# Few Shot Learning for Medical Imaging: A Comparative Analysis of
Methodologies and Formal Mathematical Framework

Jannatul Nayem
Department of Electrical and Electronic Engineering
International Islamic University Chittagong
Kumira, Sitakundu, Chittagong-4318, Bangladesh
<EMAIL_ADDRESS>
&Sayed Sahriar Hasan
Department of Electrical and Electronic Engineering
International Islamic University Chittagong
Kumira, Sitakundu, Chittagong-4318, Bangladesh
<EMAIL_ADDRESS>
&Noshin Amina
Department of Electrical and Electronic Engineering
International Islamic University Chittagong
Kumira, Sitakundu, Chittagong-4318, Bangladesh
<EMAIL_ADDRESS>
&Bristy Das
Department of Electrical and Electronic Engineering
International Islamic University Chittagong
Kumira, Sitakundu, Chittagong-4318, Bangladesh
<EMAIL_ADDRESS>
&Md Shahin Ali
Department of Biomedical Engineering
Islamic University
Kushtia, 7003, Bangladesh
<EMAIL_ADDRESS>
&Md Manjurul Ahsan
School of Industrial and Systems Engineering
University of Oklahoma
Norman, Oklahoma-73019
<EMAIL_ADDRESS>
&Shivakumar Raman
School of Industrial and Systems Engineering
University of Oklahoma
Norman, Oklahoma-73019
<EMAIL_ADDRESS>
###### Abstract

Deep learning becomes an elevated context regarding disposing of many machine
learning tasks and has shown a breakthrough upliftment to extract features
from unstructured data. Though this flourishing context is developing in the
medical image processing sector, scarcity of problem-dependent training data
has become a larger issue in the way of easy application of deep learning in
the medical sector. To unravel the confined data source, researchers have
developed a model that can solve machine learning problems with fewer data
called’ Few shot learning’. Few hot learning algorithms determine to solve the
data limitation problems by extracting the characteristics from a small
dataset through classification and segmentation methods. In the medical
sector, there is frequently a shortage of available datasets in respect of
some confidential diseases. Therefore, Few shot learning gets the limelight in
this data scarcity sector. In this chapter, the background and basic overview
of a few shots of learning is represented. Henceforth, the classification of
few-shot learning is described also. Even the paper shows a comparison of
methodological approaches that are applied in medical image analysis over
time. The current advancement in the implementation of few-shot learning
concerning medical imaging is illustrated. The future scope of this domain in
the medical imaging sector is further described.

_K_ eywords Few Shot Learning $\cdot$ Medical Imaging $\cdot$ Nomoto Model
$\cdot$ Image Classification $\cdot$ Mathematical Model

##  1 Introduction

The development and remunerative application of deep learning do not confine
to computer science but also have flourished in other disciplines. Among them,
one of the uplifting demeanors of deep learning systems is biomedicine. The
deep learning algorithm is applied in various sub-sections of biomedicine like
predicting images, quick disease detection, and biomedical image analysis [1,
2, 3]. The progress of deep learning becomes promoted in such a way that it
gives better prediction than human-level accuracy regarding classification
tasks. Medical image analysis requires a complicated understanding and
detailed study of the extracted features of an image [4, 5]. Even trained
professionals find it quite tangled to understand. The manual process of
recognizing the class of brain tumors or segmenting and annotating human
organs requires years of experience, knowledge, and practice before someone
can become an expert in this field. Nevertheless, the modern progress of deep
learning systems makes it easier than before as it can extract features faster
and learn from them to create an internal illustration of these features and
make a prediction. The processing of the model, objective, and also high level
of accuracy is always comparable with human accuracy [6, 7].

It is evident that the application of deep learning is rapidly increasing in
the medical sector. However, certain drawbacks become an obstacle in the way
of proper illustration of deep learning in the sector of medical image
processing. Among them, scarcity of labeled data and class inconsistency is
considered one of the biggest dependencies of the deep learning process. The
deep learning model’s accuracy and precision largely depend upon a large
number of the training dataset [4]. This issue might not create a big problem
for many medical cases, but there are some rare cases where a large number of
data might not be available for its confidentiality. It is hard to find
available data for some rare cases which ultimately do not provide
satisfactory results regarding deep learning image analysis for the medical
sector. Even though there is no surety that the acquiring data would be
enforceable and enduring to the model while training the dataset to solve the
data dependency problem of deep learning has to be solved in a human mind
processing way with less data [8].

Few-shot learning is the developed version of deep learning with limited data
sources to generalize entire classes of data. This method works by extracting
raw data features for differentiating the classes. Convolutional neural
networks fully depend on the depiction of a larger training dataset. The
problem of the general representation of convolutional network neural network
turns out to be a specific illustration with the help of few-shot learning. In
the following chapter, there will be a discussion and illustration of the
overview of few-shot learning and a comparison of methodological analysis of
few-shot learning approaches [9]. Few-shot learning is a model based on deep
learning systems with fewer datasets applied for training a model to make a
prediction and classification based on data analysis. This process of training
the model is different from the conventional process for simplifying the model
with higher prediction accuracy. Normally, a model trained belongs to the
previous class. The model consists of a support set with n number of examples
along with k various unseen classes. The performance of few-shot learning
determines which support set sample is associated with the query set samples
[10].

To complete the task, few-shot learning is used to develop certain models for
medical image classification. AffinityNet is one of the models that exhibits
outstanding performance on disease-type prediction by extracting local
abstract features. Another approach, the Siamese Network, is demonstrated for
retrieving pictures from medical datasets. The Triplet Network is a developed
version of the Siamese Network that identifies the modality of brain imaging.
Domain generalization is another tackling point in a few-shot learning
algorithm, especially for high-dimensional non-linear biomedical images.
Covariate shift is a tried statistical method for domain adaptation and
generalization for this sector. The gradient-based meta-learning domain
generalization agnostic method is used to improve the generalization model for
the unseen dataset for three domains: new anatomies, diseased population, and
unseen anatomies. It is validated by computed tomography (CT) vertebrae
segmentation task [11].

Few shot learning pathways are widening because of less reliability of
training data. Another significant challenge in the medical sector is to track
gastrointestinal issues, the kidney, and the liver through Endoscopy.
Nevertheless, large datasets from different clinical sources can create an
extensive label bias, making the model unusable. But a novel additive angular
margin metric model, which is a modified framework of a prototypical network,
is introduced for classifying endoscopy test samples from an unseen dataset
that is trained with less training data [12]. Even the gradient-based Reptile
and distance metric-based Prototypical networks, few-shot learning techniques,
are applied to identify skin lesion image datasets. The proposed method is
named after the Meta-Derm Diagnosis network. Here, the problem is classified
into 1-shot, 3-shot, and 5-shot classification problems and used
G-convolutions to rectify the network’s performance [13]. The requirement of
limited data makes few-shot learning limelight in this deep learning era. New
dimensions of few-shot learning applications like ophthalmology are initiated
through the practice of few-shot learning. Though deep learning is applied in
pathological clinical cases, there are some rare cases like papilledema or
anterior ischemic optic neuropathy are failed to conduct a few shot learning
methods due to the scarcity of training datasets. Convolutional neural
networks (CNNs) with the t-SNE visualization tool are incorporated within a
ROC curve (AUC) greater than 0. whose output is better than comparable other
frameworks [14].

In enhancing clinical diagnosis and treatment planning, image segmentation is
an inevitable task to annotate a huge amount of training datasets. A few shot
segmentation was proposed with a new furnished structure to solve the dilemma.
Medical Prior-based Few shot Learning Network (MPrNet) and Interactive
Learning-based Test Time Optimization Algorithm (IL-TTOA) for supporting query
image and interactive purposes to alleviate the hassle of medical experts and
to test the result of this model with the real experimentation of human
clinical dataset [15]. Therefore, another segmentation model called global
correlation network with discriminative embedding (GCN-DE) is proposed to
fasten generalize unseen datasets with spatial consistency and regularity.
This method is applicable to alleviate computational complexity by creating
convolutional layers between support and query images in feature space [16].
Furthermore, image segmentation through few-shot learning is applied
comprehensively in skin and polyp clinical datasets with implicit model
agnostic meta-learning iMAML algorithm, which embodied attention-UNet
mechanism and conjugate gradient for attaining expected results [17]. The
revolutionary contribution in image segmentation continued through the
research of 3D medical image segmentation where U-Net network, a model to
calculate the relationship between 2D support and query dataset through
bidirectional GRU modules and transfer learning technique for the betterment
of performance. The model was tested on various internal and external organ
datasets [18].

In the following chapter, there will be a discussion and illustration of the
overview of few-shot learning and a comparison of methodological analysis of
few-shot learning approaches. The chapter is designed into eight main parts.
The first two-part are about the introduction and existing work with
sufficient references. The third part is about the overview of a few shot
learning where the terminological aspects are described. The fourth part is
about the classification subsection of the few-shot learning method. The fifth
part explains the formal mathematical expression, and the sixth part compares
the methodological approaches of few-shot learning in medical imaging. In the
last two sections, the future scope of medical imaging and the chapter
overview is described in the discussion part.

##  2 Related Work

Due to the need for only a small number of training data, few-shot learning
attracts the most interest. There is immense research on the advancement of
few-shot learning in the medical sector. Recently Farkaš et al (2020) proposed
a Context Adaptive Metric Model (CAMM) with an adaptive ability consisting of
two parts Context parameter module, which accords the characteristics of the
feature extractor, and a Self-evaluation module that fine-tuned context
parameters [19]. This model can be used for extracting key features for most
of the metric models to solve the overfitting problem in few-shot learning.
Besides, another research on ensemble-based deep metric learning (EBDM)
consists of the shared part, which is used to cut short the parameter numbers
and the exclusive part for the feature extraction network in each learner.
This model can be used for image labeling for a new class with higher accuracy
[20]. Therefore, Li et al (2020) introduced a More Attentional Deep Nearest
Neighbor Neural Network (MADN4) with local descriptors and an attention
mechanism combining Convolutional Block Attention Module (CBAM) to deal with
noise problems along with local feature extraction [21]. Few-shot learning
(FSL) is used practically to distinguish between Chronic Obstructive Pulmonary
Disease (COPD) patients and asthma subjects with limited data, where Siamese-
based zero-shot, one-shot, and five-shot learning models are implemented for
the dissimilation of COPD patients from asthma [22].

For adaptation from relatively few samples in the global feature technique,
few-shot learning is an acknowledged concept in the medical field. Early
disease detection in the medical sector is a crucial challenge nowadays.
That’s why the application of Few shot learning is increasing daily in medical
image classification [23]. In addition, Ma et al (2018) Affinity Net with the
k-Nearest-Neighbor attention pooling layer based on semi-supervised few-shot
learning exhibit outstanding output on disease type prediction by extracting
abstract local features [24]. The research was continued through Siamese
Network, a first-rate network [25] which is used to recover medical images
from datasets, and Triplet Network, a more advanced Siamese Network used to
recognize the brain imaging modality [26]. Even few-shot learning is applied
in Glaucoma diagnosis successfully [27]. Also, the classification of diabetic
retinopathy has been improvised through meta-learning [28].

Over the last few years, few-shot learning has focused on medical image
segmentation, where many techniques have been initiated. One of the works from
this domain where Ronneberger et al [29] performed medical image segmentation
by U-Net with great performance. The segmentation of the condition of tissue
by color deconvolution deep neural networks have been performed by Lahiani et
al [30]. Press and excite blocks have been used to segment volumetric images
[31]. Therefore, Generative Adversarial Networks [32], 3D volumes of multiple
modalities [33], and data-augmented networks [34] have been applied for
preparing and executing one-shot biomedical image segmentation. Zhongqi et al
[35] developed an Interventional Shot Learning (IFSL) with three feasible IFSL
algorithmic effectuation based on backdoor adjustments for orthogonal
contribution with existing fine-tuning and meta-learning FSL methods.

Researchers found new dimensions for implementing few-shot learning in real-
life projects with a broader sense. They represented their new methodology of
few-shot learning to solve the segmentation problem based on medical cases.
Rabindra et al. [17] proposed an optimization-based implicit model agnostic
meta-learning (iMAML) algorithm for segmenting medical images by analyzing
unseen datasets with high accuracy. It generates a generalization method for
training skin and polyp datasets which outperform over supervised baseline
model and two few-shot segmentation approaches by over 2%–4% in dice score. In
[36], the Broader Study of the Cross-Domain Few-Shot Learning (BSCD-FSL) model
has been proposed with a varied repository of image data, including crop
disease images, satellite images, dermatology images, and radiology images.
The state-of-art meta-learning method performs better than the conventional
meta-learning process. A Semi-supervised few-shot learning model for medical
image segmentation where few unlabeled images are trained in an episodic
process to get efficient feature extraction. The model is generalized in skin
lesion segmentation datasets [37].

Additionally, the study of few-shot learning using a prototypical network
reached a new level. A model known as the additive angular metric has been
introduced as a framework for a typical network. It helps to identify between
multi-modal, multi-center, and multi-organ gastrointestinal endoscopic
unobserved data. It is used to assume the label class of test samples, and the
suggested model outperformed other models by roughly 7% [11]. Conv-4 backbone
with different backbones represented to implement the model. In addition, the
research work [16] illustrated a domain generalization model with an agnostic
meta-learning framework to improve unseen test distribution by applying a
computed tomography (CT) vertebrae segmentation approach. Shot learning is
employed in this generalized method with fewer unknown datasets. The term
"global correlation network" was used to describe an image segmentation
technique that quickly captures previously unknown classes between a support
and query image [38]. Moreover, it experimented with CT and MRI modalities and
discriminative embedding loss.

In [18], Neural Architecture Search (NAS), a network architecture, has
proposed to solve the manual trial and-error processes issues during
extracting features of unstructured data. The network developed computer
vision applications and ennobled the validity of image classification and
segmentation. The scarcity of medical data makes few-shot learning a prominent
research topic in the deep learning domain, and the research is flourishing
daily. Using the 3D image segmentation model [18], U-Net created a connection
between the data and a query image of 2D slices. In addition to this, the
features of adjacent slices are extracted using a bidirectional gated
recurrent united (GRU). In addition, transfer learning is used to identify the
targeted image’s characteristics. Three procedures are employed [39] to
establish few-shot human activity recognition (FSHAR): deep learning model
training on source domain samples, cross-domain relevance on source domain
samples and target training samples, and finally, fine-tuning to initialize
the targeted model. The Implicit Model Agnostic Meta-Learning (iMAML) model is
employed in the segmentation of medical images to address the problem of
generalizing previously unknown data [17]. It may apply practically to skin
and polyp datasets by learning from hidden training samples. Medical picture
segmentation problems with annotation are resolved with Interactive Few-shot
Learning (IFSL) [15]. It was created by Medical Prior-based Shots Learning
Network and Interactive Learning-based Test Time Optimization Algorithm (IL-
TTOA). Without prior training, it can support the requested image and optimize
the segmentation models.

##  3 Overview ff Few Shots Learning

Few shot learning, an illustration of meta-learning, and a structural
representation of the machine learning model are applied to categorize the new
data based on a few labeled datasets with its pre-trained model. Earlier,
computer vision aimed to be the only focused research domain of FSL. Still, it
is progressing with the NLP but slower due to the scarcity of natural language
data and assembled benchmarks. Since domain-related technicalities,
expressions, and the coalition is arousing difficulties, the Application of
few-shot learning in medical images is in the limelight of attention. Here, a
small number of data are trained with prior knowledge before generalizing the
model in an efficacy manner. Afterward, the data are further proceeded for
fine-tuning. The prior knowledge is applied in three processes; to augment
training data, to suppress hypothesis space, and to attain parameters.

###  3.1 Important Terms of Few-Shot Learning

To understand the concept of few-shot learning, consider two sets (C train
$\cap$ C test= $\phi$) where C train contains a larger amount of training
dataset whereas ($X_{train}^{N}$, $Y_{train}^{N}$) whereas C test has
comparatively less training dataset. From this dataset, the analogies of the
medical domain can be calculated by studying class categories related to
clinical patterns. No algorithm can perform more effectively than few-shot
learning when it comes to generalizing a model with fewer datasets. In FSL, n
is the number of classes the pre-trained model can generalize, and k is the
number of labeled samples that are part of the n number of support sets. The
more the number of ’Values, the more difficult the task is, whereas the less
the number of k values, the more difficult the task is. Moreover, one-shot
learning is shown when k=1. Zero-shot learning is the case when k=0.The
training set for the model consists of k classes and n training examples,
where n << N is a small sample of training examples drawn from the training
set of classes n $\times$ k $\ll$ $|Ctrain|$. They are defined as the Sb
support set subset in Fig. 1. On the other hand, there are other instances
outside support set Sb, such as query set Q b, which uses the support set to
gather information and feature extraction for generalization. It is composed
of recent and conventional data. These two sources of data are equally
important for validating the examples of supervised learning algorithms. As a
result, altering the query set Qb depends on modifying the support set S b.
The following model parameters $\phi$ should be learned in order to estimate
the query set f$\phi$: RD $\rightarrow$ Rd (D $\gg$ d) [12].

Figure 1: A simple illustration of a few-shot learning model containing a
support set and query set where the features are extracted from both datasets
and made decision-based on a similarity function.

##  4 Few Shot Learning Classification-Based Algorithm

Fig. 2 shows that categorizing medical images using few-shot learning is a
growth-oriented area. The classification process divides inputs into groups
based on their differences. The labeled data is categorized using a similarity
method, producing accurate results. With a smaller sample, this technique
concentrates on locating and retrieving feature data. The K-shot N-way
approach of few-shot categorization makes use of fewer data.

Figure 2: A diagram of a few shot classification-based algorithms representing
Prototypical networks, Matching networks, Relational networks, and Model-
agnostic Meta-learning.

###  4.1 Prototypical Networks

Prototypical networks [35] illustrate the concept of a single prototype made
of multiple points which represent each class. For instance, a neural network
is trained with a car image and without a car image for binary classification.
As the network includes images without a car, many unnecessary features are to
be processed within a large range that consumes computing consumes, computing
energy and time. To solve the problem, the network considers only the positive
classes rather than the negative classes. Prototypical networks operate in
this incantation where the prototype is constructed with the most momentous
characteristics of the positive classes that are matchable with unknown and
unseen samples in the future. An internal low-dimensional embedding of
discrete data is made in the whole class. An embedding in a neural network
means containing a large number of car images that are elucidated as a single
vector. This method solves the categorical variables issue and resembles
similar entities in a vector space. This embedding method is also used to
lessen the loss of the task. The equation illustrates the prototype:

$L_{k}=\frac{1}{S_{b}^{k}}\sum_{(X_{i},Y_{i})\in S_{b}^{k}}f_{\phi}(X_{i})$
(1)

$d(f_{\phi}(X),L_{k}=\arccos\frac{f_{\phi}(x)\cdot L_{k}}{f_{\oplus}(x)\cdot
L_{k}}$ (2)

$p_{\emptyset}\left(y_{k}\mid
X\right)=\frac{e^{\cos\left(d\left(f_{\phi}(X)L_{k}\right)\right)}}{\sum_{k^{\prime}}e^{\cos\left(d\left(f_{\phi}(X),L_{k}\right)\right)}},\quad
k^{\prime}\in[1,\ldots,k]$ (3)

$J_{\varnothing}=-\log p_{\varnothing}(\langle y_{k}\rangle X)$ (4)

The network calculates the $M$-dimensional vector $L_{k}$, where
$\phi\in\mathbb{R}^{d}$ is a prototype representation, $x_{i}$ is a
$d$-dimensional feature vector, and $Y_{i}$ is the corresponding label for
support set $S_{b}$ as well as for every class $k$ (see Eq. (1)). Afterward,
it determines the distance $d(\cdot)$ between the query example $X$ and the
prototype representations $\phi$ of any class $k$ (see Eq. (2)). It provides
probability in accordance with Eq. (3). After evaluating two mostly used
distance metrics: Euclidean and cosine, cosine metric turns out to be more
effective in continuous disease progression. Therefore, for the query example
$X\in Q_{b}$, the parameters are computed using stochastic gradient descent
(SGD) to reduce the average negative log probability (see Eq. (4)) of the
target label $y_{k}$.

Figure 3: A representation of the flowchart of a prototypical network, after
selecting the sample, the class prototype, the distance between query and
prototype, loss and propagation are calculated, and the launch training.

Fig. 3 shows that after training the network, the query of unseen samples is
compared with the internal embedding of the class. Then the attributes are
dimensionally reduced and compared with the similarity function for further
results.

###  4.2 Matching Networks

Matching networks [40] is another classification model which endeavors to
learn the working of a classifier using fewer data with the help of memory
augmentation. This network assimilates the $k$-nearest neighbor’s algorithm,
which needs no training dataset, and a conventional neural network that needs
thousands of samples to learn the model. The equation illustrates an attention
mechanism $\alpha$, which compares $\hat{x}$ and $x_{i}$ for accessing memory.

To establish the matching network, the input image $x_{i}$ and their
corresponding label $y_{i}$ are represented as a support set
$S={(x_{i},y_{i})}_{i=1}^{k}$. Then a classifier, $c_{s}(x)$, maps the support
set. The probability of a new example $\hat{x}$ in this network falling into a
certain class of labels must be estimated, and this likelihood is represented
by $P(\hat{y}\mid\hat{x},S)$.

The problem can be mathematically formulated as determining the output
category with the maximum probability (see Eq. (5)). The calculated output is
defined by the given equation:

$\hat{y}=\sum_{i=1}^{k}a(\hat{x},x_{i})y_{i}$ (5)

Figure 4: The Block diagram of the matching network where the support set is
fed into an embedding function g for mapping and attention mechanism x for
identifying the unseen examples and finding the probability function f of the
matching rates with the known label.

Therefore, the attention mechanism basically measures the cosine distance
between support set examples and new examples. Hence, the process goes through
the SoftMax function for normalizing the output in the range between 0 to 1.
Then the support set passes through an embedding function g, generally a
bidirectional LSTM for mapping the support set. The encoding function g embeds
the full set S based on other elements of the set and each individual xi and
becomes g (xi, S). Suppose a small batch B is considered when the training
examples are few. Generally, the matching network extracts the data from the
given support set S by encoding function f and reduces error, as shown in Fig.
4.

###  4.3 Relational Networks

Relational networks (RNs) [41], a sub-section of a neural network, deals with
relational reasoning with the help of plug-in components. The construction of
this network is to co-relate between two input samples based on reasoning. The
function that is used for the relational network is given below:

$RN(O)=f_{\phi}\sum_{i,j}g_{\theta}(O_{i,}O_{j})$ (6)

O is considered a set of objects used for function fϕ and gθ. The function gθ
determines the relationship between object pairs. Suppose a traditional Multi-
Layer Perceptron model is applied to extract all the objects from the input
object pair only once by conducting dimensionality reduction through the
complexity n2. Another significant characteristic is that it neither depends
on input nor output order. This formulates the relation between the objects.
Only images or only text do not define a relational network. This network only
pursues the input that is in the embedding form. The illustrating object
semantics can be neglected to make the model dynamic. Relation network work
regarding the distance metrics for performing classification. Generally, fixed
metric (Euclidean or cosine) and conventional metric((linear) Mahalanobis
metric) are used for fixed feature representation. Still, the Relation network
is trained to learn deep embedding and non-linear metrics through similarity
functions. This is particularly useful because fixed metric works on the basis
of linear separability after the embedding and emphases choosing fixed metrics
like Euclidean, cosine, or Mahalanobis. In contrast, the Relation network
develops a non-linear similarity metric which is better at embedding and
classifying matching/mismatching pairs. And this network executes a flexible
function approximator for the efficacy of the model. As the majority of few-
shot learning models employ four convolutional blocks for the embedding
module, the network adopts the same architectural configuration for a fair
assessment; see Fig. 5. To be specific, each convolutional block contains some
particular layers named batch normalization layer, a ReLU nonlinearity layer,
and a 64-filter 3$\times$3 convolution. A 2$\times$2 max-pooling layer is
likewise present in the first two blocks but not in the last two. As a result,
the network can be employed the output feature maps for the relation module’s
additional convolutional layers. Furthermore, two convolutional blocks and two
fully connected layers comprise the relation module where 3$\times$3
convolution with 64 filters for an individual convolutional block along with
batch normalization, ReLU non-linearity, and 2$\times$2 max-pooling. In order
to maintain an acceptable range for the relation score, all connected layers
are ReLU apart from the output layer.

Figure 5: an illustration of a relation network framework that incorporates
six convolutional blocks for embedding purposes (a) in few-shot learning (b)

###  4.4 Model-Agnostic Meta-Learning

Model-Agnostic Meta-Learning [42] model is eminent for its supple translation
and solution for a comprehensive range of problems. When data availability
increases, the method gains whippy adaptability during execution. The meta-
learning method trains a small data set in such a way that it can eliminate
over-fitting. The actual objective of this method is to reduce the loss of
functions for newly assigned tasks. Suppose $\theta$ is the parameter vector
used for an individual task selected at the time of the training phase from
the support set. Afterward, the network is trained with a few swatches to
generate feedback for that particular task. Subsequently, a test set is
exercised to evaluate the model’s performance as well as its parameters.
Furthermore, fθ defines the parameterized function associated with the
parameter vector $\theta$. The parameter vector $\theta$ changes to
$\theta^{\prime}_{i}$ when the model is loaded with a new task Ti. Hence, This
task is done by fine-tuned parameter where $\alpha$ defines the rate of
learning, L illustrates the loss function of Ti task, and fθ represents the
model (see Eq. 7). Henceforth, the batch-wise format is followed in this model
with a few numbers of examples. Equation 1 for this model is given by,

$\theta^{\prime}i=\theta-\alpha\delta{\theta}L_{T_{i}}(f_{\theta})$ (7)

In addition, Model-Agnostic Meta-Learning is applied in the domain of few-shot
learning to implement a new function of supervised task from the given
previous similar tasks. The model is applicable regarding few-shot regression
and classification. Regression simply requires a few data points from a
continuous-valued function to determine the result. Prior to that, comparable
statistical features are input into the model. In the case of supervised
regression and classification problems, the model considers the horizon $H=1$,
timestep subscript on $x_{(t)}$ as it works with the single input and output.
The task $T_{i}$ propagates $K$ i.i.d. observations $x$ from $q_{i}$, and the
error between the output of $x$ and its corresponding target value $y$ is
considered the task loss. To find the output of the loss function, cross-
entropy is used for supervised classification (see Eq. 8), and mean-squared
error (MSE) is used for regression as shown in Eq. (9) where $x^{(j)}$ defines
the input pair sample and $y^{(j)}$ illustrates the output pair sample. The
loss function of the regression model is given below:

$L_{T_{i}}(f_{\theta})=\frac{1}{K}\sum_{j=1}^{K}(f_{\theta}(x^{(j)})-y^{(j)})^{2}$
(8)

Correspondingly, the cross-entropy loss for discrete classification tasks has
the following form:

$L_{T_{i}}(f_{\varphi})=\sum_{(x^{(j)},y^{(j)})\sim T_{i}}y^{(j)}\log
f_{\varphi}(x^{(j)})+(1-y^{(j)})\log(1-f_{\varphi}(x^{(j)}))$ (9)

##  5 Formal Mathematical Statements of Few Shot Learning Problems

The most intriguing challenge relates to how AI models generalize the useful
training data and memorize label data, in addition to how they learn from
training examples. The deep learning model is more efficient as a result of
the continual process of obtaining the answers to these centralized inquiries.
Few-shot learning has recently emerged as one of the trendy topics in the
field of deep learning [43]. With a few examples of training data, several
algorithms, and models are demonstrated to be useful for greater
generalization. This paper will describe the mathematical underpinnings of a
few generalized few-shot learning problems and their solutions. To build up a
concrete mathematical foundation, the generalized problems of few-shot
learning are categorized into two parts: learning from new examples or
learning a new class from less dataset.

###  5.1 Problem 1(learning from new examples)

Let $U$, $U\subset\mathbb{R}^{d}$ where $U$ defines the input object modeling
(see Eq. 1).

$F:U\rightarrow L$ (10)

where $F$ is a classifier and further illustrated $f:U\rightarrow X$,
$X\subset\mathbb{R}^{n}$, $X$ is the latent space of classifier. And let
$U_{new}={u_{1},\ldots,u_{k}}$, $k\in\mathbb{N}$; $\mathbb{N}$ is the natural
number, $u_{i}\in U_{new}$ defines a new finite set of classifier $F$. Let
$l_{new}\in L$ represents a label of a new object $U_{new}$. Therefore,
$p_{e}$ is denoted for a positive number in the $(0,1]$ range. Discovering a
method $A(U_{new})$ that generates a function $g^{*}:X\rightarrow L$ such that
for $u$ taken from the distribution $P_{u}$ (see Eq. 11 and Eq. 12):

$\mathrm{P}(F[g^{*}\circ f(u)]=l_{\text{new}}\text{ for all }u\in
U_{\text{new}})\geq p_{n}$ (11)

And

$P(F[g^{*}\circ f(u)]=F[g\circ f(u)])\geq p_{e}$ (12)

###  5.2 Solution of problem 1 with theorem

From Eq 10, classifier $F$ is defined, and let
$U_{\text{new}}={u_{1},\ldots,u_{k}}$, $k\in\mathbb{N}$, $u_{i}\in
U_{\text{new}}$ defines a new finite set of classifier $F$. Let
$l_{\text{new}}\in L$ represent a label of the new object connected to new
elements.

Let $Y={x_{1},\ldots,x_{k}}$, where $x_{i}=f(u_{i})$, $i=1,\ldots,k$, is
defined as the explanation of the set $U_{\text{new}}$ in the classifier’s
latent space.

$\bar{x}=\frac{1}{k}\sum_{i=1}^{k}x_{i}$ (13)

Being the representation’s practical average,

$(x_{\bar{}},x_{i})\geq 0\quad\text{for all }x_{i}\in Y$ (14)

The outline is,

$g^{*}:g^{*}(x)=\begin{cases}\ell_{\text{new }},&\text{ if
}\left(\frac{\bar{x}}{\|\bar{x}\|},x\right)-\theta\geq 0\\\ g(x),&\text{
otherwise }\end{cases}$ (15)

Calculated by,

$\theta=\min_{i\in{1,\ldots,k}}{(\frac{\bar{x}}{\bar{x}},x_{i})}$ (16)

is a means of solving Problem 1,

$p_{e}=1-C_{x}/2[r(1-\theta^{2})^{1/2}]^{n}$ (17)

Where Cx is a constant.

###  5.3 Problem 2 (learning from new class)

From Eq. 10, classifier $F$ is defined and let
$U_{\text{new}}={u_{1},\dots,u_{k}}$, where $k\in\mathbb{N}$, $u_{i}\in
U_{\text{new}}$ is a finite independent sample from a distribution that is
uniformly distributed $P_{\text{new}}$ and $l_{\text{new}}\in L$ represents a
new label for every individual element from $P_{\text{new}}$. Therefore,
$p_{e}$ and $p_{n}$ are denoted as positive numbers in the $(0,1]$ range.
Discovering a method $A(U_{\text{new}})$ that generates a function
$g^{*}:X\rightarrow L$ such that for $u$ taken from the distribution
$P_{\text{new}}$, see Eq. 18 and Eq. 19.

$P(F[g^{*}\circ f(u)]=l_{new})\geq p_{n}$ (18)

$P\left[F[g^{*}\circ f(u)]=F[g\circ f(u)]\right]\geq p_{e}$ (19)

###  5.4  Solution of problem 2 with theorem

From Equation 10, the classifier $F$ is defined. Let
$U_{new}={u_{1},\ldots,u_{k}}$, where $k\in\mathbb{N}$ and $u_{i}\in U_{new}$,
be a finite independent sample from a distribution that is uniformly
distributed $P_{new}$, and let $l_{new}\in L$ represent a new level to every
individual element from $P_{new}$ [44]. Let $Y={x_{1},\ldots,x_{k}}$, where
$x_{i}=f(u_{i})$ for $i=1,\ldots,k$, be defined as the explanation of the set
$U_{new}$ in the classifier’s latent space.

$\bar{x}=\frac{1}{k}\sum_{i}x_{i}$ (20)

Being the representation’s practical average and let $\delta$ $\epsilon$ (0,1)
illustrates,

$\Delta=\bar{x}-(\frac{v^{2}}{k}+\frac{k-1}{k}v\delta)^{\frac{1}{2}}>0$ (21)

Then the outline is,

The equation will be inserted here… (22)

Calculated by,

$\theta\in[\max{\Delta-v,0},\Delta]$ (23)

is a means of solving Problem 2,

$p_{n}=\left(1-\frac{C_{new,x}}{2}\left[\rho\left(v^{2}-(\Delta-\theta)^{2}\right)^{\frac{1}{2}}\right]^{n}\right)\times\left(1-C_{new}\left(\frac{k(k-1)}{2}\right)\left[\rho
v\left(1-\delta^{2}\right)^{\frac{1}{2}}\right]^{n}\right)$ (24)

$p_{e}=1-\frac{C_{x}}{2}\left[\rho\left(1-\theta^{2}\right)^{\frac{1}{2}}\right]^{n}$
(25)

Where Cx and Cnew are constant.

Table 1: An illustration of the different methodological approaches, their publishing year, the purpose of the selected study, training and test data type of few-shot learning over 2018 to 2021 in the medical domain. Year |  | Purpose Of
---
the Research
| Research
---
Approach
| Field Of Training
---
and Testing
Domain
Reference
2018 |  | Text Classification
---
on large scale for
medical purpose
| In this paper, they used
---
state-of-the-art methods to
bring
to pass the fine-grained
evaluation. The few and
zero-shot
methods are evaluated
for two
medical datasets
Microwave Monolithic
Integrated Circuit 2
and Microwave
Monolithic Integrated
Circuit 3.
| Medical,
---
departure
report,
medical coding
[45]
2018 |  | Multi-label
---
Medical coding
Classification
| A neural network
---
architecture is built
from a few-shot
learning to match
network and
multi-label loss
functions. CNN also
used to outdo the
models. The motive of
this paper is to guide t
he EMR dataset for
countable multi-label
outcomes.
medical | [46]
2018 |  | Named entity
---
recognition (NER)
for medical records
| Assess five developments in
---
NNR to
enhance the NLP models.
Layer-wise initialization,
]hyperparameter tuning,
combining pre-training data,
custom word embeddings,
and optimizing out of
vocabulary.
medical | [47]
2019 |  | Medical text concept
---
extraction through
normalization
| Sanctuary for few-shot
---
learning
that is built on UMLS data
and pre-trained
word embeddings. The
outsail of this process
is the average participant
and exhibiting
the potential feasibility.
| medical (Adverse
---
drug reaction)
[48]
2019 |  | Named Entity
---
Recognition (NER)
for medical documents
| Key phrases in medical
---
documents are identified
and categorized using NER.
Hybrid Bi-LSTM and CNN
with four input layers.
clinical | [49]
2019 |  | Information
---
retrieval task
in the biomedical and
life science sector
through
entity normalization
| The concept normalization
---
method is used with
the amalgamation
of distributional semantics,
ontological
knowledge, and weak
supervision
which is applied to BB-norm
for microbial habitats and
phenotypes represented
in the text.
biological | [50]
2020 |  | Multi-label document
---
classification
through
graph aggregation
model
| The paper represents a
---
multi-graph
knowledge aggregation
model
which
is trained to combine the s
tructural
information from multiple
labels
graphs. The model is used as a
sub-module of the previous
natural
language for few-shot learning.
medical | [51]
2020 |  | Collecting data
---
from
electronic health
records.
| A combined model is
---
applied
in this paper to extract the
salient
information from the
CRIS dataset
for training and testing
the statistical
model and corporate a
fine-tuning
model for better efficacy. This
method is
used in the real project of
drug-related
information by
amalgamating
state-of-the-art
active learning paradigms
that
outperform the existing
methods.
Clinical | [52]
2020 |  | Medical data
---
classification
| Based on multi-modal
---
feature fusion
and small sample learning
techniques,
a classification method is
applied in
this paper for identifying the
information
of Alzheimer’s patients.
The features of
this proposed model is
extracted
at the vector level. Therefore,
a small
a sample learning
network is
fabricated by the KNN
attention pooling layer and
the convolutional
network (CNN).
MRI data | [52]
2020 |  | Sequence tagging
---
through Named Entity
Recognition (NER)
| The paper is illustrated a
---
prototypical
network and relation module
for trigger identification to
measure
the distance of biomedical
events.
Here, a self-attention
mechanism is
proposed for using fully
complex
biomedical knowledge
which is known as
external knowledge.
biomedical | [53]
2021 |  | Negation scope
---
resolution in
clinical text through
concept extraction
| The paper represented a
---
method of
zero-shot cross-lingual
transfer by
using negation scope
resolution
for multilingual information
extraction from clinical texts
which is considered a
universal
approach. This work shows
the
possibility of a better
output not
only with the English
language
but also with Spanish and
French
clinical texts without
dominions of
target training data or language.
Therefore,
data concentration by exploiting
it and MLT setup are used for
better performance.
clinical | [54]
2021 |  | Name normalization of
---
biomedical names by
specified domain
semantics
| A Deep Averaging
---
Network (DAN)
model is used
to solve the problem of
biomedical
name representation
by aligning encoded
names with more
domain-specific
semantics and conceptual
grounding.
DAN’s
feed-forward encoding
architecture makes it
scalable for use in literal s
ynonymy and
semantic relatedness tasks,
and it has shown
expected results in various
classifications
of biomedical names
without requiring
LSTM order. The model
performs well
in categorizations,
ontologies, and
benchmarks.
Biomedical | [55]
2021 |  | Context extraction of
---
molecular feature of
drug response prediction
| In this study, a flexible neural
---
network model which
may be modified for
different cell line situations
were applied. This system
accommodated quickly
in case of
switching different tissue
types
and moving from cell line
models to the clinical subject
and also including
patient-derived tumor
cells and
patient-derived
xenografts.
Biomedical | [56]
2021 |  | Domain knowledge
---
extraction
from biomedical entities
| The BioGraphSAGE
---
technique
removes biological existence
relations from literature by
using a
Siamese graph neural network
and structured databases as
domain knowledge.
The use of the two qualities
semantic and positional
helps to recognize
connections
between distant elements
in the same literature.
Biomedical entities | [57]
2021 |  | Retrieving
---
information
from
biomedical name
representation
| This paper shows three
---
different
approaches, a balanced
comparison
examination of several
exemplary,
a modified baseline method,
and a
the new experimental
setting for
evaluating
the cross-domain
generalization
ability.
When the feature backbone
is shallow, the result states
that minimizing intra-class
variation is an emerging
component.
Biomedical | [58]

##  6 Future Scope

Few shot learning is progressing continuously in terms of performance which
are represented in previous works. However, the algorithm has some drawbacks
in the case of implementation. Here, a well-defined and efficient baseline is
significant. The algorithm can be tested with a better algorithm if it can
experiment against suitable criteria. Chen et al. [59] and Dhillon et al. [60]
proposed picturizing such baselines for differentiating few-shot learning
algorithms. Moreover, there need to be further experiments for the improvement
of performance for a few shot learning on medical images. However, extensive
testing and analysis are required to expect promising results from a few shot
learning-used algorithms for use in a practical clinical setup. The black box
architectures of deep networks are not promoted with the change of performance
in medical applications [61]. Few-shot learning will vastly be used for the
classification of images, and segmentation is illustrated in [62] for
diagnosis and validation of medical images; few-shot learning can be a great
supporting tool. Furthermore, future works have a wide range of opportunities
through the practice session. For flourishing technology, Magnetic Resonance
Imaging (MRI) is required a magnetism concept and radio graph technique for
analyzing body tissues and structures. The peaking aim of few-shot learning is
to train a model with fewer examples like text-based data humans, semantics
complexities, syntax, and structure altogether make it difficult for the model
to generalize and learn information, especially with the low number of
examples used and evolved exceptional terminologies applied in medical
identification texts. There is always a question about the utility of FSL and
the area s underexplored [62].

##  7 Conclusion

The recent development and advancement of a few shot learning are represented
in this paper. Few shot learning method is applied with limited data to solve
the data dependency of deep learning. Especially the problems can be defined
and explained through the few-shot learning classification process. Approaches
of Few shot learning in executed for NLP in the medical domain. Some
approaches to few-shot learning are proposed in various papers, especially
classification. General performances of few-shot learning are suitable for
real-world application and further research on improving performance. The deep
discussion about the few-shot learning application has been assessed by
researchers. Finally, future opportunities and applications with limited
datasets need to be addressed. This chapter concludes the comprehensive
explanation of a few shot learning for the future.

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