methods
primarily aim to obtain meta-knowledge that may be utilized to enhance the
optimization performance. A well-known example is MAML [8], which aims to
learn good initialization parameters in such a way that a few iterations of
inner learning algorithm yields a classifier that performs well on validation
data.

All the above methods are used in few-shot learning setting. In this paper, we
modify MAML[8] such that it can handle sparse classes or class imbalance. For
validation of the approach we apply it to melody extraction problem. MAML
focuses on learning good initialization parameters for a model trained on the
source domain so that it quickly adapts to the target domain with little
training data.

###  II-D Existing works on active learning

Active learning is the technique by which the model aims to select the most
useful samples from a pool of unlabeled samples and provide them to the
annotator for labeling. It is done to reduce the cost of labeling by
simultaneously maintaining high performance of the model. There are three
major approaches of selection of samples from unlabeled samples namely,
uncertainty-based approach, diversity-based approach and expected model
change. The uncertainty-based approach [27][28] determines the amount of
uncertainty and measures it to choose uncertain samples. The diversity-based
approach [29][30] chooses a variety of samples that reflect the entire
distribution of the unlabeled samples. The expected model change [31][32]
refers to the selection of data points that would result in the most
significant change to the current model parameters or outputs, assuming
knowledge of their corresponding labels. The uncertainty of a sample is
determined by the probability of a predicted class [33] or the entropy of
class posterior probabilities [34]. Lewis et al. [33] used only one classifier
to select those samples where the classifier is least confident. Gal et al.
[35] employ the Monte Carlo Dropout technique [36] to derive uncertainty
estimates from deep networks by conducting several forward passes.

In this work, we use normalized true class probability of the sample as the
uncertainty measure for selecting samples in active learning approach.

Figure 1: Class imbalance in the (a) source domain (MIR1K) and different
target domains (b) ADC2004, (c) MIREX05 and (d) HAR. Class 0 represents the
non-voiced class and classes 1-506 represent voiced pitch classes ranging from
A1(55 Hz) to B6(1975.7 Hz). Samples corresponding to non-voiced class are not
shown as they are highly disproportionate in comparison to the voiced classes.

##  III Methodology

The audio waveforms are merged into a mono channel and then downsampled to
8kHz. Since the audios are of different duration, we have divided the audios
into 5-second chunks. By using short-time Fourier transform, we calculate the
magnitude spectrogram of the audio chunks. The spectrogram of dimension
$F\times M$ is calculated using a 1024-point Hanning window and a hop size of
10ms, where $F$ is the number of frequency bins and $M$ is the number of time
frames. The spectrogram is given as an input to the model such that each time
frame $M$ is classified into one of the $C=506$ pitch classes, including a
non-voiced class. The voiced pitch classes range from A1 (55 Hz) to B6 (1975.7
Hz) with a resolution of 1/8 semitone.

###  III-A Pre-training

Let the source training dataset be $D_{1}^{S}=\\{(X_{i},Y_{i})\\}_{i=1}^{I}$,
where $X_{i}$ is the spectrogram of dimension $F\times M$ and
$Y_{i}\in\\{0,1\\}^{C\times M}$ is a one-hot vector over $c$ classes for every
time frame $M$. The time frames of the spectrogram corresponding to the non-
voiced class could dominate the voiced classes, thus introducing class
imbalance detailed in Fig. 1.

We pre-train the base model $f_{[\phi,\theta]}$ on the $D_{1}^{S}$ dataset.
Here, $\phi$ and $\theta$ are the feature extractor layers and classifier
layer, respectively. Initially, the trainable parameters $\phi$ and $\theta$
are randomly initialized. With the spectrogram $X_{i}$ as the input, the base
model $f_{[\phi,\theta]}$ predicts an output distribution $\hat{Y}_{i}$ of
dimension $506\times M$ by computing softmax output for each of the $c$
classes at each time frame $m=0,1,..,M-1$. The number of time frames
corresponding to each class $c$ is given by $T_{c}=\sum_{i,m}Y_{imc}$. During
training, the base model parameters $\phi$ and $\theta$ are updated using the
gradient descent algorithm as:

$\begin{gathered}{[\phi,\theta]}{\leftarrow}{[\phi,\theta]}-{\alpha}{\nabla}_{\\![\phi,\theta]}L_{wce}{(\,f_{[\phi,\theta]})\,}\end{gathered}$
(1)

where $\alpha\in\mathbb{R}_{+}$ is the learning rate and $L_{wce}$ is the
weighted categorical cross-entropy loss to handle the class imbalance defined
as:

$\begin{gathered}L_{wce}=-\sum_{i,m,c}w_{c}Y_{imc}\log(\hat{Y}_{imc})\end{gathered}$
(2)

where $w_{c}\in\mathbb{R}_{+}$ is inversely proportional to $T_{c}$. The base
model $f_{[\phi,\theta]}$ is trained for $E_{1}$ epochs. The feature extractor
layers $\phi$ will not be updated and hence remain frozen in the subsequent
training steps.

Figure 2:  Different confidence criteria derived from the output of the base
model $f_{[\phi,\theta]}$. In maximum class probability (a), the correct and
incorrect predictions overlap considerably. In true class probability (b), the
overlap is very small and correct and incorrect predictions are well
separated. Normalized true class probability (c), serves as the ground truth
for training the confidence model $f_{\psi}$ where the correct predictions are
assigned a value of 1 and the incorrect predictions are in the range [0,1). In
(d), we show the output of the confidence model $f_{\psi}$ when trained
considering (c) as the confidence criteria.

###  III-B Confidence-model training

Consider a sample $(X_{i},Y_{i})$. With the spectrogram $X_{i}$ as the input,
the pre-trained base model $f_{[\phi,\theta]}$ predicts the probabilistic
predictive distribution $P(\hat{Y}_{i}|[\phi,\theta],X_{i})$ of dimension
$506\times M$. The predicted pitch class at each time frame is obtained by
using argmax over the column values in that time frame. We denote these
predicted pitch classes by $\hat{y}_{i}$ which is of dimension $M$. But in
addition to the pitch classes predicted by the base model, we are also
interested in the ability of the base model to recognize when its prediction
is wrong, i.e., base model should be able to provide confidence values for its
predictions. Ideally, for a suitable confidence criteria, a high value of
confidence should indicate the correctness of the base model prediction, and a
low value of confidence indicative of a wrong prediction.

A standard confidence criteria to obtain confidence value is to consider the
softmax probability corresponding to the predicted pitch class at each time
frame. This is also termed as Maximum Class Probability (MCP). The MCP values
for each time frame $m$ is obtained by

$\begin{gathered}\underset{c}{max}\;P(\hat{Y}^{(m)}_{i}=c|[\phi,\theta],X_{i})\\\
=P(\hat{Y}^{(m)}_{i}=\hat{y}^{(m)}_{i}|[\phi,\theta],X_{i})\end{gathered}$ (3)

It is observed that MCP leads to high confidence values for both correct and
incorrect predictions, making the base model over-confident on the wrong
predictions as depicted in Fig. 2(a). The true class at each time frame of
$Y_{i}$ is computed similarly to that for $\hat{Y}_{i}$, i.e., by using argmax
over the column values for each time frame in ${Y}_{i}$. We denote these true
classes (ground truth) by $y^{*}_{i}$ which is of dimension $M$. For an
incorrectly predicted time frame $m$, the probability associated with the true
class $P(\hat{Y}^{(m)}_{i}=y^{*(m)}_{i}|[\phi,\theta],X_{i})$ would be a low
value, indicating that the base model is less confident. Therefore, True Class
Probability (TCP) is a much suitable criteria than MCP for obtaining
confidence as mentioned in [37]. From Fig. 2(b), we observe that even for
correct predictions given by the pre-trained base model $f_{[\phi,\theta]}$,
the TCP value could be less than 0.50. To overcome this shortcoming, we
consider normalized TCP (TCP-n) as the confidence criteria which for every
time frame $m$ is given by:

$\begin{gathered}c_{i}^{*(m)}=\frac{P(\hat{Y}^{(m)}_{i}=y^{*(m)}_{i}|[\phi,\theta],X_{i})}{P(\hat{Y}^{(m)}_{i}=\hat{y}^{(m)}_{i}|[\phi,\theta],X_{i})}\end{gathered}$
(4)

The TCP-n criteria has strong theoretical guarantee compared to TCP, as the
correct predictions will be assigned a value of 1 and the incorrect
predictions will be in the range [0,1) depicted in the Fig. 2(c). Since the
true classes $y^{*}_{i}$ are not available when estimating confidence on
target samples, therefore, the we need a model that learns the TCP-n
confidence values of the training samples in $D_{1}^{S}$ dataset.

To learn the TCP-n confidence values, we build a confidence model with
parameters $\psi$ on top of the feature extractor layers $\phi$ of the pre-
trained base model $f_{[\phi,\theta]}$. With the spectrogram $X_{i}$ as the
input, the complex features extracted from the features extractor layers
$\phi$ are fed to the confidence model with parameters $\psi$ that outputs a
confidence prediction $\hat{c}_{i}=f_{\psi}(X_{i})$. Here, $\hat{c}_{i}$ is of
dimension $M$, i.e., a scalar confidence value $\hat{c}_{i}^{(m)}\in[0,1]$ is
predicted at each time frame $m$. This model framework is similar to the one
mentioned in [37]. During training, we aim to learn the parameters $\psi$ such
that $\hat{c}_{i}$ is close to the TCP-n confidence values $c^{*}_{i}$
calculated in eq. 4. The parameters $\psi$ are updated using the gradient
descent algorithm as:

$\begin{gathered}\psi{\leftarrow}\psi-{\alpha}{\nabla}_{\psi}{L_{conf}{(\,f_{\psi})\,}}\end{gathered}$
(5)

where $\alpha\in\mathbb{R}_{+}$ is the learning rate and $L_{conf}$ is the
mean squared loss defined as:

$\begin{gathered}L_{conf}=\frac{1}{I}\sum_{i=1}^{I}(\hat{c_{i}}-c^{*}_{i})^{2}\end{gathered}$
(6)

The framework of the confidence model is depicted in Fig. 3. The confidence
model is trained for $E_{2}$ epochs. Fig. 2(d) depicts the distribution of the
output confidence values of the confidence model $f_{\psi}$ which demonstrates
how well it has learned the TCP-n confidence criteria on $D_{1}^{S}$.

Figure 3: Here, $\phi$ and $\theta$ represents the pre-trained feature
extractor (F.E) layers and classifier layer respectively. $\psi$ represents
parameters of the confidence model. $L_{conf}$ is calculated at a particular
time frame $m=5$. Similarly, the confidence loss is calculated at every time
frame and then the confidence model is trained.

###  III-C Active-Meta-Learning

In this section, we explain in detail how confidence-based active learning
combined with model agnostic meta-learning helps to better generalize to the
target domain. Given the pre-trained base model $f_{[\phi,\theta]}$ and the
trained confidence model $f_{\psi}$, the active-meta-learning is divided into
two stages as follows:

####  III-C1 Active-Meta-training

Let another source training dataset be
$D_{2}^{S}=\\{(X_{b},Y_{b})\\}_{b=1}^{B}$, where $X_{b}$ and $Y_{b}$ are
defined in the same way as $D_{1}^{S}$. Every sample in $D_{2}^{S}$ is
considered an episode $b$.

For a particular episode $b$, consider two models $f_{[\phi,\theta^{b}]}$ and
$f_{\psi^{b}}$, where the layers $\phi$ are same as the feature extractor
layers of the pre-trained base model, $\theta^{b}$ are the trainable
parameters that are custom initialized by the classifier weights of the pre-
trained base model, i.e., $\theta^{b}=\theta$ and $\psi^{b}$ are the trainable
parameters that are custom initialized by the weights of the trained
confidence model, i.e., $\psi^{b}=\psi$.

With the spectrogram $X_{b}$ as the input, the model $f_{[\phi,\theta^{b}]}$
predicts an output $\hat{Y}_{b}=f_{[\phi,\theta^{b}]}(X_{b})$ of the dimension
$506\times M$. We compute the predicted pitch class at every time frame $m$ of
$\hat{Y}_{b}$ as discussed in III-B and denote these predicted classes by
$\hat{y}_{b}$ which is of dimension $M$. For an episode $b$, there is a true
class associated with every $m$ time frame of $Y_{b}$ which can be computed as
in III-B. We denote the true classes (ground truth) by $y^{*}_{b}$ which is of
dimension $M$.

The frequency of each class $c$ present in the ground truth $y^{*}_{b}$ is
calculated by $f_{c}^{g}=\frac{n_{c}}{M}$, where $n_{c}$ is the total number
of time frames corresponding to class $c$. The weight of each class is given
by $w_{c}^{g}=\frac{1}{f_{c}^{g}}$, with the value being assumed as zero for
the classes not present in the ground truth $y^{*}_{b}$. A point to note here
is that we do not assign the class weights according to the class distribution
across the entire source domain $D_{2}^{S}$, because these weights may not
accurately reflect the current distribution of ground truth pitch classes in
the episode $b$. Also upon comparing the predicted pitch classes to the ground
truth pitch classes in an episode $b$, some classes maybe under or over-
predicted. Therefore, we calculate the class weights dynamically for the
current episode by modifying the class weights $w_{c}^{g}$ as,

Figure 4: Active-Meta-learning framework for polyphonic melody adaptation. In
active-meta-training, for an episode $b$, ILO is performed on $T_{b}^{S}$ such
that the model parameters $\theta^{b}$ and $\psi^{b}$ are updated. Further OLO
is performed on $T_{b}^{Q}$ to update parameters $\theta$ and $\psi$. The same
procedure is repeated for all episode $b$ in source domain. In active-meta-
testing, for an episode $b^{\prime}$ the episode parameters are initialized as
$\theta^{b^{\prime}}=\theta$ and $\theta^{b^{\prime}}=\psi$ and are used to
adapt on $T_{b^{\prime}}^{S}$ (single iteration of ILO) and predict on
$T_{b^{\prime}}^{Q}$.

$\begin{gathered}{w_{c}^{{}^{\prime}g}}={w_{c}^{g}}\times e^{\lambda|\Delta
w_{c}|},{c=0,1,2,...,505}\end{gathered}$ (7)

where $\lambda\in\mathbb{R}_{+}$ is a scaling factor. We calculate $\Delta
w_{c}$ for all classes $c$ as $\Delta w_{c}=(w_{c}^{g}-w_{c}^{p})/w_{c}^{g}$,
where $w_{c}^{p}$ represents the weights of the predicted pitch classes
$\hat{y}_{b}$ calculated in a similar way as $w_{c}^{g}$. Large value of
$\Delta w_{c}$ for a particular class $c$ means that we emphasize more for the
model to learn this class as it is under or over-predicted. We name this class
weighting technique as meta-weighting (MW).

With the same spectrogram $X_{b}$ as the input, the complex features extracted
from the feature extractor layers $\phi$ are fed to the model $f_{\psi^{b}}$
and it predicts an output $\hat{c}_{b}=f_{\psi^{b}}(X_{b})$ of dimension $M$,
i.e., we have a confidence value associated with each time frame.

Algorithm 1 Active-Meta-training Algorithm

0: $\alpha$,$\beta$: learning rates

0: Pre-trained base model parameters [$\phi,\theta$] and confidence model
parameters $\psi$ ; frozen $\phi$

1: for $E_{3}$ number of epochs do

2: for all episodes $b$ in $D_{2}^{S}$ dataset do

3: Initialize $\theta^{b}=\theta$ and $\psi^{b}=\psi$

4: Compute the estimated pitch classes at each time frame from
$\hat{Y}_{b}=f_{[\phi,\theta^{b}]}(X_{b})$

5: Compute the confidence values at each time frame as
$\hat{c}_{b}=f_{\psi^{b}}(X_{b})$

6: Select $K$ time frames corresponding to low confidence values in
$\hat{c}_{b}$ to form support set $T_{b}^{S}=\\{m_{1},...,m_{K}\\}$ and the
rest $M-K$ time frames as the query set $T_{b}^{Q}$

7: Compute the updated parameters $\theta^{b}_{N}$ using $T_{b}^{S}$ by ILO
($N$ update steps) as in eq . 8

8: Calculate updated $c^{*}_{b}$ from
$\hat{Y}_{b}=f_{[\phi,\theta_{N}^{b}]}(X_{b})$ as in eq. 4

9: Compute the updated parameters $\psi^{b}_{N}$ using $T_{b}^{S}$ by ILO ($N$
update steps) as in eq. 9

10: Update $\theta$ and $\psi$ using $T_{b}^{Q}$ by OLO (one update step) as
in eq. 10 and eq. 11

11: end for

12: end for

13: Obtained updated parameters $\theta$ and $\psi$

Algorithm 2 Active-Meta-testing Algorithm ($s=1$)

0: $\alpha$: learning rate

0: $\theta$ and $\psi$ from Algorithm 1

1: for all episodes $b^{\prime}$ in $D^{T}$ dataset do

2: Initialize $\theta^{b^{\prime}}=\theta$ and $\psi^{b^{\prime}}=\psi$

3: Compute the estimated pitch classes at each time frame from
$\hat{Y}_{b^{\prime}}=f_{[\phi,\theta^{b^{\prime}}]}(X_{b^{\prime}})$

4: Compute the confidence values at each time frame as
$\hat{c}_{b^{\prime}}=f_{\psi^{b^{\prime}}}(X_{b^{\prime}})$

5: From $\hat{c}_{b^{\prime}}$, select $K$ least confident time frames as the
support set $T_{b^{\prime}}^{S}=\\{m_{1},...,m_{K}\\}$ and provide them to the
annotator to annotate and the rest $M-K$ time frame as the query set
$T_{b^{\prime}}^{Q}$

6: Compute the updated parameters $\theta^{b^{\prime}}_{N}$ using
$T_{b^{\prime}}^{S}$ by ILO ($N$ update steps) as in eq.8

7: Calculate updated $c^{*}_{b^{\prime}}$ from
$\hat{Y}_{b^{\prime}}=f_{[\phi,\theta_{N}^{b^{\prime}}]}(X_{b^{\prime}})$ as
in eq. 4

8: Compute the updated parameters $\psi^{b^{\prime}}_{N}$ using
$T_{b^{\prime}}^{S}$ by ILO ($N$ update steps) as in eq. 9

9: From the model with updated parameters $\theta_{N}^{b^{\prime}}$, obtain
the estimated pitch classes on the query set from output
$\hat{Y}_{b^{\prime}}=f_{[\phi,\theta_{N}^{b^{\prime}}]}(X_{b^{\prime}})$

10: end for

To create the support set $T_{b}^{S}$ for an episode $b$, we consider $K$ time
frames corresponding to the low confidence values in $\hat{c}_{b}$. It is
denoted by $T_{b}^{S}=\\{m_{1},m_{2},...,m_{K}\\}$. This means that the model
$f_{[\phi,\theta^{b}]}$ is least confident at these $K$ time frames. The query
set $T_{b}^{Q}$ for an episode $b$ consists of rest of the $M-K$ time frames.
The classifier layer $\theta^{b}$ of the model $f_{[\phi,\theta^{b}]}$ is
trained on the support set $T_{b}^{S}$ of episode $b$ and is given by the
following equation:

$\begin{gathered}{\theta}_{i}^{b}={\theta}_{i-1}^{b}-{\alpha}{\nabla}_{\\!\theta_{i-1}^{b}}{L_{T_{b}^{S}}}({f_{[\phi,\theta_{i-1}^{b}]}})\end{gathered}$
(8)

where ${\alpha}\in\mathbb{R}_{+}$ is the learning rate of the model,
${\theta}_{i}^{b}$ are the updated weights of the classifier layer of the
model $f_{[\phi,\theta^{b}]}$ after $i$ steps. The loss
${{L}_{{T}_{b}^{S}}}({f_{[\phi,\theta_{i-1}^{b}]}})$ after ${(i-1)}$ update
steps is calculated as the weighted categorical cross-entropy loss as
mentioned in eq. 2 by using the updated weights $w_{c}^{{}^{\prime}g}$
calculated in eq. 7 for the classes corresponding to the $K$ time frames
present in $T_{b}^{S}$. After $N$ update steps, the updated parameters become
${\theta}^{b}_{N}$. For the same spectrogram $X_{b}$, the updated model
$f_{[\phi,{\theta}^{b}_{N}]}$ predicts an output
$\hat{Y}_{b}=f_{[\phi,{\theta}^{b}_{N}]}(X_{b})$ of dimension $506\times M$.
We calculate the updated $c^{*}_{b}$ from $\hat{Y}_{b}$ as in eq. 4.

Further the model $f_{\psi^{b}}$ is updated on the support set $T_{b}^{S}$ of
episode $b$ and is given by following equation:

$\begin{gathered}{\psi}_{i}^{b}={\psi}_{i-1}^{b}-{\alpha}{\nabla}_{\\!\psi_{i-1}^{b}}{L_{T_{b}^{S}}}({f_{\psi_{i-1}^{b}}})\end{gathered}$
(9)

where $\alpha\in\mathbb{R_{+}}$ is the learning rate of the model,
${\psi}_{i}^{b}$ are the updated weights of the model $f_{\psi^{b}}$ after $i$
steps. The loss ${L_{T_{b}^{S}}}({f_{\psi_{i-1}^{b}}})$ after $(i-1)$ update
steps is calculated as in eq. 6, considering $\hat{c}_{b}$ and updated
$c^{*}_{b}$ corresponding to the $K$ time frames in $T_{b}^{S}$. After $N$
updates, the updated parameters become $\psi_{N}^{b}$. This process of
updating the models $f_{[\phi,\theta^{b}]}$ and $f_{\psi^{b}}$ on the support
set is called inner-loop optimization (ILO). After ILO, the models
$f_{[\phi,\theta^{b}]}$ and $f_{\psi^{b}}$ becomes $f_{[\phi,\theta_{N}^{b}]}$
and $f_{\psi_{N}^{b}}$ respectively, where the updated parameters learn
episode specific knowledge and confidence values respectively, and are used
for inference on the query set ${T}_{b}^{Q}$.

The parameters $\theta$ and $\psi$ are updated using the loss over the query
set ${T}_{b}^{Q}$. This process of updating $\theta$ and $\psi$ is called
outer-loop optimization (OLO) which is expressed by,

$\begin{gathered}{\theta}{\leftarrow}{\theta}-{\beta}{\nabla_{\theta}}{{L}_{{T}_{b}^{Q}}}{(\,f_{{\theta}_{N}^{b}})\,}\end{gathered}$
(10)

$\begin{gathered}{\psi}{\leftarrow}{\psi}-{\beta}{\nabla_{\psi}}{{L}_{{T}_{b}^{Q}}}{(\,f_{{\psi}_{N}^{b}})\,}\end{gathered}$
(11)

where $\beta\in\mathbb{R}_{+}$ is the learning rate,
${L}_{{T}_{b}^{Q}}(f_{{\theta}_{N}^{b}})$ is the weighted categorical cross-
entropy loss calculated as mentioned in eq. 2 by using the updated weights
$w_{c}^{{}^{\prime}g}$ calculated in eq. 7 for the classes corresponding to
$M-K$ time frames in $T_{b}^{Q}$ and ${L}_{{T}_{b}^{Q}}(f_{{\psi}_{N}^{b}})$
is the mean-squared loss calculated as mentioned in eq. 6, with $\hat{c}_{b}$
and $c^{*}_{b}$ corresponding to the $M-K$ time frames in $T_{b}^{Q}$.

For an episode $b$, we perform $N$ updates on both the models in inner-loop
optimization, and only one update on both the models in the outer-loop
optimization. The updated model $f_{[\phi,\theta]}$ and $f_{\psi}$ for one
episode is used to initialize the model $f_{\theta^{b}}$ and $f_{\psi^{b}}$
for the next episode $b$. The entire inner-loop and outer-loop optimization
process (two-stage optimization) is repeated for all the episodes $b$ in the
$D_{2}^{S}$ dataset in source domain for $E_{3}$ number of epochs. The final
updated models $f_{[\phi,\theta]}$ and $f_{\psi}$ learn knowledge across all
episodes. The algorithm for active-meta-training is mentioned in Algorithm 1.

####  III-C2 Active-Meta-testing

In this stage, we test the trained models $f_{[\phi,\theta]}$ and $f_{\psi}$
on the target domain. Let the target dataset be
$D^{T}=\\{X_{b^{\prime}}\\}_{b^{\prime}=1}^{B}$, where $X_{b^{\prime}}$ is the
spectrogram of shape $F\times M$.

After active-meta-training, the updated model parameters $\theta$ and $\psi$
now act as good initialization parameters for the model that adapts to the
audios of different singers or genres. For a particular episode $b^{\prime}$
in the target domain, the model $f_{[\phi,\theta^{b^{\prime}}]}$ is
initialized as $\theta^{b^{\prime}}=\theta$ and the confidence model
$f_{\psi^{b^{\prime}}}$ is initialized as $\psi^{b^{\prime}}=\psi$. With the
spectrogram $X_{b^{\prime}}$ as the input, the model predicts an output
$\hat{Y}_{b^{\prime}}=f_{[\phi,\theta^{b^{\prime}}]}(X_{b^{\prime}})$. We
compute the predicted pitch class at every time frame of
$\hat{Y}_{b^{\prime}}$ as discussed in III-B and denote it by
$\hat{y}_{b^{\prime}}$. With the same spectrogram $X_{b^{\prime}}$ as the
input, the confidence model $f_{\psi^{b^{\prime}}}$ predicts an output
$\hat{c}_{b^{\prime}}=f_{\psi^{b^{\prime}}}({X_{b^{\prime}}})$. In each
iteration of inner-loop optimization, we select $K$ least confident frames
from $\hat{c}_{b^{\prime}}$ as the support set $T_{b^{\prime}}^{S}$. The time
frames in the support set are given to the annotator. The annotator annotates
and thus provide ground truth pitch classes $y^{*}_{b^{\prime}}$ to these
frames. We name the process of confidence-based time frame selection for
annotation as active adaptation (AA). The $N$ update steps are performed over
the model parameters $\theta^{b^{\prime}}$ on support set $T_{b^{\prime}}^{S}$
as in eq. 8 where the class weights ${w^{\prime}}_{c}^{g}$ for the ground
truth pitch classes corresponding to the $K$ time frames in
$T_{b^{\prime}}^{S}$ are calculated as in the eq. 7. After $N$ update steps,
the updated parameters become ${\theta}^{b^{\prime}}_{N}$. We calculate the
updated $c^{*}_{b^{\prime}}$ in the similar way as in III-C1. The confidence
model $f_{\psi^{b^{\prime}}}$ is updated on the support set as in eq. 9
considering $\hat{c}_{b^{\prime}}$ and updated $c^{*}_{b^{\prime}}$
corresponding to $K$ time frames in $T_{b^{\prime}}^{S}$. The above ILO
process is repeated for $s$ number of iterations. In this way, we adapt to
$sK$ time frames. After adapting on $sK$ frames, the performance of the model
with the final updated parameters $\theta^{b^{\prime}}_{N}$ is finally
evaluated on the query set containing $M-sK$ time frames. The results are
averaged over the query set of all episodes in $D^{T}$ to assess the
generalizability of the model. The algorithm for active-meta-testing for
single iteration ($s=1$) of ILO is mentioned in Algorithm 2. The entire
proposed method of active-meta-learning catering to class imbalance is denoted
by w-AML. The framework for interactive melody adaptation is depicted in Fig.
4.

##  IV HAR : Hindustani alankaar and raga dataset

The HAR dataset created consists of 523 audio files (alankaars and ragas) of
about 6.84 hours. The dataset is created by two Hindustani classical
vocalists. There are 259 audio files recorded by first vocalist of about 2.6
hours. There are 264 audio files recorded by second vocalist of about 4.24
hours.

For recording the audios, the audio setup necessitates simultaneous playback
and recording. To create the dataset, the tanpura and percussion instruments
are played. The simultaneous playback and recording of audio unavoidably
introduce a time shift in time synchronization. Typically, the time shift in
audio playback and recording remains constant for a given recording setup and
equipment, so it can be mitigated through a one-time calibration and time
shifting of one of the audio files to achieve a zero relative time shift.

Given the above described audio setup, audio playback is conducted via
headphones so that it is not recorded in the channel recording the singing.
Each vocalist determines the scale of tanpura and the BPM (beats per minute)
of the percussion. The singing audio is time shifted to maintain time
synchronization and the annotations are obtained by Praat [38]. The polyphonic
dataset is created by mixing the time-shifted audio with the tanpura and
percussion audio to maintain time synchronicity.

Our recording setup includes an Audio-Technica AT2020 cardioid condenser
microphone and a laptop with a 12th GenIntel Core i5-12500H 12-core processor.
For recording, the Audacity software [39] is used.

##  V Experiments

###  V-A Data

For the melody adaptation task, we have used
MIR1K111https://sites.google.com/site/unvoicedsoundseparation/mir-1k as the
source data $D^{S}$ which contains 1000 Chinese karaoke clips corresponding to
19 singers, out of which we consider 739 audios corresponding to first 14
singers in $D_{1}^{S}$ and 261 audios corresponding to remaining singers in
$D_{2}^{S}$. For each dataset $D_{1}^{S}$ and $D_{2}^{S}$, we divide the train
and validation data audios in the ratio 90:10, such that there are 665 train
and 74 validation audios in $D_{1}^{S}$ and 235 train and 26 validation audios
in $D_{2}^{S}$, i.e., a total of 900 train and 100 validation data audios in
$D^{S}$. The total training dataset consists of about 2.2 hours of data. No
data augmentation is performed. We have tested the performance of the model on
the three target datasets $D_{1}^{T}$:
ADC2004222http://labrosa.ee.columbia.edu/projects/melody/, $D_{2}^{T}$:
MIREX05note1 and $D_{3}^{T}$: HAR333https://zenodo.org/record/8252222. The
proposed model is only trained for singing voice melody, so we have selected
only those test samples that contained melody sung by humans. As a result, 12
clips in ADC2004($D_{1}^{T}$) and 9 clips in MIREX05($D_{2}^{T}$) are
selected. Since we divide the audios into 5-second chunks, we have a total of
1925 train and 236 validation audio chunks in $D^{S}$, with 1535 train and 189
validation audio chunks in $D_{1}^{S}$ and 390 train and 47 validation audio
chunks in $D_{2}^{S}$. Further, we have 43, 60 and 2847 audio chunks in
$D_{1}^{T}$, $D_{2}^{T}$ and $D_{3}^{T}$ respectively.

###  V-B Experiment setting

In this paper, we employ a basic deep CNN model as the base model to carry out
the melody extraction task. The base model consists of 4 convolutional layers
having [64,128,192,256] filters each using kernels of size $5\times 5$ with
batch normalization and ReLU activation followed by a dense layer having 512
nodes with ReLU activation and a Timedistributed classifier layer with 506
nodes with softmax activation. The calculated spectrogram is of dimension
$F\times M$, where $F=513$ frequency bins and $M=500$ time frames. The
confidence model consists of a dense layer having 256 nodes with ReLU
activation followed by a layer of single node with sigmoid activation.

In the proposed experiment, we pre-train the base model on train data in
$D_{1}^{S}$ for $E_{1}=450$ epochs as in eq. 1 with a learning rate of
$1\times 10^{-5}$. After pre-training the base model, we train the confidence
model on same $D_{1}^{S}$ dataset for $E_{2}=200$ epochs as in eq. 5 with a
learning rate of $1\times 10^{-5}$. We perform active-meta-training on train
data in $D_{2}^{S}$. For ILO, we consider $K=10$ time frames as the support
set. We update the weights of the classifier and confidence model with $N=10$
inner-loop updates on the support set as in eq. 8 and eq. 9 with the learning
rate of $1\times 10^{-5}$, respectively. The same learning rate is used for
OLO. We consider $\lambda=0.2$ in eq. 7. The entire two-stage optimization
process is repeated for $E_{3}=400$ epochs. During active-meta-testing on each
of the target domain datasets $D_{1}^{T}$,$D_{2}^{T}$and $D_{3}^{T}$, we
consider a single iteration ($s=1$) of ILO by selecting $K=10$ time frames as
support set. We update the weights of the classifier and confidence model with
$N=10$ inner-loop updates on the support set as in eq. 8 and eq. 9 with a
learning rate of $1\times 10^{-5}$ respectively and predict on the rest
$M-K=490$ time frames.

We compare the performance of our proposed algorithm with the baseline
algorithms. To maintain the valid comparison, we keep the same source and
target domains across all the baseline experiments. We categorize the baseline
experiments into two categories: Non-adaptive and Adaptive experiments. We
explain the experiments as follows:

  1. 1.

Non-adaptive experiment: We perform classical training (CT) on the base model.
We pre-train the base model on the train data in $D^{S}$ for 450 epochs by
using eq. 1 with a learning rate of $1\times 10^{-5}$. No adaptation on the
target data is performed. The trained model is used to evaluate the
performance on the validation dataset and target datasets -
$D_{1}^{T}$,$D_{2}^{T}$ and $D_{3}^{T}$. The other non-adaptive baselines
include Patch-based CNN [5], Attention Network [17] and SegNet [15]. We have
obtained the results of these experiments on the audios in validation data in
$D^{S}$ and target datasets $D_{1}^{T}$,$D_{2}^{T}$ and $D_{3}^{T}$ by
downloading their online source codes and compiling the results on our dataset
configuration. The baselines are also trained using CT.

  2. 2.

Adaptive experiments: We compare our proposed algorithm with the following
adaptive baselines:

     * •

Fine-Tuning (FT) [40]: We pre-train the base model in the same way as in CT.
We do not consider an additional confidence model in this method. After pre-
training, we update the classifier by adapting on randomly selected $K=10$
time frames of audio episodes in the each target dataset. We name this as
random adaptation (RA). We evaluate the adapted model on the rest of the
$M-K=490$ time frames for each audios in target datasets.

     * •

MAML [8]: We pre-train the base model on the train data in $D_{1}^{S}$ for 450
epochs as in eq. 1 with a learning rate of $1\times 10^{-5}$. We do not
consider an additional confidence model. During meta-training on the train
data in $D_{2}^{S}$, for ILO we consider random $K=10$ time frames as the
support set and update the weights of the classifier with $N=10$ inner-loop
updates as in eq. 8 with a learning rate of $1\times 10^{-5}$. The same
learning rate is used for OLO. The entire two-stage optimization process is
repeated for 450 epochs. Note that during meta-training no class weights are
considered as in original MAML [8], i.e., no MW. During meta-testing on the
target datasets $D_{1}^{T}$,$D_{2}^{T}$ and $D_{3}^{T}$, we perform RA by
considering $K=10$ time frames as the support set. We evaluate the adapted
model on the query set, i.e., rest of $M-K=490$ frames for each episode in the
target datasets.

The performance metrics considered are raw pitch accuracy (RPA), raw chroma
accuracy (RCA) and overall accuracy (OA). All these metrics are computed by
using a standard mir-eval[41] library with a pitch detection tolerance of 50
cents. We further perform the proposed w-AML with different values of support
set size, i.e., $K=10,15,20$ to understand the effect of increasing support
set size.

TABLE I: Performance metrics with the base model used by us and other baseline methods on the validation dataset (source dataset) and the three target datasets. All models are trained using CT. No adaptation used.  Experiments | MIR1K-val | ADC2004 | MIREX05 | HAR
---|---|---|---|---
RPA | RCA | OA | RPA | RCA | OA | RPA | RCA | OA | RPA | RCA | OA
Patch-based CNN[5] | 86.12 | 86.25 | 86.88 | 76.30 | 76.70 | 78.40 | 74.30 | 81.20 | 82.20 | 62.20 | 60.60 | 61.89
Attention Network[17] | 88.67 | 88.34 | 89.30 | 76.30 | 76.50 | 77.40 | 77.80 | 77.80 | 84.40 | 65.40 | 66.32 | 66.55
SegNet[15] | 89.10 | 89.16 | 90.10 | 82.70 | 84.90 | 81.60 | 78.40 | 79.70 | 78.60 | 68.34 | 69.32 | 65.63
Our base model | 88.64 | 88.90 | 88.45 | 79.26 | 80.55 | 79.90 | 81.88 | 82.15 | 81.30 | 75.43 | 76.70 | 75.90
TABLE II: Performance metrics with adaptive methods on the three target datasets. Here, MW, AA and RA stand for meta-weighting, active adaptation and random adaptation, respectively.  Experiments | ADC2004 | MIREX05 | HAR
---|---|---|---
Method | MW | AA | RA | RPA | RCA | OA | RPA | RCA | OA | RPA | RCA | OA
FT [40] | - | ✗ | ✓ | 80.34 | 81.45 | 80.98 | 81.16 | 81.98 | 82.10 | 76.45 | 77.10 | 76.88
MAML [8] | ✗ | ✗ | ✓ | 81.10 | 82.56 | 81.41 | 83.16 | 84.57 | 83.28 | 77.70 | 78.12 | 78.10
w-AML(Ours) | ✓ | ✓ | ✗ | 86.40 | 87.01 | 86.15 | 87.23 | 88.15 | 87.80 | 80.60 | 80.99 | 81.45
TABLE III: Raw pitch accuracy on three target datasets for different support set size $K$ Experiment | ADC2004 | MIREX05 | HAR
---|---|---|---
$K=10$ | $K=15$ | $K=20$ | $K=10$ | $K=15$ | $K=20$ | $K=10$ | $K=15$ | $K=20$
w-AML(Ours) | 86.40 | 87.20 | 88.95 | 87.23 | 88.45 | 89.99 | 80.60 | 81.55 | 82.01
TABLE IV: Ablation study on the three target datasets. Here, MW, AA and RA stand for meta-weighting, active adaptation and random adaptation, respectively.  Experiments | ADC2004 | MIREX05 | HAR
---|---|---|---
Method | MW | AA | RA | RPA | RCA | OA | RPA | RCA | OA | RPA | RCA | OA
w-MAML | ✓ | ✗ | ✓ | 83.50 | 84.81 | 84.99 | 85.39 | 86.88 | 85.95 | 77.34 | 78.45 | 77.14
AML | ✗ | ✓ | ✗ | 81.32 | 82.56 | 81.99 | 82.12 | 83.88 | 81.80 | 75.78 | 76.55 | 75.98
w-AML(Ours) | ✓ | ✓ | ✗ | 86.40 | 87.01 | 86.15 | 87.23 | 88.15 | 87.80 | 80.60 | 80.99 | 81.45
Figure 5: RPA on the query set of size $(M-sK)$ vs $s$ for a typical episode
from the three target datasets. Here, $s=0$ means no adaptation is performed.

##  VI Results and discussions

Table I depicts the comparison of the performance of each method on the
validation data from source domain and the different target domain datasets.
We observe that the performance of each method trained using CT degrades in
extracting melody from the target domains. This illustrates how model
performance is adversely affected by domain shift. HAR dataset consists of
hindustani classical music samples which differs from those of MIR1K dataset
in terms of singing styles, musicological structure and background
instruments. The effect of this large domain shift clearly reflects in poor
performance of all models on HAR dataset. Further, we observe that our base
model performs better on the target domains MIREX05 and HAR. Even though our
base model does not perform well on ADC2004 data, we see that with various
domain adaptation methods the performance of the base model can further be
improved as shown in Table II.

Table II depicts the different domain adaptation methods applied to our base
model and we observe that each method improves the results on the target
domain data as compared to Table I. Further, the table shows the comparison of
our proposed w-AML method to the other adaptive baseline methods, i.e., FT and
MAML. Even though both the baselines use RA, MAML performs better than FT.
This observation is in line with the findings in previous literature [8].
Also, the original MAML algorithm does not cater to class imbalance problem.
The proposed w-AML outperforms both the baselines as it addresses class
imbalance and uses AA instead of RA.

From Table III we observe that the performance of the model increases as we
increase the support set size because the model is able to adapt on more
number of time frames. This is justified because the model performance
increases when large amount of annotated data is given to the model. But our
aim is to obtain a robust model by adapting on as minimal a number of least
confident frames as possible, hence we consider $K=10$. The adaptation
performance of our w-AML method is shown in Fig. 5. The plot shows gradual
improvement in RPA on the query set of a typical episode from three target
datasets after $s$ iterations of inner-loop optimization on support sets.

##  VII Ablation studies

To study the effect of various components of the proposed method, we perform
ablation studies. The The following ablation experiments are carried out:

  * •

w-MAML: In this experiment, we modify the original MAML algorithm [8] such
that during meta-training, it caters to class imbalance and uses MW to update
classifier layer. No separate confidence model is trained, hence RA is
performed. The rest of the method is same as described in MAML under adaptive
experiments.

  * •

AML: In this experiment, we use our proposed w-AML method with a slight
modification that during active-meta-training and active-meta-testing, class
imbalance is not catered, hence no MW is applied.

The results of these ablation experiments are presented in Table IV. In
w-MAML, although the class imbalance is catered, the performance degrades
because RA is performed as compared to AA in w-AML. In AML, although AA is
performed, the performance degrades because it does not cater to class
imbalance as compared to w-AML.

##  VIII Conclusion

In this work, we have studied the problem of domain shift in polyphonic melody
extraction. To handle this problem, we have proposed a novel interactive
melody adaptation algorithm based on active-meta-learning, that also handles
severe class imbalance problem in audio data. The proposed algorithm is model-
agnostic and can be applied to any non-adaptive model to further improve the
performance. The algorithm can be used for speeding up the annotation of
audios in different domains that can be used in various downstream
applications of melody extraction.

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