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@@ -30,6 +30,15 @@
\setkomafont{disposition}{\normalfont\bfseries}
\usepackage{etoolbox}
\usepackage{titlesec}
\setcounter{secnumdepth}{4}
\titleformat{\paragraph}
{\normalfont\normalsize\bfseries}{\theparagraph}{1em}{}
\titlespacing*{\paragraph}
{0pt}{3.25ex plus 1ex minus .2ex}{1.5ex plus .2ex}
\graphicspath{{./resources/}}
\addbibresource{~/Documents/library.bib}
@@ -181,7 +190,7 @@ Traditionally, cardiac auscultation has been performed manually using a standard
stethoscope, with the aim of detecting heart defects aurally. This has been a
fundamental method for detecting heart valve disorders for over a century.
However, auscultation is a skill that requires training and can only usually be
performed by a medial professional, such as a GP. As a result, manual
performed by a medical professional, such as a GP. As a result, manual
auscultation is significantly susceptible to human error~\parencite{Hanna2002}.
Automation of this method using technology may be provide a solution, and
recent research has shown promise in this area. A large amount of research has
@@ -224,14 +233,14 @@ signal~\parencite[p.4]{Pavlopoulos2004}. This presents a significant issue when
attempting to analyse and compare a database of signals, as variations in
recordings and artefacts caused by factors other than heart sounds will most
likely interfere with analysis and comparison methods. To account for this,
pre-processing methods are widely used, aiming to standardize a database. This
pre-processing methods are widely used, aiming to standardise a database. This
is also used as a way to accentuate features of the data that are expected to
be relevant for classification.\\
A common method employed is the use of decimation and a static filter to remove
A common method employed is the use of decimation and static filters to remove
unwanted spectral content that is most likely noise~\parencite{Liang1997a,
Homsi2016, Springer2016, Gupta2007}. This helps reduce higher frequency noise
such as speech, microphone movement, breething and other interference caused
such as speech, microphone movement, breathing and other interference caused
externally. Signals are commonly downsampled to around 1--4KHz, with
anti-aliasing filter specifications varying across the literature. Generally,
highpass chebychev or butterworth filters are favoured with cutoff frequencies
@@ -243,17 +252,17 @@ Pavlopoulos2004}, continuous wavelet transform (CWT)~\parencite{Langley2016} or
wavelet package decomposition (WPD)~\parencite{Liang1998}, are commonly used to
separate components of a signal based on their spectral content.
Wavelet transforms are popular as, unlike Fourier transforms, they are well
localized in both the time and frequency domain. This allows for the analysis
localised in both the time and frequency domain. This allows for the analysis
of PCG signals across multiple frequency bands whilst maintaining transient
temporal events in the resulting decomposition~\parencite[p.93]{Ari2008}.
This may be used for analysis of transient events such as murmurs, that may
consist of higher frequency components than normal heart sounds.
\subsection{Signal Segmentation}\label{Segmentation}
Algorithms for the segmentation of PCG data aim to extract the structure of
the signal over time. This is a key stage in the analysis of PCG signals, as the
structure and relationships between the fundamental heart sounds (FHSs) form
the basis for much of further analysis performed on PCG data.\\
Algorithms for the segmentation of PCG data aim to extract the structure of the
signal over time. This is a key stage in the analysis of PCG signals, as the
structure of the signal and relationships between the fundamental heart sounds
(FHSs) form the basis for much of further analysis performed on PCG data.\\
% TODO: insert segmented graph of PCG cycle
@@ -267,9 +276,9 @@ Shannon energy envelope, achieving good accuracy across 37 recordings of
children~\parencite{Liang1997b}. The algorithm aimed to segment the data by
first extracting the envelope, then applying adaptive rule based thresholds, to
determine peaks corresponding to segmentation points. When comparing results to
hand annotated ground truth data, the system achieved a reported accuracy score
hand-annotated ground truth data, the system achieved a reported accuracy score
of 84\%. However, due to the small sample size, and potential lack of noise in
the database used, this may not translate to a larger database recorded in
the database used, this may not translate well to a larger database recorded in
sub-optimal conditions.\\
More recent methods used spectral representations to assist in the splitting of
the FHSs, in particular using wavelet decomposition. These methods tend to
@@ -283,9 +292,9 @@ for this choice is based on the number of S1s and S2s detected, and the number
of artefacts discarded for each frequency band. This method achieved an
improved accuracy of 93\% across a larger database of 77 recordings. This
suggests that the algorithm is as robust if not more so than previous work by
Liang et\ al.\\
Liang et al.\\
Vepa et.\ al proposed a wavelet decomposition based method that uses a
Vepa et al.\ proposed a wavelet decomposition based method that uses a
combination of simplicity and envelope features~\parencite{Vepa2008}. This
approach attempts to improve robustness when analysing signals of varying
quality by using multiple complimentary features. This allows the method to base
@@ -293,13 +302,14 @@ decisions on a variety of statistical properties. Evaluating the algorithm on a
collection of 160 heart cycles from a variety of sources, a reported accuracy
of 84\% was achieved.\\
More recently, a variety of machine learning methods have been implemented with reasonable
success. Gupta et.\ al presented a method that applies $k$-means clustering to
replace standard threshold based methods for determining peak classification in
a standard envelope based segmentation algorithm~\parencite{Gupta2007}. This achieved a reported
accuracy of 90.29\%. Due to the envelope based method for feature extraction,
this method is still suceptible to noise and artefacts that occur within the
frequency bands of the heart sounds.\\
More recently, a variety of machine learning methods have been implemented with
reasonable success. Gupta et al.\ presented a method that applies $k$-means
clustering to replace standard threshold-based methods for determining peak
classification in a segmentation algorithm based on standard
envelopes~\parencite{Gupta2007}. This achieved a reported accuracy of 90.29\%.
Due to the envelope-based method for feature extraction, this method is still
suceptible to noise and artefacts that occur within the frequency bands of the
heart sounds.\\
Sepehri et.\ al proposed a method that combines neural networks with Power
Spectral Density (PSD) estimates~\parencite{Sepehri2010}. By exploiting the
@@ -308,7 +318,7 @@ range, a neural network is trained to separate these sounds from other events,
such as noise and murmurs. This method achieved a reported 93.6\% accuracy on a
significantly larger database than previous methods detailed.\\
Most significant success in segmentation algorithms has been observed through use
The most significant successes in segmentation algorithms have been observed through use
of probabilistic models such as Hidden Markov Models (HMMs). Early research
using these models by Ricke et.\ al utilised embedded HMMs to model the 4
states of the PCG and their transitions~\parencite{Ricke2005}. MFCCs and
@@ -327,7 +337,7 @@ DHMM is a modified HMM that considers the duration of the current state when
calculating the probability of transition to another state. This modification
scored a reported sensitivity of 98.8\% and a positive predictivity of
98.6\%.\\
Building on previous work using HMMs, Springer et.\ al presented a segmentation
Building on previous work using HMMs, Springer et al.\ presented a segmentation
algorithm by using hidden semi-markov models (HSMMs) in combination with
logistic regression~\parencite{Springer2016}. Use of Hidden semi markov model
allows for a priori information on the duration of the current state to be used
@@ -400,16 +410,17 @@ flutter, and heart valve disease. This section outlines some key research
into these areas, alongside initial research into general abnormality
detection.\\
Reed et.\ al implemented a simple general classification algorithm using artificial
neural networks (ANNs) and wavelet decomposition~\parencite{Reed2004}. As
initial work into this field, preprocessing such as segmentation is not
performed and features remain relatively simple when compared to more recent
methods. Also, due to the comparitively small sample size used for training (1
patient per abnormality, 4 cycles per patient), a reported accuracy of 100\%
would likely generalise poorly. This does however, serve as an early example of
limited success in general heart sound classification.\\
Reed et al.\ implemented a simple general classification algorithm using
artificial neural networks (ANNs) and wavelet
decomposition~\parencite{Reed2004}. As initial work into this field,
preprocessing such as segmentation is not performed and features remain
relatively simple when compared to more recent methods. Also, due to the
comparitively small sample size used for training (1 patient per abnormality, 4
cycles per patient), a reported accuracy of 100\% would have a strong
possibility of generalising poorly. This does however, serve as an early
example of limited success in general heart sound classification.\\
Maglogiannis et.\ al presented a classifier for discrimination of heart valve
Maglogiannis et al.\ presented a classifier for discrimination of heart valve
disease from regular heart sounds using an SVM (Support Vector Machine)
classifier~\parencite{Maglogiannis2009}. Roughly 100 features were extracted
from the signal, based on direct analysis of each heart cycle component (S1,
@@ -440,9 +451,9 @@ representations (TFR) such as short-time fourier transform, wavelet transforms,
Wigner-Ville distribution etc\ldots, with a $k$-nearest neighbour classifier
(k-NN) for systolic murmur detection~\parencite{Quiceno-Manrique2010a}. This
work highlights the effectiveness of alternative TFRs to traditional fourier
methods. This method also employs Principle Component Analysis (PCA) for the
mapping of a high dimensional feature space to a lower dimension, for the
benefit of computational performance. Features were evaluated using a database
methods. This method also employs Principle Component Analysis (PCA), ie.\ the
mapping of a high dimensional feature space to a lower dimension, in order to
improve computational performance. Features were evaluated using a database
of of 22 patients, 6 of which were labeled as having a systolic murmur. The
highest reported accuracy was achieved using MFCCs as the primary feature
vector achieving a 98\% accuracy on 10-fold cross validation.\\
@@ -452,9 +463,9 @@ coronary artery disease through detection of small
murmurs~\parencite{Schmidt2015}. A large number of features are
calculated to provide vectors for classification; Parametric spectral features
such as ARMA are used, alongside instantaneous frequency and octave power
measurements. Complexity features such as sample entropy and simplicity are
measurements. Complexity features, such as sample entropy and simplicity, are
also calculated in an attempt to exploit the likely stochastic nature of
murmurs, when compared to normal heart sounds. Given the large number of
murmurs when compared to normal heart sounds. Given the large number of
features calculated, PCA is used to retain only the most relevant information.
Quadratic discriminant analysis (QDA) is then used as a classifier to provide a
final accuracy score of 73\%.\\
@@ -544,73 +555,72 @@ This section summarises some of the key works presented for the challenge,
including some of the most accurate models, and a baseline classifier
provided to participants as a starting point.\\
A simple baseline classifier was provided to participants in order to
demonstrate the basic structure of systems expected for
entries~\parencite{Liu2016}. The classifier extracted a selection of 20 basic
features, primarily focused on relative timings and amplitudes of heart sounds.
A binary logistic regression model is chosen for classification. From the 20
extracted features, 13 were selected based on their statistical significance,
measured using foreward liklihood ratio selection. The system achieved a
reported score of 66\% on the test set, giving a baseline score for participants
to build on. In addition, the system was trained using leave-one-out cross
validation. By removing a single training database on each fold, the
generalisation of the algorithm trained on all other databases could then be
evaluated. Results showed that performance decreased significantly when
training via this method, giving an average accuracy of 59\%, with training
database $b$ scoring as low as 47\%. This could suggest that individual
databases in the database are not sufficiently represented by other databases,
or that features do not model abnormalities sufficiently.\\
This baseline classifier was provided in order to demonstrate the basic
structure of systems expected for entries~\parencite{Liu2016}. The classifier
extracted a selection of 20 basic features, primarily focused on relative
timings and amplitudes of heart sounds. A binary logistic regression model was
chosen for classification. From the 20 extracted features, 13 were selected
based on their statistical significance, measured using forward liklihood ratio
selection. The system achieved a reported score of 66\% on the test set, giving
a baseline score for participants to build on. In addition, the system was
trained using leave-one-out cross validation. By removing a single training
database on each fold, the generalisation of the algorithm could then be
evaluated, training on all other databases. Results showed that performance
decreased significantly when training via this method, giving an average
accuracy of 59\%, with training database $b$ scoring as low as 47\%. This
could suggest that individual databases in the database are not sufficiently
represented by other databases, or that features do not model abnormalities
sufficiently.\\
Homsi et.\ al proposed a system that utilised 131 time domain, STFT based and
wavelet based features, combined with nested ensemble classifiers to produce an
accuracy score of 84.48\%~\parencite{Homsi2017}. This algorithm combines many
commonly used features in previous PCG related literature such as wavelet
decomposition based features, MFCCs and Shannon Energy. The system also uses a
total of 40 classifiers, 20 for signals labeled to be `standard' and 20 for
thos labeled as `atypical'. A mixture of Random Forrest, LogitBoost and
Cost-Sensitive Classifiers (CSC) are used to classify signals in parallel. Final
results are combined using a rule based decision, designed through manual
Homsi et.\ al proposed a system that utilised 131 time domain, STFT-based and
wavelet-based features which, when combined with nested ensemble classifiers,
produced an accuracy score of 84.48\%~\parencite{Homsi2017}. This algorithm
combines many commonly-used features in previous PCG related literature such as
wavelet decomposition based features, MFCCs and Shannon Energy. The system also
uses a total of 40 classifiers, 20 for signals labeled to be `standard' and 20
for thos labeled as `atypical'. A mixture of Random Forrest, LogitBoost and
Cost-Sensitive Classifiers (CSC) are used to classify signals in parallel.
Final results are combined using a rule-based decision, designed through manual
experimentation.\\
% TODO: Read into accuracy results for this method more closely
Potes et.\ al present a similar approach to that of Homsi et.\
al~\parencite{Potes2016}. 124 similar TFR features are extracted
and used as vectors for an AdaBoost classifier. This was combined with a deep
learning approach using a Convolutional Neural Network (CNN) classifier. The
signal was decomposed into 4 frequency bands and segmented, to provide input to
the CNN. Results from both AdaBoost and CNN classifiers were then combined
using a set descision rule. This method produced the highest score on the test
set for the challenge at 86.02\%.\\
Potes et al.\ presented a similar approach to that of Homsi et
al.~\parencite{Potes2016}. 124 similar TFR features were extracted and used as
vectors for an AdaBoost classifier. This classifier was then combined with a
deep learning approach using a Convolutional Neural Network (CNN) classifier.
The signal was decomposed into 4 frequency bands and segmented, to provide
input to the CNN. Results from both AdaBoost and CNN classifiers were then
combined using a set descision rule. This method produced the highest score on
the test set for the challenge at 86.02\%.\\
Zabihi et.\ al take an alternative approach by choosing not to segment PCG data
in the pre-processing stage~\parencite{Zabihi2016}. This is with the intention of reducing
computational complexity of the resulting algorithm. In addition, the proposed
method utilizes a wrapper sequential forward
feature selection (SFS) and Linear Predictive Coefficients (LPC) for the reduction
of features used for classification. This benefits the system by removing correlated and irrelevant
features, Thus reducing computational complexity and removing irellevant noise
from feature vectors prior to training.
Final classifications are determined through cascaded ensembles of ANNs. The
signal is first classified as either of high or low sound quality, and then as
normal or abnormal. The system achieved a final score of 85.9\% on the hidden
test set.\\
Zabihi et al.\ took an alternative approach by choosing not to segment PCG data
in the pre-processing stage~\parencite{Zabihi2016}. This was with the intention
of reducing computational complexity of the resulting algorithm. In addition,
the proposed method utilizes a wrapper sequential forward feature selection
(SFS) and Linear Predictive Coefficients (LPC) for the reduction of features
used for classification. This benefits the system by removing correlated and
irrelevant features, thus reducing computational complexity and removing
irellevant noise from feature vectors prior to training. Final classifications
are determined through cascaded ensembles of ANNs. The signal is first
classified as either of high or low sound quality, and then as normal or
abnormal. The system achieved a final score of 85.9\% on the hidden test set.\\
Plesinger et.\ al opted to develop a new for of machine learning algorithm
Plesinger et al.\ opted to develop a new form of machine learning algorithm
based on probability assesment~\parencite{Plesinger2017}. In this method,
features are mapped to histograms and thought of as probability distributions.
weights are applied based on number of occurences of each feature, and a
probability function is generated. This can then be used to calculate the
Weights are applied based on the number of occurences of each feature, which in
turn generates a probability function. This can then be used to calculate the
estimated classification of a new data point. From the 228 extracted features,
53 features were then selected based on calculated sensitivity and specificity
scores using generated histograms. This allowed for the training scores to be
automatically optimized by the algorithm.\\
Kay et.\ al present a method using ANNs, a wide variety of features and PCA for
feature reduction. The algorithm scores well on the test set. However, this
work is most noteable for it's rigurous evaluation by authors, using leave on
out cross validation for a clearer understanding of the generalisation of the
algorithm, as well as highlighting issues with the underlying database that are
discussed in Section~\ref{Database}
Kay et al.\ present a method using ANNs, a wide variety of features and PCA for
feature reduction~\parencite{Kay2017}. The algorithm scores well on the test
set. However, this work is most notable for it's rigorous evaluation by
authors, using leave-one-out cross validation for a clearer understanding of
the generalisation of the algorithm, as well as highlighting issues with the
underlying database that are discussed in Section~\ref{Database}
\newgeometry{margin=1cm} % modify this if you need even more space
@@ -650,21 +660,20 @@ A database representative of real-world PCG signals was needed to train models
and evaluate the proposed method effectively. A number of criteria were
identified as necessary for the success of the proposed project:
\begin{itemize}
\item It was required that the database contained sufficient PCG data, so
that a model trained to discriminate between said signals would
in theory generalise to new PCG data.
\item A theme present in almost all previous research is that of noise. As
real-world classification would likely be performed in sub-optimal
conditions the database should contain a mixture of clean and noisy
signals that represent a variety of real world situation. If this is
not possible, noise could potentially be added to clean signals to
simulate this.
\item As this project aims to provide a general abnormality detection
algorithm, it must be able to differentiate healthy signals from a
variety of individual pathologies. This should be reflected in the
database through inclusion of a variety of signals representing
different pathological heart conditions.
\item Reliably labeled data is key for generating a reliable model
\item The database must contain sufficient PCG data, so that a model
trained to discriminate between said signals would, in theory, generalise
to new PCG data.
\item The database should contain a mixture of clean and noisy signals that
represent a variety of real world situations, as real-world
classification would likely be performed in sub-optimal conditions. If
this is not possible, noise could potentially be added to clean signals
to simulate this.
\item Healthy signals must be able to be differentiated from a variety of
individual pathologies in order to provide a general abnormality
detection algorithm. This should be reflected in the database through
inclusion of a variety of signals representing different pathological
heart conditions.
\item Data must be reliably labelled in order to generate a reliable model
(paticularly when using machine learning methods, as in the proposed
project). Labels should ideally be verified by a trained professional.
\end{itemize}
@@ -673,22 +682,23 @@ Two viable options were then considered based on the above criteria:
\begin{enumerate}
\item The Physionet challenge database
\item Generation of a synthetic dataset via methods such as that proposed
by Almasi et.\ al~\parencite{Almasi2011}
by Almasi et al.~\parencite{Almasi2011}
\end{enumerate}
Generation of synthetic data was considered as few well formed alternative
databases exist other than the Physionet challenge data. The database curated
Generation of synthetic data was considered as few well-formed alternative
databases exist, other than the Physionet challenge data. The database curated
for the Physionet challenge was selected for this project, as it fulfilled the
criteria sufficiently and posed less of a risk in terms of signal quality, due
to all signals being produced in real-world environments. However, synthesis
to all signals being produced in real-world environments. However, synthesis
of PCG data remains an interesting possibility for improving evaluation of
classification systems and is discussed in Section~\ref{FurtherWork}.
classification systems and could be considered for the generation of additional
samples in future work.
\subsection{Database Summary}
The selected database is significantly larger and contains a wider variety of
signal conditions than any database used for previous research (as detailed in
table~\ref{PriorWorkTable}). It is released as an open-source resource and is
documented in significant detail by Liu et.\ al~\parencite{Liu2016}. The lack
documented in significant detail by Liu et al.~\parencite{Liu2016}. The lack
of any alternative databases, comparable in size or variety of content, perhaps
makes this resource the current standard for PCG analysis projects. In
addition, by replicating the conditions of the Physionet challenge, results can
@@ -716,7 +726,7 @@ There are a number of issues with the acquired database that have been
highlighted, both through previous literature and through development of the
project. These have been considered throughout development and evaluation of
the project.\\
A significant issue highlighted by Liu et.\ al is the large number of normal
A significant issue highlighted by Liu et al.\ is the large number of normal
recordings compared to pathological recordings. This creates a clear class
imbalance issue that can result in over-inflated classification
results. This is considered in
@@ -724,11 +734,9 @@ Section~\ref{Resample}.\\
Another key issue is the difference between the databases used by participants of the
Physionet challenge, and the available data that was acquired for this project.
% TODO: Update to reflect use of quality labels that have now been found
For unknown reasons, information such as patient labels and signal quality
labels used for training many of the challenge participant's
models have not been made available publicly and so could not be
used in this project. A solution to the lack of signal quality labels is
proposed in Section~\ref{Quality}.\\
For unknown reasons, information such as patient labels used for training many
of the challenge participant's models have not been made publicly available and
so could not be used in this project.\\
The lack of access to the hidden test set used for evaluating challenge entries
also had a significant impact on evaluation. An alternative method for
evaluating using only the data provided has been proposed in
@@ -745,8 +753,8 @@ attention when neccesary. It is clear from previous research that machine
learning methods for classification have shown the most promise in this area,
and that ensemble methods have been largely sucesful in improving
classification accuracy of base classifiers~\parencite{Homsi2017, Potes2016}.
However, one such method that has recently shown significant success and is not
present in recent literature is the stacking
However, one such method that has recently shown significant success in other
fields, but is not present in recent PCG analysis literature, is the stacking
meta-classifier~\parencite[p.498]{Tobergte2013a}. The presented system was
therefore designed to explore the potential for this classification method in
the context of PCG signal classification. This section details the four key
@@ -759,12 +767,13 @@ classification (Section~\ref{class}) and optimisation (Section~\ref{optimise}).
\subsection{Preprocessing}\label{preprocessing}
It quickly became apparent that, due to significant variations in the available
data (as a result of noise, variations in recording equipment etc...), that the
data (as a result of noise, variations in recording equipment etc...), the
effective preprocessing of such data would be a critical factor when designing
the system. This section details the most significant preprocessing steps taken
in order to both minimize noise, and extract the basic structure of the signal.
the system. This section details the most significant preprocessing steps
taken, in order to both minimize noise and extract the basic structure of the
signal.
\subsubsection{Downsampling}
\subsubsection{Signal decimation}
A common method employed to simultaneously reduce computation time and remove
extraneous information is to decimate the input signal by an integer factor.
According to shannon sampling theorem, a digital signal can only represent
@@ -776,25 +785,24 @@ subsequent operations. An anti-aliasing filter must also be applied to the
signal in order to filter harmonic distortion generated by the process.
As it is commonly stated in the literature that little relevant information in
PCG signal is found above 400Hz, all signals were resampled to 1KHz giving a
500Hz cutoff frequency, using a 8th order zero-phase Chebyshev type I filter.
500Hz cutoff frequency, using an 8th order zero-phase Chebyshev type I filter.
\subsubsection{Resampling dataset}\label{Resample}
\subsubsection{Dataset resampling}\label{Resample}
A common issue with data collected from the real world is the imbalance of
classes in data. As noted by Liu et. al~\parencite{Liu2016}, this is the case
classes in data. As noted by Liu et al.~\parencite{Liu2016}, this is the case
with the available dataset, as there are less pathological signals than healthy
signals. This presents an issue with classification tasks, as imbalance can
have a negative impact on classification of the minor
class~\parencite{Longadge2013}. In this context, this would potentially have a
significant impact on classification accuracy for abnormal samples, so must be
handled appropriately.
class~\parencite{Longadge2013}. In this context, this would potentially impact
classification accuracy for abnormal samples, so must be handled appropriately.
Two common methods for approaching this are bootstrap resampling (sampling with
replacement) and jacknife resampling (sampling without replacement). Both
methods have been used accross previous literature, however, jacknife
resampling was chosen for this project. This was to avoid overfitting the
classification model as a result of
the multiple identical samples generated using the bootstrap method. It is
noted that this method does result in a significant loss of information,
reducing the dataset size from 3240 samples to 944.
methods have been used accross previous literature. However, jacknife
resampling was chosen for this project in an effort to avoid overfitting the
classification model as a result of the multiple identical samples generated
using the bootstrap method. It is noted that this method does result in a
significant loss of information, reducing the dataset size from 3240 samples to
944.
\subsubsection{Signal Segmentation}
%TODO: Generate segmentation plot
@@ -802,7 +810,7 @@ With one notable exception~\parencite{Langley2016}, previous classification
algorithms rely heavily on the ability to segment signals into the four
fundamental heart sounds. This is a key prerequisite to the extraction of
relevant features. The defining of signal structure allows for the
relationships between it's components to be analysed as described in
relationships between it's components to be analysed, as described in
Section~\ref{featEx}. To faciliatate the development of robust agorithms for
the Physionet challenge, participants were provided with an implementation of
Springer's HSMM based segmentation algorithm. As the highest scoring algorithm
@@ -976,7 +984,7 @@ alternative method for abnormality detection than those presented in previous
literature.
% TODO:Insert stacking classifier diagram
\subsection{Base Classifiers}
\subsubsection{Base Classifiers}
Clearly, an important consideration when using any ensemble method is the
selection of the base classifiers. In order for any ensemble method to perform
well, it must be constructed using a selection of classifiers that individually
@@ -989,7 +997,7 @@ discussed in Section~\ref{optimise}. The following sections detail the final
selection used; A combination of SVM and Naive-Bayes classifiers, with a
Logistic Regression meta classifier.
\subsubsection{SVM}\label{SVM}
\paragraph{SVM}\label{SVM}
The SVM classifier aims to fit a hyperplane to data that maximises the
separability between classes. This results in a model that has been shown to
generalise well in many cases, as maximising separability between classes is
@@ -1008,7 +1016,7 @@ model, allowing for non-linear relationships that are likely to be present in
the large variety of features to be well represented in classification. Choice
of kernals, and relevant hyperparameters is detailed in Section~\ref{optimise}.
\subsubsection{Naive-Bayes}
\paragraph{Naive-Bayes}
Commonly used in text classification problems, where there is typically a
high-dimensional feature space, Naive Bayes classification uses Bayes rule to
determine the probability of classification, given a vector of features. This
@@ -1044,7 +1052,7 @@ quickly to obtain initial results. Despite the inclussion of more complex
models, this model was chosen via automatic selection for the final model.
Refer to section~\ref{PSOp} for further details.
\subsubsection{Logistic Regression}
\paragraph{Logistic Regression}
Logistic regression is a regression model that aims to fit as hyperplane to
data points by minimizing a cost function using weighted features.
By applying weights to feature vectors then applying a sigmoid function, a
@@ -1279,10 +1287,11 @@ problem, Naive Bayes treats features individually. Could explain why it
performed well
Relationships between features likely with features such as wavelets, perhaps
captured by SVMs
Discuss issues with database e
\section{Further Work}\label{FurtherWork}
Handle silent sections of audio such as those highlighted by Goda et.\
al~\parencite{Goda2016}
Synthesis of synthetic PCG signals
Particle swarm Would ideally be placed inside feature selection
% TODO: Consider talking about resampling using Homsi2016 method