<prompt> Hlalosa sepheo sa tlhahlobo ea likarolo tsa sehloohonan  <response>: Instruction in English: Explain the purpose of principal component analysis . Response in English: Principal component analysis PCA is a statistical technique used to reduce the dimensionality of a dataset while retaining as much variability as possible. In other words, it is used to condense large sets of data into a smaller, more manageable set of variables, while still retaining the most important information.PCA works by identifying the underlying structure of the data, extracting the principal components, which are directions in which the data varies the most. These principal components can then be used to create new variables that capture as much of the variability in the data as possible while reducing the number of dimensions of the dataset.The main purposes of using PCA are:1. Dimensionality Reduction: PCA is used to reduce the number of variables in a dataset while retaining as much information as possible. This can be helpful when dealing with datasets with a large number of variables, making them easier to analyze and visualize.2. Data Compression: By reducing the dimensionality of a dataset, PCA can also be used as a form of data compression, where the compressed data is represented with fewer variables.3. Noise Reduction: PCA can also be used to denoise data by removing variables with little variability, which are often considered as noise.4. Feature Extraction: PCA can be used to transform data into new variables that are a linear combination of the original variables. These new variables, or features, can then be used in machine learning models, to improve their predictive power.Overall, the main purpose of principal component analysis is to uncover patterns within a dataset by condensing the data into its most important elements, thereby simplifying the analysis and improving its interpretability. . Response in Sesotho: Principal component analysis PCA ke mokhoa oa lipalo-palo o sebelisoang ho fokotsa boholo ba dataset ha o ntse o boloka phapang e ngata kamoo ho ka khonehang. Ka mantsoe a mang, e sebelisoa ho kopanya lihlopha tse kholo tsa data ho lihlopha tse nyenyane, tse laolehang haholoanyane, ha li ntse li boloka boitsebiso ba bohlokoa ka ho fetisisa. PCA e sebetsa ka ho tsebahatsa sebopeho sa motheo sa lintlha, ho ntša likarolo tse ka sehloohong, e leng litaelo tseo data e fapaneng haholo ka tsona. Likarolo tsena tse ka sehloohong li ka sebelisoa ho theha mefuta e mecha e nkang phapang e ngata ea data kamoo ho ka khonehang ha e ntse e fokotsa palo ea litekanyo tsa dataset. Sepheo se seholo sa ho sebelisa PCA ke: 1. Phokotso ea Bophahamo: PCA e sebelisetsoa ho fokotsa palo ea mefuta-futa ho dataset ha e ntse e boloka boitsebiso bo bongata kamoo ho ka khonehang. Sena se ka ba molemo ha u sebetsana le li-dataset tse nang le palo e kholo ea mefuta-futa, ho etsa hore ho be bonolo ho li hlahloba le ho li bona ka mahlo a kelello. 2. Khatello ea Boitsebiso: Ka ho fokotsa boholo ba dataset, PCA e ka boela ea sebelisoa e le mokhoa oa ho hatella data, moo data e hatelitsoeng e emeloa ka mefuta e fokolang. 3. Phokotso ea Lerata: PCA e ka boela ea sebelisoa ho etsa denoise data ka ho tlosa mefuta-futa e nang le phapang e fokolang, eo hangata e nkoang e le lerata. 4. Feature Extraction: PCA e ka sebelisoa ho fetola data hore e be mefuta e mecha eo e leng motsoako oa linear oa mefuta-futa ea pele. Liphetoho tsena tse ncha, kapa likarolo, li ka sebelisoa mefuteng ea ho ithuta ea mochini, ho ntlafatsa matla a tsona a ho bolela esale pele. Ka kakaretso, sepheo sa mantlha sa tlhahlobo ea karolo ea mantlha ke ho sibolla lipaterone ka hara pokello ea data ka ho koahanya lintlha ho likarolo tsa eona tsa bohlokoa, ka ho etsa joalo ho nolofatsa tlhahlobo le ho ntlafatsa tlhaloso ea eona. 