Principal Component Analysis is an unsupervised learning approach used in machine learning to reduce dimensionality. A statistical procedure uses an orthogonal transformation to turn observations of correlated characteristics into a set of linearly uncorrelated data. The Principal Components are the newly altered characteristics. It is one of the most widely used exploratory data analysis and predictive modeling tools. It is also a well-known method for extracting strong patterns from a given dataset by decreasing variances.
In general, PCA seeks the lower-dimensional surface to project the high-dimensional data. PCA works by taking the variance of each characteristic into account since the high attribute reveals a good separation between the classes and so decreases dimensionality. Enroll in the PG Program in AI and Machine Learning to learn about Image processing, movie recommendation systems, and optimizing power allocation across multiple communication channels are some real-world uses of PCA. Because it is a feature extraction approach, it includes the key variables while excluding the least important ones.
What do you mean by Principal Component?
The Principal Components are a straight line that captures most of the data‘s variance and has a magnitude and direction. The primary components are perpendicular projections of data onto lower-dimensional space.
Let us now move to the next PCA subject in Machine Learning.
The PCA method is based on the following mathematical concepts:
- Variance and Covariance
- Eigenvalues and Eigen factors
The following are some definitions that are commonly used in the PCA algorithm:
- Dimensionality: Dimensionality refers to the number of characteristics or variables in a particular dataset. It is, more simply, the number of columns in the dataset.
- Correlation: This term refers to how closely two variables are connected. For example, if one of the variables changes, the other variable also changes. The correlation coefficient varies from -1 to 1. In this case, -1 implies that the variables are inversely proportional to each other, whereas 1 shows that the variables are directly proportional.
- Orthogonal: It specifies that variables are not connected, so the correlation between the two variables is 0.
- Eigenvectors: A square matrix M and a non-zero vector v are provided. If Av is the scalar multiple of v, then v is an Eigenvector.
- Covariance Matrix: A Covariance Matrix is nothing but a matrix that contains the covariance between two variables.
Principal Components in PCA- Analysis In Machine Learning
The Principal Components are the new converted features or the result of PCA, as stated above. The number of these Principal components is either equal to or fewer than the number of original features in the dataset. The following are some of the qualities of these primary components:
- The linear combination of the original characteristics must be the main component.
- These components are orthogonal, which means that the correlation between the two variables is 0.
- When the significance of each component drops from 1 to ‘n,’ it signifies that the 1 PC is the most important, and the ‘n’ PC is the least important.
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