L9: Time-complexity issue with PCA | efficient computation for high-dimensional data
Welcome to Lecture 13 of the course "Machine Learning Techniques" by Prof. Arun Rajkumar. Full Course: https://study.iitm.ac.in/ds/course_pa... Video Overview This lecture addresses the first major issue encountered when applying Principal Component Analysis (PCA) to high-dimensional datasets: computational complexity. Specifically, when the number of features (d) is much larger than the number of data points (n), directly computing the covariance matrix and its eigenvectors becomes prohibitively expensive (O(d_)). This video presents a clever workaround using matrix transformations and eigenvalue decomposition of a smaller matrix (n _ n), dramatically reducing the computational burden. Learn how to find the principal components efficiently, even when dealing with a vast number of features. About IIT Madras' online Bachelor of Science programme IIT Madras offers four-year BS programmes that aim to provide quality education to all, irrespective of age, educational background, or location. The BS programme has multiple levels, which provide flexibility to students to exit at any of these levels. Depending on the courses completed and credits earned, the learner can receive a Foundation Certificate from IITM CODE (Centre for Outreach and Digital Education), Diploma(s) from IIT Madras, or BSc/BS Degrees from IIT Madras. For more details, Visit: https://www.iitm.ac.in/academics/stud... #PCA #PrincipalComponentAnalysis #HighDimensionalData #FeatureReduction #DimensionalityReduction #Eigenvalues #Eigenvectors #CovarianceMatrix #MachineLearning #DataScience #ComputationalComplexity #Algorithm #DataAnalysis #MatrixTransformation #LinearAlgebra #KernelPCA #EfficientAlgorithms #AppliedML #BigDataML #Optimization
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