Applied Topological Data Analysis to Deep Learning? Hands-on Arrhythmia Classifi...

Applied Topological Data Analysis to Deep Learning? Hands-on Arrhythmia Classification!

Healthcare is an exciting world to be working in. Every controlled performance enhancement somewhat means saving or improving lives. As a consequence, good enough generalization is not something you can get complacent about.

N ow comes the question of how to do it. Some do enhance their inference by augmenting the size of their dataset, others the quality, others use brand new models, and others invent their own techniques. No need to quote it, but the rise of deep learning is probably the best example. Today, I will aim for the last option: innovate in the description of your data. Let me introduce you to one: Topological Data Analysis . Also abbreviated TDA , it is a recent field that emerged from various research in applied topology and computational geometry. It aims at providing well-founded mathematical, statistical and algorithmic methods to exploit the topological and underlying geometric structures in data. Generally visualized on three-dimensional data, TDA can also be useful in other cases, such as time-series. Interested? :grinning:

As I want this article to be practical, I will refer you to an article I wrote previously, exposing a few theoretical concepts. Feel free to spend a few minutes to immerse yourself around the multiple topics TDA has to offer to you. This article is an excerpt from the work I conducted when I worked in the AI laboratories of Fujitsu in Tokyo, in partnership with the Datashape team from the INRIA (French Research Institute). Tears are running along my cheeks as I, unfortunately, cannot share the entire work, but you should have everything you need to get it done with that Github and that paper .

What are arrhythmias?

H ere is no surprise, but you should know that heart attacks and strokes are among the five first causes of death in the US. As it concerns everyone out there, it is no wonder that companies like Apple are targetting the sector as we talk by developing their own smart monitors. It turns out that your heart is probably the most awesome muscle in your whole body: it functions 24/24 7/7 without interruption, and do it in a very rhythmic way. However, it sometimes fails at keeping the pace, would it be because of alcohol, blitz love, intense exercise or horror movies. Some of those failures may end up lethal. Arrhythmias are one type of failure, being an umbrella term for a group of conditions describing irregular heartbeats, in terms of shape or frequency. Detecting those events and monitoring their frequency may be of huge help to supervise your health and make sure you get access to the right health interventions when needed. That, however, requires smart monitoring.

Get your hands dirty!

M achine Learning! That sounds like the way to smart monitoring! But it requires more than having a fancy model. Here is a good thing, people have been working hard to facilitate research by providing a family of open-source data sets . Those are available on the Physionet platform and named after the conditions they describe: MIT-BIH Normal Sinus Rhythm Database, MIT-BIH Arrhythmia Database, MIT-BIH Supraventricular Arrhythmia Database, MIT-BIH Malignant Ventricular Arrhythmia Database, and MIT-BIH Long Term Database. Those databases are made of single-channel ECGs , each sampled at 360 Hz. Two or more cardiologists independently annotated each record, whose disagreements were resolved to obtain the reference annotations for each beat. We may already be grateful!

The annotations also have the advantage of relieving us from the heartbeat detection problematic, which isn’t much of a barrier: baseline drift and wavelet transform or 1D-CNN both do work properly as a solution.

How to describe heartbeats?

E CGs being one-dimensional time series in our case, how to describe both their shape and time relationships? That is a very general problematic, transposable to lots of domains. Here is where topology will help!

Let’s begin with the temporal information we want from those heartbeats. At the scale of a single one, the retrieved intervals are the ones depicted on the left ( PQRST events ). That information is highly linked to the shape already. At the scale of the ECG itself, we also need to retrieve the RR-intervals , which are the delay in between consecutive R peaks and thus quantify the general rhythm (and its abnormality).

From there, you may already think about building your models using the features exposed above (add some FFT / Wavelets / Chaos Theory / … in the equation). The results obtained from such features (combined with SVM, Boosted Trees or NNs) are good but not satisfactory enough. Time information is not the problem: it is all about the shape of those heartbeats. They indicate a very complex mechanism in the heart itself, and individual differences do imply a huge variability from the very beginning. We thus need a model able to capture the patterns without overfitting to an average pattern resulting from the single pool of individuals we have. That is certainly where the beauty of Topological Data Analysis reaches its peak, at least regarding time-series.

Among the main challenges faced for arrhythmia classification generalization, we find individual differences, and specifically bradycardia and tachycardia . TDA, and more precisely persistent homology theory , powerfully characterizes the shape of the ECG signals in a compact way, avoiding complex geometric feature engineering. Thanks to fundamental stability properties of persistent homology, the TDA features appear to be very robust to the deformations of the patterns of interest in the ECG signal, especially expansion and contraction in the time axis direction. This makes them particularly useful to overcome individual differences and potential issues raised by bradycardia and tachycardia.