# Nearest Neighbor Methods

### KNN visualization in just 13 lines of code

Let's play around with datasets to visualize how the decision boundary changes as'k' changes. Let's have a quick review… K Nearest Neighbor(KNN) algorithm is a very simple, easy to understand, versatile and one of the topmost machine learning algorithms. In k-NN classification, the output is a class membership. An object is classified by a plurality vote of its neighbours, with the object being assigned to the class most common among its k nearest neighbours (k is a positive integer, typically small). If k 1, then the object is simply assigned to the class of that single nearest neighbour.

### The Basics: KNN for classification and regression

Data science or applied statistics courses typically start with linear models, but in its way, K-nearest neighbors is probably the simplest widely used model conceptually. KNN models are really just technical implementations of a common intuition, that things that share similar features tend to be, well, similar. This is hardly a deep insight, yet these practical implementations can be extremely powerful, and, crucially for someone approaching an unknown dataset, can handle non-linearities without any complicated data-engineering or model set up. As an illustrative example, let's consider the simplest case of using a KNN model as a classifier. Let's say you have data points that fall into one of three classes.

### Benefit of Interpolation in Nearest Neighbor Algorithms

The over-parameterized models attract much attention in the era of data science and deep learning. It is empirically observed that although these models, e.g. deep neural networks, over-fit the training data, they can still achieve small testing error, and sometimes even {\em outperform} traditional algorithms which are designed to avoid over-fitting. The major goal of this work is to sharply quantify the benefit of data interpolation in the context of nearest neighbors (NN) algorithm. Specifically, we consider a class of interpolated weighting schemes and then carefully characterize their asymptotic performances. Our analysis reveals a U-shaped performance curve with respect to the level of data interpolation, and proves that a mild degree of data interpolation {\em strictly} improves the prediction accuracy and statistical stability over those of the (un-interpolated) optimal $k$NN algorithm. This theoretically justifies (predicts) the existence of the second U-shaped curve in the recently discovered double descent phenomenon. Note that our goal in this study is not to promote the use of interpolated-NN method, but to obtain theoretical insights on data interpolation inspired by the aforementioned phenomenon.

### Exercise Classification with Machine Learning (Part I)

The first post will focus on a more algorithmic approach using k-Nearest Neighbors to classify an unknown video, and in the second post, we'll look at an exclusively machine learning (ML) approach. Code for everything we're going to cover can be found on this GitHub repository. The algorithmic approach (Part I) is written in Swift and is available as a CocoaPod. The ML approach (Part II) is written in Python/TensorFlow and can be found as part of the GitHub repository. We want to build a system which takes as input a video of a person performing an exercise and outputs a class label which describes the video.

### Efficient Task-Specific Data Valuation for Nearest Neighbor Algorithms

Given a data set D containing millions of data points and a data consumer who is willing to pay for X to train a machine learning (ML) model over D, how should we distribute this X to each data point to reflect its "value"? In this paper, we define the "relative value of data" via the Shapley value, as it uniquely possesses properties with appealing real-world interpretations, such as fairness, rationality and decentralizability. For general, bounded utility functions, the Shapley value is known to be challenging to compute: to get Shapley values for all N data points, it requires O(2 N) model evaluations for exact computation and O(N N) for (ϵ, δ)-approximation. In this paper, we focus on one popular family of ML models relying on K-nearest neighbors (KNN). The most surprising result is that for unweighted KNN classifiers and regressors, the Shapley value of all N data points can be computed, exactly, in O(N N) time -- an exponential improvement on computational complexity!

### Efficient Task-Specific Data Valuation for Nearest Neighbor Algorithms

Given a data set D containing millions of data points and a data consumer who is willing to pay for X to train a machine learning (ML) model over D, how should we distribute this X to each data point to reflect its "value"? In this paper, we define the "relative value of data" via the Shapley value, as it uniquely possesses properties with appealing real-world interpretations, such as fairness, rationality and decentralizability. For general, bounded utility functions, the Shapley value is known to be challenging to compute: to get Shapley values for all N data points, it requires O(2 N) model evaluations for exact computation and O(N N) for (ϵ, δ)-approximation. In this paper, we focus on one popular family of ML models relying on K-nearest neighbors (KNN). The most surprising result is that for unweighted KNN classifiers and regressors, the Shapley value of all N data points can be computed, exactly, in O(N N) time -- an exponential improvement on computational complexity!

### K Nearest Neighbor Algorithm In Python - Towards Data Science

K-Nearest Neighbors, or KNN for short, is one of the simplest machine learning algorithms and is used in a wide array of institutions. KNN is a non-parametric, lazy learning algorithm. When we say a technique is non-parametric, it means that it does not make any assumptions about the underlying data. In other words, it makes its selection based off of the proximity to other data points regardless of what feature the numerical values represent. Being a lazy learning algorithm implies that there is little to no training phase.

### Implement K-Nearest Neighbors classification Algorithm

I have written this post for the developers and assumes no background in statistics or mathematics. The focus is mainly on how the k-NN algorithm works and how to use it for predictive modeling problems. Classification of objects is an important area of research and application in a variety of fields. In the presence of full knowledge of the underlying probabilities, Bayes decision theory gives optimal error rates. In those cases where this information is not present, many algorithms make use of distance or similarity among samples as a means of classification.