<prompt> Hlalosa tlhahlobo ea likarolo tsa mantlha thutong ea mochininan  <response>: Instruction in English: Explain the principal components analysis in machine learning . Response in English: Principal Component Analysis, or PCA, is a dimensionality-reduction technique in machine learning used to project high-dimensional data into a lower-dimensional space. In other words, PCA is used to reduce the number of variables in a dataset while preserving the most significant information it contains. By reducing the dimensionality of the data, it makes it easier to visualize and analyze, while also reducing the noise, redundancy and collinearity in the data.The PCA algorithm works by identifying a new set of orthogonal axes, called principal components, that capture the largest amount of variation in the data. The first principal component represents the direction in which the data varies the most; the second principal component represents the direction of the second-most variance, and so on. The algorithm also tries to keep the principal components uncorrelated with each other.In practice, PCA is performed by calculating the eigenvectors and eigenvalues of the data covariance matrix. The eigenvectors with the highest eigenvalues are the principal components, and the data can be transformed by projecting it onto these vectors.In summary, PCA is a powerful tool in machine learning and data analysis, allowing for the simplification of complex datasets while retaining important information. It can be used for tasks such as data visualization, noise filtering, feature extraction, and data compression. . Response in Sesotho: Principal Component Analysis, kapa PCA, ke mokhoa oa ho fokotsa boholo ba ho ithuta ka mochine o sebelisetsoang ho hlahisa lintlha tse phahameng sebakeng se tlaase. Ka mantsoe a mang, PCA e sebelisetsoa ho fokotsa palo ea mefuta-futa ho dataset ha e ntse e boloka tlhahisoleseding ea bohlokoa ka ho fetisisa eo e nang le eona. Ka ho fokotsa boholo ba data, e etsa hore ho be bonolo ho bona le ho e sekaseka, ha e ntse e fokotsa lerata, redundancy le collinearity ho data. Algorithm ea PCA e sebetsa ka ho tsebahatsa sehlopha se secha sa lilepe tsa orthogonal, tse bitsoang likarolo tse ka sehloohong, tse hapang palo e kholo ea phapang ea data. Karolo ea pele ea sehlooho e emela tataiso eo data e fapaneng haholo ka eona; karolo ea bobeli ea sehlooho e emela tataiso ea phapang ea bobeli ka ho fetisisa, joalo-joalo. Algorithm e boetse e leka ho boloka likarolo tse ka sehloohong li sa kopane. Ha e le hantle, PCA e etsoa ka ho bala li-eigenvectors le li-eigenvalues tsa data covariance matrix. Li-eigenvector tse nang le li-eigenvalues tse phahameng ke tsona tse ka sehloohong, me data e ka fetoloa ka ho e hlahisa ho li-vector tsena. Ka bokhutšoanyane, PCA ke sesebelisoa se matla sa ho ithuta mochine le tlhahlobo ea lintlha, e lumellang ho nolofatsa li-dataset tse rarahaneng ha li ntse li boloka boitsebiso ba bohlokoa. E ka sebelisoa bakeng sa mesebetsi e kang pono ea data, ho sefa lerata, ho ntša likarolo, le khatello ea data. 