# Line Estimation

Before I start my post, I want to inform you that there might be an unclear succession between the posts I publish. I am doing my best to keep them in order, but as a general rule in life, nothing is guaranteed! I mean there are so many things that I want to write about, and every time I want to write, something comes to my mind which is not necessarily directly related to my previous posts. So please bear with me on this. Continue reading

# Similarity and Distance Functions

Let’s go back to our posts on distance functions. The initial idea was to calculate the distance between two points or between one point and a set of points in a 2d space. Within the discussion, we often stated that one point is more “similar” to the set, than the other point. So, maybe what we are actually trying to calculate is the similarity between two entities (either being a point or a set). The problem is that similarity is a subjective matter, so we need an objective measure, and that’s why we have chosen distance. Continue reading

# Eikosograms

Yesterday, I was thinking about the first time I realized the difference between two random variables being disjoint rather than independent. The difference was very confusing at the time for me, and I think the reason is related to Venn diagrams. Continue reading

# Variance or Standard Deviation

I just found out that I made a mistake in my previous post (it is fixed now). There, I argued that in order to calculate the distance between a point and a set (which has unequal variances along different dimensions), we can use the following formula:

# The Mighty Distance Function – Part 3

So here we are again, with some new proposals for the distance function between a point and a set. In the previous post, we became familiar with the variance measure and two methods to map points into a new space so that the distance function in the new space behaves the same way as what intuitively seems right! Continue reading

# The Mighty Distace Function – Part 2

So in our previous step, we went over some possible approaches to define a distance function between a point and a set. At the end we saw that calculating distance between the point and the average (mean) point of the set seems to be the best possible solution. I am afraid that it is not always that easy. Continue reading

# The Mighty Distance Function – Part 1

I’ll start my posts with the distance function, as I believe a complete understanding of it, provides the basic idea behind most of the ML algorithms. Some of the approaches which come next are closely related to some known algorithms in ML, but I am not going to name any of them, as I believe that a complete understanding of the intuition behind any of them is more important than their names. Continue reading