Our original data has n features, and we wish to reduce them to k features, where k << n. We assume that L≈XV where L is some low-rank matrix, X is the original data and V is a projection operator. It assumes that we have a high-dimensional representation of data that is, in fact, embedded in a low-dimensional space.
Let’s examine the model to help us further describe PCA. A Closer Look at PCA (Principal Component Analysis) PCA also allows us to visualize data and allow for the inspection of clustering/classification algorithms. Other benefits of PCA include reduction of noise in the data, feature selection (to a certain extent), and the ability to produce independent, uncorrelated features of the data. PCA can help us improve performance at a very low cost of model accuracy. Models running on very high dimensional data might perform very slow-or even fail-and require significant server resources. Most, if not all, algorithm performance depends on the dimension of the data. This helps us deal with the “curse of dimensionality”. For example, by reducing the dimensionality of the data, PCA enables us to better generalize machine learning models. PCA is an unsupervised learning technique that offers a number of benefits. According to Wikipedia, PCA (or Principal Component Analysis) is a “statistical procedure that uses orthogonal transformation to convert a set of observations of possibly correlated variables…into a set of values of linearly uncorrelated variables called principal components.” The Benefits of PCA (Principal Component Analysis) PCA is a dimensionality reduction framework in machine learning.
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