Task

Dataset Processing

• I have been completely using the Infty dataset for analysis. The set consists of 30 mathematical documents on the order of 10 pages each.
• I have trimmed down the csv files to only the information I need, and removed odd labellings.
  
• I have written a Matlab script to extract all of the labelled characters and their corresponding labellings (an id which corresponds to latex and mathml representations).
  

Preprocessing

• This took the bulk of my effort, which is what I anticipated.
  
• My original goal in preprocessing was to extract parametric polynomial skeletal curves for parts of the characters. I found this to be a difficult task, and found that a sequence of constant-length line segments would give better results faster.
  
• I extract chains of line segments in the following manner:
  
1. Choose randomly two black points, move one of the points closer to the other until the length is as given (ie scale their difference vector).
   
2. Adjust this original segment to be as close to the center of "blackness" as possible.
   
3. Add a point to the chain, and adjust this segment as in 2.
4. Repeat on both sides of the original segment.
   

• The results produced the chains I wanted, as shown below:

Plsa

• I have begun implementing plsa in Matlab, and I have found a matlab implementation online. I may supplement my implementation with parts of the implementation I found, or possibly parts of a faster C implementation.
  
• My plan for linking my preprocessing to plsa is very simple as of now:
• Extract random chains (let's say 10 chains) for each character.
  
• For each chain:
• For each segment of each chain I have been able to find the standard deviation of near black points from the segment. This gives the "width" of the segment.
  
• Find the "widths" of the segments in the chain.
  
• Find the angle between each segment and the previous segment
  
• Reduce each of the above two vectors into vectors of some prechosen length (let's say 10) by composing and averaging respectively. These combine to form the descriptor for the chain.
• Run kmeans on the descriptors (of size 20 each) extracted to produce classes of chains. There is a matlab kmeans function.
  
• Classify the chains.
  
• The class chains form the input vocabulary to plsa, each character a document and each chain a word. Running plsa is now straightforward.
  

Summary

• I have accomplished the most important tasks I set out to do for the milestone, and I believe I am on track to produce character classification code in the next few weeks.

References