𝐏𝐫𝐢𝐧𝐜𝐢𝐩𝐚𝐥 𝐂𝐨𝐦𝐩𝐨𝐧𝐞𝐧𝐭 𝐀𝐧𝐚𝐥𝐲𝐬𝐢𝐬 (𝐏𝐂𝐀), was one of the earliest methods used to 𝐝𝐞𝐭𝐞𝐫𝐦𝐢𝐧𝐞 𝐭𝐡𝐞 𝐜𝐨𝐫𝐫𝐞𝐥𝐚𝐭𝐢𝐨𝐧𝐬 among data and to reduce the dimensionality of the space, 𝑿, by projecting it into a lower dimensional space 𝒁. 𝐏𝐂𝐀 attempts to find a mapping 𝒇 that preserves, to the 𝐠𝐫𝐞𝐚𝐭𝐞𝐬𝐭 𝐞𝐱𝐭𝐞𝐧𝐭 𝐩𝐨𝐬𝐬𝐢𝐛𝐥𝐞, 𝐭𝐡𝐞 𝐯𝐚𝐫𝐢𝐚𝐧𝐜𝐞 of the data points…