Machine learning with vector images

[Ubermensch]

In the digit recognition example, the pixels of the image are split into two features, density and symmetry, to identify the digits. In case of raster graphics, the pixels are the primary unit of which ML could be done and they are uniform.

But in case of vector graphics like SVG, or co-ordinate systems, the co-ordinates and paths are explicit or denoted by a mathematical function. How could the image recognition analogy apply to this problem?

Taking the example of a SVG file, I can parse the co-ordinates and path transformations but how could I put them into matrix form since each SVG file would have different number of co-ordinates and path transformations (and of course attributes for color,strokes, etc).

[htlin]

Originally Posted by Ubermensch

In the digit recognition example, the pixels of the image are split into two features, density and symmetry, to identify the digits. In case of raster graphics, the pixels are the primary unit of which ML could be done and they are uniform.

But in case of vector graphics like SVG, or co-ordinate systems, the co-ordinates and paths are explicit or denoted by a mathematical function. How could the image recognition analogy apply to this problem?

Taking the example of a SVG file, I can parse the co-ordinates and path transformations but how could I put them into matrix form since each SVG file would have different number of co-ordinates and path transformations (and of course attributes for color,strokes, etc).

Interesting question and I believe it is an ongoing research issue. Of course, we can try to extract fixed-length feature vectors using ideas similar to those used in pixel-based image learning. Or, there are some learning algorithms that do not necessarily require using fixed-length vectors for representing the data, and can thus be possibly applied to the SVG learning case you are describing. For instance,

* Nearest Neighbor models, which generally only require a suitable similarity function.
* Kernelized Support Vector Machines, which requires the instances to map to a "computable" inner-product space

Some related discussions can be found in the following workshop:

http://www.dsi.unive.it/~icml2010lngs/

Hope this helps.

[Ubermensch]

Thanks for the reply (always good to get reply from the author)

The link and the corresponding resources are a lot useful and it would take some serious reading from me to properly understand them. The reply pretty much answered my first question regarding the geometric interpretation of vector spaces.

From the resources, it seems that an indepth knowledge of Riemannian geometry and algebraic geometry is required to visualize more abstract spaces (looks too tough for me at my level)