A few weeks ago I had to figure out how to perform a mapping of pandas column values to other values. This was not necessarily a discrete mapping, as in the initial column value needed to match a range.

The dataframe I was working with resembled the following:

   value
0     88
1      3
2      5
3     65
4     72
5     54

And there were a set of conditions by which I needed to replace. Think of it like this, if the above were a group of marks for an exam, I would want to map it based on the value ranges.

This was purely out of sheer need, and this was the fastest way I could’ve gotten it done (I ended up learning a LOT about CLI and the awk command from this, so I’m really grateful for that)

The problem: I have a column in a utf-8 CSV file of type Integer, which should actually be type string and zero-padded up to (let’s say length N).

~/projects/awk_pad ❯ cat out.csv             
a,Y,1
b,N,10
c,Y,12223253

What I want, is the following (output from the cat tool):

This is taken from Diffusion Convolutional Neural Networks (referenced in the footer). According to the authors, a diffusion convolution scans a diffusion process across each node. Analog to biology, where the information is allowed to propagate conditional of its density and environment.

It was applied to node classification, edge classification and graph classification, but node-classification is the task I wanted to focus on. When first presented, it was a novel way to effectively apply convolutions (invariant to location and rotation), to arbitrarily-structured data (i.e. graphs). Based on the results presented, the DCNN model outperformed a probabilistic-relational model in citation (a conditional-random field, no I do not know much about that) in graph topic-classification.

Origin Story

Recently, I was trying to disect the original DCNN Paper which utilized a diffusion kernel to more readily make use of implicit graph-structure in common tasks such as node, edge and graph classification. However, an existing implementation I fonund had a curious piece of notation which led me down the rabbithole of Tensor calculus.

Coordinates are maps used to solve a given problem. A coordinate transform allows mapping from one frame of reference to another (converting from a map of your high school, to the location of your high school in reference to where it is in the city, compared to a country-wide map).

This summarizes my initial set of basic notes surrounding the adjacency matrix representation of a graph

There are multiple ways of representing graph-structured data. One of the most common ways is using the adjacency matrix, where connections between nodes are represented in a row-column format.

For example:
$$ A = \begin{bmatrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0 \end{bmatrix} $$