# The Curse of Dimensionality

August 17, 2018You can find more information about the following topic on my website http://www.dubikatz.com/publications-dubi-katz-dov-katz.html

The **curse of dimensionality** refers to various phenomena that arise when analyzing and organizing data in high-dimensional spaces (often with hundreds or thousands of dimensions) that do not occur in low-dimensional settings such as the three-dimensional physical space of everyday experience.” (https://en.wikipedia.org/wiki/Curse_of_dimensionality)

This is a funny definition if I’ve ever seen one. It implies that our everyday experience is low dimensional and therefore the data associated with it is easy to analyze and organize. But if the 3D world we live in was so simple, why is AI struggling to make sense of it?

The answer is that the above definition is both right and wrong. It’s wrong because the world we live in is very very very high dimensional. Sure, our space is three dimensional. But our visual perception of it is composed of millions of pixels refreshed multiple times per second. Therefore our visual data of the simple 3D space around us actually has millions of dimensions.

At the same time, this definition is exactly right. Or at least, it exposes a brilliant truth: it must be possible to organize the data pertaining to the world around us in a low dimensional form. Otherwise, how can any intelligent creature with finite resources (read: humans) make sense of it?

One of my favorite example is the dimensionality of a line. We all remember from school that a line can be described using the equation y=ax+b. In short, a line can be described using two parameters: a & b. Now, imagine tilting your head such that the line rotates to be parallel with the ground (or: x axis). Now, you can describe the line using a single number: y=c (or: the height of the line parallel to the x axis).

This simple example illustrates that perspective or representation is key. If you look at the data the right way, a high dimensional state space becomes lower dimensional. And, in the lower dimension representation, problems are easier to solve, and it becomes possible to make sense of a high dimensional world.

This article by Dov Katz found here: https://medium.com/@dubikatz/the-curse-of-dimensionality-83a254e3d09a

# Dov Katz – The growing popularity of virtual reality

August 10, 2018The Oculus Rift headset is a product of the brilliants minds of Oculus engineers. One of them is Dov Katz. He is an Israeli national who moved to the United States to further hone his knowledge about robotics and the computer technology as a whole. He graduated from Tel Aviv University in Israel with a degree in computer science and electrical engineering in 2004. He had his Ph.D. and masters degrees in 2008 and 2011 from the University of Massachusetts Amherst and his focus of the study was on perception and learning for autonomous manipulation. His postdoc fellowship was at the Robotics Institute, Carnegie Mellon University.

The Oculus Rift headset is just one of his achievements working as a senior engineer and the head of computer vision for Oculus; a company that was bought out by Facebook for $2 billion including cash and stocks. Dov Katz goal is to enable machines to intelligently interpret visual information in our daily environments.

**More info on Dov Katz here:**