K-Nearest Neighbors (KNN) Algorithm

The posterior probability P(ωi|x) is the same as maximizing p(x|ωi).P(ωi)

Non-parametric methods require assumptions about the population parameters

The K-NN algorithm uses a distance function to classify new cases

The Bayes’ decision rule is used to minimize the posterior probability

Parametric methods do not require any assumption about the population parameters

The K-NN algorithm is a complex algorithm that requires a lot of training data

The decision tree model is a type of parametric method

The prior probability is calculated based on the relative numbers of classes in the population

The K-NN algorithm uses a single nearest neighbor to classify new cases

The posterior probability is calculated based on the prior probability and the likelihood

K-Nearest Neighbors (KNN) Classifier

KNN is a simple algorithm that stores all available cases and classifies new cases based on a similarity measure (distance function).
A case is classified by a majority voting of its neighbors, with the case being assigned to the class most common among its K nearest neighbors measured by a distance function.

Euclidean Distance

Euclidean distance is a common distance function used in KNN classification.
The Euclidean distance between two points (x1, y1) and (x2, y2) is calculated as √((x2 - x1)^2 + (y2 - y1)^2).

KNN Example

Points are classified as GOOD or BAD based on their features (Durability and Strength).
P5 (3,7) is classified as GOOD based on the majority voting of its 3 nearest neighbors.
The 3 nearest neighbors of P5 are P3 (3,4), P4 (1,4), and P1 (7,7).

KNN Pseudocode

No specific pseudocode is provided, but the general algorithm is described.

Unsupervised Methods

In unsupervised classification, the class labels are unknown, and the data are plotted to see whether they cluster naturally.
If K=1, then the case is simply assigned to the class of its nearest neighbor.

k-Nearest-Neighbor (k-NN) Classifier

k-NN classifier uses a distance function to find the k nearest neighbors of a new input vector x.
The object is assigned to the most frequently occurring class among its k nearest neighbors.

Parametric and Non-Parametric Methods

Parametric methods involve maximizing the posterior probability, P(ωi|x), which is the same as maximizing p(x|ω1).P(ωi)).
Non-parametric methods do not require making assumptions about the population parameters.
Examples of non-parametric methods include KNN, Decision Tree Model, etc.

This quiz is based on the K-Nearest Neighbors algorithm, a supervised machine learning method used for classification and regression tasks. It involves calculating distances between data points, like Euclidean distance, to find the nearest neighbors. This is a fundamental concept in data science and machine learning.