I have been exploring Nearest Neighbours Methods which are commonly adopted for solving classification problems. In the context of Indoor localisation, such methods are employed to identify LoS and NLoS propagation modes. This blog post basically provides a Jupyter Notebook to try this classification on your own using openly available data-set for UWB Localisation. The link for Jupyter notebook is here and the Markdown version is provided in this post.

It is difficult to appreciate that Bayes classifier yields smallest probability of error for a classification problem. As a matter of fact, as shown by Cover et al. the nearest neighbour classifier has twice the classification error at least asymptotically when compared to optimal Bayes classifier. It is not trivial to show that Bayes classifier has the lowest error rate. This rate is only achievable when joint distribution of data and associated class are known. Measure theoretic treatment and proof for this can be found here.

In this blog post, I summarie how Bayes Classifiers operation. Let \((X,Y)\) be a pair which takes values in \(\mathbb{R}^d\times\mathcal{Y}=\{1,2,...,K\}\) where \(Y\) is the class label associated with the observation \(X\). The classification problem involves selecting class label \(Y|X=x\).Therefore the problem can be concisely stated as:
Input: \(X=x\in \mathbb{R}^d\)
Output: \(Y\in\mathcal{Y}\)
Goal: To learn \(C(x):\mathbb{R}^d\rightarrow\mathcal{Y}\)
Joint Distribution: The joint distribution of \((X,Y)\) is given by \(P(X,Y)\)
Loss Function: As \(\mathcal{Y}\) is a discrete valued-set the squared-error function makes less sense, in this case the loss function can be defined as

I wrote these slides many, many moons ago. They potentially need a rewrite with enhanced interactivity, which could be easily harnessed from modern day JavaScript frameworks. However, these notes are still useful reference for new graduate students. Link to PDF

Like other industries, Telecom industry has also been impacted by the ongoing pandemic crisis. We summarised the Impact of COVID19 on Telecoms industry in the written evidence submitted to the DCMS Committee. This can be found here and is reproduced below.