About the author: Hidalgo earned a B.S. in Electrical Engineering and an M.S. in Computer Science, with a concentration in AI, from Stanford University. As a master student, Hidalgo researched artificial intelligence and was the teacher assistant for Andrew Ng's Machine Learning Course and Stefano Ermon's Probabilistic Graphical Models Course. He also holds an M.B.A. from the Stanford Graduate School of Business.

It is well known that a small number of variables is often sufficient to effectively describe high-dimensional data. This number is called the intrinsic dimension (ID) of the data. What is not so commonly known is that the ID can vary within the same dataset. This fact has been highlighted in technical discussions, but seldom exploited to gain practical insight in the data structure. Here we develop a simple and robust approach to cluster regions with the same local ID in a given data landscape. Surprisingly, we find that many real-world data sets contain regions with widely heterogeneous dimensions. These regions host points differing in core properties: folded vs unfolded configurations in a protein molecular dynamics trajectory, active vs non-active regions in brain imaging data, and firms with different financial risk in company balance sheets. Our results show that a simple topological feature, the local ID, is sufficient to uncover a rich structure in high-dimensional data landscapes. Introduction From string theory to science fiction, the idea that we might be glued onto a lowdimensional surface embedded in a space of large dimensionality has tickled the speculations of scientists and writers alike. When it comes to multidimensional data, however, such situation is quite common rather than a wild speculation: data often concentrate on hypersurfaces of low intrinsic dimension (ID).

Machine learning is helping urbanists confirm–or disprove–long-standing theories about cities. Why do certain neighborhoods feel safe while some feel dangerous? Why are others considered beautiful? How do cities develop and change over time? And most importantly, how can we quantify these observations about the way we perceive cities, and use it to plan urban areas that are more equitable?

Why do certain neighborhoods feel safe while some feel dangerous? Why are others considered beautiful? How do cities develop and change over time? And most importantly, how can we quantify these observations about the way we perceive cities, and use it to plan urban areas that are more equitable? César Hidalgo, the director of the Collective Learning group at the MIT Media Lab, has spent years using crowdsourced data and machine vision technology to build models of cities that can answer questions that statistics and surveys simply can't.

PARIS – In a city hit by chronic pollution and traffic problems, Paris officials are experimenting with a self-driving shuttle linking two train stations in the French capital. Two electric-power EZ10 minibuses, which can carry up to six seated passengers, were put into service Monday and will be tested until early April between the Lyon and Austerlitz stations in Paris. The GPS-guided vehicle is free and will be running seven days a week. "To respond to the pollution emergency in big urban zones it is urgent to innovate with new transportation systems that are more environmentally friendly," said Catherine Baratti-Elbaz, head of the local district where the test is taking place. Jean-Louis Missika, a Paris deputy mayor in charge of innovation, said self-driving vehicles "will change the urban landscape in a spectacular fashion" within the next 20 years.