Data analysis is a challenging task. Traditional data analysis tools, despite their effectiveness, still have some drawbacks.
Topological data analysis (TDA) offers a general framework for analyzing data, with the advantages of extracting information from large volumes of high-dimensional data.
Using TDA, a local startup L2F, along with EPFL scientists, has developed a model called Giotto-tda that can predict when a systemic shift is about to occur. The model is expected to help scientists identify when events like a stock-market crash, earthquake, traffic jam, coup d’etat, or train-engine malfunction are about to occur.
Scientists drew on TDA techniques to concoct a novel methodology dependent on the way that when a system arrives at a critical state, the data points addressing the system start to form shapes that change its overall structure. By closely monitoring a system’s data points clouds, scientists can distinguish the system’s normal state and, hence, when an unexpected change is unavoidable.
Another advantage of TDA is that it’s versatile to noise, which means the signs don’t get contorted by immaterial data.
With Giotto-tda, the TDA can be used to model just about any data set (such as gravitational waves). The data contained in these sets feed the model’s machine-learning algorithm, improving the accuracy of its predictions and providing warning signs.
Scientists tested the model on the stock-market crashes in 2000 and 2008. They looked at daily price data from the S&P 500 – an index commonly used to benchmark the financial market state – from 1980 to the present day and compared them with the forecasts generated by their model. The price-based graph showed numerous peaks that exceeded the warning level in the run-up to the two crashes.
The signals were very clear with Giotto-tda, as the peaks indicating the upcoming crashes were well above the warning level. That means TDA is a more robust method for making sense of volatile movements that may indicate a looming crash.
- Guillaume Tauzin et al. giotto-tda: A Topological Data Analysis Toolkit for Machine Learning and Data Exploration. arXiv:2004.02551