## Wednesday, February 01, 2006

### a jordan sighting, a null space, and a google robot!

A few days ago, my friend John spotted Michael Jordan in Wean Hall. I commented that John should have had Jordan draw a graphical model on a piece of paper (or just draw it on his arm with a permanent marker) and autograph it!

On another note, I saw this image in a paper called Object Categorization by Learned Universal Visual Dictionary by Winn, Criminsci, and T. Minka. This image, which depicts a rough human segmentation of an image of a cow, contains a 'null' space. In Statistical Machine Learning class, we reviewed some linear algebra and thus talked about the 'null space' associated with a linear operator.

1. Is that really a null space? I mean its filled with the molecules which non-robots utilize to live (air; oxygen). Also under some excitation wavelength an emmision spectra will be released by the "null" space causing something that is visible. What about objects with in water? Would the water be considered a null space? That could be disasterous in my mind as the robot may consider a pool of water as null space but as it approaches this null space and falls in, it'll realize the only thing that is null at this point is its own electronics. Do you understand what I am asking? Or am I misunderstanding the concept of a null space, is it just a means of classifying that space in which nothing of interest lies?

2. Here, null space is just a means of classifying that space in which nothing of interest lies. I wasn't trying to be too deep, just wanted to draw a connection between the concept of null space in linear algebra (the subspace of vectors x such that Ax=0 is the null space of the operator A) and that mysterious region on the cow image.

3. Anonymous12:01 AM

So that image was produced through the use of linear algebra alone?

4. That image was produced by a fast and rough human segmentation of an image into semantic object categories.

The space 'null' was labeled as such by the human. Consider recognition as an operator R, where the equation [ R(i) = o ] means that recognition (R) applied to the image vector (i) equals the object vector (o). The null space of R is the set of images (or image regions) that cannot be mapped to an object representation (cannot understand). These vectors map to the null object (defined as zero).

Null(R) = {i | R(i) = 0}