Gokulm29 Dimensionality Reduction Using Kmeans Clustering

k-means clustering is a method of vector quantization, originally from signal processing, that aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean (cluster... This results in a partitioning of the data space into Voronoi cells. k-means clustering minimizes within-cluster variances (squared Euclidean distances), but not regular Euclidean distances, which would be the more difficult Weber problem: the mean optimizes squared errors, whereas only the geometric median minimizes Euclidean distances. For instance, better Euclidean solutions can be found using k-medians and k-medoids. The problem is computationally difficult (NP-hard); however, efficient heuristic algorithms converge quickly to a local optimum. These are usually similar to the expectation–maximization algorithm for mixtures of Gaussian distributions via an iterative refinement approach employed by both k-means and Gaussian mixture modeling.

They both use cluster centers to model the data; however, k-means clustering tends to find clusters of comparable spatial extent, while the Gaussian mixture model allows clusters to have different shapes. The unsupervised k-means algorithm has a loose relationship to the k-nearest neighbor classifier, a popular supervised machine learning technique for classification that is often confused with k-means due to the name. Applying the 1-nearest neighbor classifier to the cluster centers obtained by k-means classifies new data into the existing clusters. This is known as nearest centroid classifier or Rocchio algorithm. Given a set of observations (x1, x2, ..., xn), where each observation is a d {\displaystyle d} -dimensional real vector, k-means clustering aims to partition the n observations into k (≤ n) sets S... variance).

Formally, the objective is to find: a r g m i n S ⁡ ∑ i = 1 k ∑ x ∈ S i ‖ x − μ i ‖ 2 = a r... μ i = 1 | S i | ∑ x ∈ S i x , {\displaystyle {\boldsymbol {\mu _{i}}}={\frac {1}{|S_{i}|}}\sum _{\mathbf {x} \in S_{i}}\mathbf {x} ,} | S i | {\displaystyle |S_{i}|} is the... This is equivalent to minimizing the pairwise squared deviations of points in the same cluster: a r g m i n S ⁡ ∑ i = 1 k 1 | S i | ∑... Since the total variance is constant, this is equivalent to maximizing the sum of squared deviations between points in different clusters (between-cluster sum of squares, BCSS).[1] This deterministic relationship is also related to the... The term "k-means" was first used by James MacQueen in 1967,[2] though the idea goes back to Hugo Steinhaus in 1956.[3] The standard algorithm was first proposed by Stuart Lloyd of Bell Labs in... Forgy published essentially the same method, which is why it is sometimes referred to as the Lloyd–Forgy algorithm.[5]

This project focuses on applying dimensionality reduction techniques to high-dimensional datasets, a critical step in preprocessing data for machine learning and visualization tasks. The notebook provides a comprehensive implementation and explanation of various dimensionality reduction algorithms and their applications. Additionally, the project incorporates the Gaussian Naive Bayes (GaussianNB) classifier to analyze the effectiveness of dimensionality reduction techniques in predictive modeling. The project also includes exploratory data analysis (EDA), metrics evaluation, and timing analysis to measure the performance and efficiency of the methods. Dimensionality reduction is essential for simplifying complex datasets while preserving significant patterns and structures. This project explores:

Below are the Python libraries used in this project: Make sure you have a Google account and access to Google Colab. Install the required libraries directly in the Colab notebook using the following commands: import requests import zipfile import io A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity.© Copyright 2025 IEEE - All rights reserved. Use of this web site signifies your agreement to the terms and conditions.

K-Means Clustering groups similar data points into clusters without needing labeled data. It is used to uncover hidden patterns when the goal is to organize data based on similarity. Suppose we are given a data set of items with certain features and values for these features like a vector. The task is to categorize those items into groups. To achieve this we will use the K-means algorithm. "k" represents the number of groups or clusters we want to classify our items into.

The algorithm will categorize the items into "k" groups or clusters of similarity. To calculate that similarity we will use the Euclidean distance as a measurement. The algorithm works as follows: The goal is to partition the dataset into k clusters such that data points within each cluster are more similar to each other than to those in other clusters. Selecting the right number of clusters is important for meaningful segmentation to do this we use Elbow Method for optimal value of k in KMeans which is a graphical tool used to determine the... arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

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