PCA Is Just Eigenvectors

A cloud of 2-D points stretches along one diagonal far more than any other, and that direction of maximum spread is the first principal component. The surprise is where it comes from: it isn't found by guessing and checking — it's exactly the top eigenvector of the covariance matrix, the little matrix that records how your features vary together. Solve Σu = λu and the principal components just fall out, each paired with an eigenvalue that tells you how much variance lives along its direction. Rank them, keep the few with big eigenvalues, throw the rest away — which is why, in so many real datasets, most of your data really is useless. #shorts *Follow Me* ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ 🐦 X: @datamlistic https://x.com/datamlistic 📸 Instagram: @datamlistic https://www.instagram.com/datamlistic 📱 TikTok: @datamlistic https://www.tiktok.com/@datamlistic 👔 Linkedin: https://www.linkedin.com/company/datamlistic *Channel Support* ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ The best way to support the channel is to share the content. ;) If you'd like to also support the channel financially, donating the price of a coffee is always warmly welcomed! (completely optional and voluntary) ► Patreon: https://www.patreon.com/datamlistic ► Bitcoin (BTC): 3C6Pkzyb5CjAUYrJxmpCaaNPVRgRVxxyTq ► Ethereum (ETH): 0x9Ac4eB94386C3e02b96599C05B7a8C71773c9281 ► Cardano (ADA): addr1v95rfxlslfzkvd8sr3exkh7st4qmgj4ywf5zcaxgqgdyunsj5juw5 ► Tether (USDT): 0xeC261d9b2EE4B6997a6a424067af165BAA4afE1a #shorts #pca #machinelearning