feat: documents KNN algorithms section

src/algorithm/neighbour/mod.rs

@@ -1,3 +1,35 @@
+//! # Nearest Neighbors Search Algorithms and Data Structures
+//!
+//! Nearest neighbor search is a basic computational tool that is particularly relevant to machine learning,
+//! where it is often believed that highdimensional datasets have low-dimensional intrinsic structure.
+//! The basic nearest neighbor problem is formalized as follows: given a set \\( S \\) of \\( n \\) points in some metric space \\( (X, d) \\),
+//!  the problem is to preprocess \\( S \\) so that given a query point \\( p \in X \\), one can efficiently find a point \\( q \in S \\)
+//!  which minimizes \\( d(p, q) \\).
+//!
+//! [The most straightforward nearest neighbor search algorithm](linear_search/index.html) finds k nearest points using the brute-force approach where distances between all
+//! pairs of points in the dataset are calculated. This approach scales as \\( O(nd^2) \\) where \\( n = \lvert S \rvert \\), is number of samples and \\( d \\) is number
+//! of dimentions in metric space. As the number of samples  grows, the brute-force approach quickly becomes infeasible.
+//!
+//! [Cover Tree](cover_tree/index.html) is data structure that partitions metric spaces to speed up nearest neighbor search. Cover tree requires \\( O(n) \\) space and
+//! have nice theoretical properties:
+//!
+//! * construction time: \\( O(c^6n \log n) \\),
+//! * insertion time \\( O(c^6 \log n) \\),
+//! * removal time: \\( O(c^6 \log n) \\),
+//! * query time: \\( O(c^{12} \log n) \\),
+//!
+//! Where \\( c \\) is a constant.
+//!
+//! ## References:
+//! * ["The Art of Computer Programming" Knuth, D, Vol. 3, 2nd ed, Sorting and Searching, 1998](https://www-cs-faculty.stanford.edu/~knuth/taocp.html)
+//! * ["Cover Trees for Nearest Neighbor" Beygelzimer et al., Proceedings of the 23rd international conference on Machine learning, ICML'06 (2006)](https://homes.cs.washington.edu/~sham/papers/ml/cover_tree.pdf)
+//! * ["Faster cover trees." Izbicki et al., Proceedings of the 32nd International Conference on Machine Learning, ICML'15 (2015)](http://www.cs.ucr.edu/~cshelton/papers/index.cgi%3FIzbShe15)
+//! * ["The Elements of Statistical Learning: Data Mining, Inference, and Prediction" Trevor et al., 2nd edition, chapter 13](https://web.stanford.edu/~hastie/ElemStatLearn/)
+//!
+//! <script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS_CHTML"></script>
+
 pub(crate) mod bbd_tree;
+/// tree data structure for fast nearest neighbor search
 pub mod cover_tree;
+/// very simple algorithm that sequentially checks each element of the list until a match is found or the whole list has been searched.
 pub mod linear_search;