In order for the model to be used for more than two cardiac functions fur-ther research is needed. Collection motion data from several animals en-sure a more robust and presumably better performing model.
Addition-5.3. FUTURE WORK
ally, attaching a gyroscope to the pacemaker lead would give information about the rotation of the heart. Having more information could further aid the model
It was proposed that the technique described in this project could be used in conjunction with ECG. Such a combination would need further research in order to validate the technique.
This project has not investigated the use of ensemble learners. That is, com-bining several classifiers and predict based on what the majority of the clas-sifiers predict. A different approach could be to use clasclas-sifiers which can output probability. The probability could then be interpreted as the how close the heart is from being in one of the cardiac functions.
An approach were the classifier at all times knew the baseline, and instead predicted the transition from baseline to another dysfunction would be of clinical use, since baseline is often the initial cardiac function.
Lastly, it is worth mentioning that an anomaly detector would be benefi-cial. When there are motion data that does not belong to any of the different classes, the model should not attempt to predict any of them, but instead predict that an abnormality was seen.
Appendices
Appendix A
MATLABs decision tree split criterions
MATLABsR split criterion functions for decision tree is provided. The split criterion is what defines which node to create next. Let p(i|t)denote the fraction of inputs belonging to a classiat a given nodet.
Gini’s Diversity Index The Gini’s Diversity index (gdi) is the most broadly used [65] and is given by:
Gini(t)=1−
∑
c i=1[p(i|t)]2 (A.1) wherecis the number of classes. A node with just one class (a pure node) has Gini index 0; otherwise the Gini index is positive.
Deviance The Deviance is given by:
Deviance(t)=−
∑
c i=1p(i|t)log2p(i|t) (A.2)
Twoing rule Unlike the gdi, twoing rule will search for two classes that will make up together more than 50% of the data. It will maximize the following change-of-impurity measure: The above equation is maximized wherePl andPr are the fractions of ob-servations that split to the left and right respectively, andtl andtrrefers to left and right child node.
Little research has been devoted in understanding which of the equations works best for different kinds of problems. Like in many other ares of ma-chine learning, all three must be tried and tested to see which one performs best.
Appendix B
MATLABs SVM kernels
The provided by MATLAB to be used in MATLABs SVM classifier is shown in the table below.
Name Values
Gaussian radial basis function (RBF) exp−||~
x−~y0||2 (2σ2)
or exp −γ||~x−~y0||2 Polynomial (1+~x·~y0)d1
Linear ~x·~x
Table B.1: MATLABs SVM kernels. σ and γ and d are hyperparameters which must be set on beforehand outside of the training process. Hyperpa-rameters is reviewed in section 2.5.3.
Kernels can also be though of as a similarity measure. Naturally, if the problem is linearly separable in the original space, the transformation is not needed. This is known as the linear kernel. The polynomial kernel will, in contrast with the linear kernel, calculate feature conjunctions up to the order ofddimensions. Setting the order too high will fit the data well, but will not generalize. The RBF kernel will intuitively, create bell-shaped curves centered around every support vector, where a support vector is a feature vector touching the margin, seen in figure 2.14. Sigma controls the width of the bell. A large sigma gives a pointed bump, while a small sigma gives a softer and more broad dump. Consequently, setting the sigma too small will make the classifier unable to recognize the pattern in the data.
Setting the sigma it too will make the classifier overfit, meaning that it only represents the current training data, but it cannot generalize to new and unseen data.
1d = number of dimensions
Appendix C
Statistics
C.1 Feature selection methods
Relieff Relieff randomly selects examples, denotedRiand searches for its knearest neighbours from the same class called nearest hitHandknearest neighbours from the other class, called nearest missM. Relieff updates the rank for all features depending on their values forRi,MandH. If instance RiandHhave different values of the featureF, then the featureFseparates two instances with the same class which is not desirable so the rank of that feature is decreased. On the other hand, if instanceRiandMhave different values of the featureFthen the feature separates two instances with differ-ent class values which is desirable so the rank of the feature is increased.
Figure C.1: Figure showing the basic idea of the Relieff feature selection algorithm withkset to one.
Relieff is one of the most successful [17] feature selection methods Robnik et al. [55](1997) has shown that Relieff is effective at detecting relevant features, even when these features are highly dependent on other features.
Robniket al.[56](2003) also showed that it is robust in the number of nearest
neighbors as long as it remains relatively small. A drawback of Relieff is its randomicity. It was mentioned that it chooses examples at random, hence the results can vary in each run of the algorithm. Additionally, a scheme for selecting the number of features to include is necessary, as Relieff only ranks the features. One way to solve this is by sorting the features based on its assigned rank, and then iteratively include the highest ranked feature not yet included and classify for each time. This is done until all features has been included, and the number of features that yielded the best results is used.
Correlation-based feature selection (CFS) Correlation-based Feature Selection (CFS) introduced by Hall [26] and is built on the following hypothesis:“A good feature subset is one that contains features highly correlated with (predictive of) the class, yet uncorrelated with (not predictive of) each other.”
CFS is a filter approach and uses a function that gives a feature subset S consisting of k features a merit according to:
MeritSk = q krc f k+k(k−1)rf f
(C.1)
Therc f is the average feature-class correlation andrf f is the average value of all feature-feature correlation. CFS starts with an empty set of features and adds the feature giving the highest merit given by equation C.1. This is known as a best-first search. It does so until five consecutive fully ex-panded non-improving subsets has been created. Consequently, CFS out-puts the best subset found, instead of ranking all features, thus eliminating the need for a scheme to select the number of features to include, as in Re-lieff.
Because CFS makes use of all the training data at once, it tends to give better results than the wrapper used by Hallet al. on small datasets [27].
The weakness of CFS is the best-first search approach. When a feature is added, it cannot be removed at later stages, thus CFS is susceptible to local optima. However, the number of features created will not be substantial, thus the probability of it getting stuck in a local optimum is limited.
C.2 P-value
When investigating a result from hypothesis testing, the p-value will state how likely the hypothesis is. More specifically, in hypothesis testing, some event is tested on a sample data to see if the event actually has an effect. An example of event and sample data can be some drug applied on a group of rats. With the result in hand, one would like to know if the difference seen on the sample data was because of chance, or because the event actually had an effect, i.e. investigating if the drug is actually working. The way this is solved is by first creating a null hypothesis denotedH0which is the hypothesis stating that there isnoeffect. An alternative hypothesis H1 is
C.2. P-VALUE
also created, which is the hypothesis stating that thereisan effect. The p-value is defined as the probability, under the assumption thatH0is true, of obtaining a result equal or more extreme than what was actually observed.
Examples of test statistics calculating the p-value are: z-test [42], Student’s t-test [61], and the Kolomogorov-Smirnov test [46]. If the p-value is below some predefinedαvalue, usually 0.05, the null hypothesis can be rejected, hence the eventdidhave an effect on the group.
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