Free Practice Questions for Databricks Databricks-Certified-Professional-Data-Scientist Exam

The method based on principal component analysis (PCA) evaluates the features according to the projection of the largest eigenvector of the correlation matrix on the initial dimensions, the method based on Fisher's linear discriminant analysis evaluates. Them according to the magnitude of the components of the discriminant vector.

The first principal component corresponds to the greatest variance in the data, by definition. If we project the data onto the first principal component line, the data is more spread out (higher variance) than if projected onto any other line, including other principal components.

Explanation :

The difference between their properties can be promptly summarized as follows:

Table Description automatically generated

Principal component analysis . or PCA, is a technique for taking a dataset that is in the form of a set of tuples representing points in a high-dimensional space and finding the dimensions along which the tuples line up best. The idea is to treat the set of tuples as a matrix M and find the eigenvectors for MMT or M T M . The matrix of these eigenvectors can be thought of as a rigid rotation in a high-dimensional space. When you apply this transformation to the original data, the axis corresponding to the principal eigenvector is the one along which the points are most "spread out,11 More precisely this axis is the one along which the variance of the data is maximized. Put another way, the points can best be viewed as lying along this axis, with small deviations from this axis.

In classification, our job is to predict what class an instance of data should fall into. Another task in machine learning is regression. Regression is the prediction of a numeric value. Most people have probably seen an example of regression with a best-fit line drawn through some data points to generalize the data points. Classification and regression are examples of supervised learning. This set of problems is known as supervised because we're telling the algorithm what to predict.

The sample space is defined by two mutually-exclusive events - it rains or it does not rain. Additionally, a third event occurs when the weatherman predicts rain. You should consider Bayes' theorem when the following conditions exist.

• The sample space is partitioned into a set of mutually exclusive events {A1, A2,... :An}.

• Within the sample space, there exists an event B: for which P(B) > 0.

• The analytical goal is to compute a conditional probability of the form: P( Ak B).

Principal component analysis (PCA) involves a mathematical procedure that transforms a number of (possibly) correlated variables into a (smaller) number of uncorrelated variables called principal components. The first principal component

accounts for as much of the variability in the data as possible, and each succeeding component accounts for as much of the remaining variability as possible.

The first principal component corresponds to the greatest variance in the data. The blue line is evidently this first principal component, because if we project the data onto the blue line, the data is more spread out (higher variance) than if projected

onto any other line, including the yellow one.

Linear regression models a linear relationship of a scalar dependent variable y to one or more explanatory independent variables x to build a model of coefficients.