Principal component
A principal component is an orthogonal direction in transformed data space that captures a ranked amount of variation in the data.
Data Without Labels
A principal component is an orthogonal direction produced by principal component analysis that captures a ranked amount of variation in the data.
- How it is used
- Reduces high-dimensional datasets while retaining important variation for further analysis and modeling.
- How deep it goes
- Defines ranked orthogonal directions and connects them to eigenvalue decomposition, but defers nonlinear dimensionality-reduction methods.
- Examples
- Uses house-value estimation, weighted variable combinations, vector-space projections, and successive orthogonal directions.
- What you can do after
- Apply PCA to replace many numeric variables with fewer variance-ranked components for subsequent analysis.
Math and Architectures of Deep Learning
The projection values of data onto a principal axis in PCA, representing coordinates along that direction.
- How it is used
- Uses projected coordinates to expose dominant variation, reduce dimensionality, compress data, and represent document topics.
- How deep it goes
- Explains variance maximization, covariance eigenvectors, projections, dimensionality reduction, compression, and SVD computation.
- Examples
- Uses geometric 2D and 3D projections, compressed datasets, correlated document terms, and a 500-vector PyTorch SVD experiment.
- What you can do after
- Apply it via PCA or SVD to project data, retain dominant coordinates, reduce dimensions, and identify high-variance topics.
Read how Math and Architectures of Deep Learning explains principal component →
Outlier Detection in Python
A principal component is an orthogonal direction representing a decreasing amount of variance in data after successive components are selected.
- How it is used
- Uses transformed coordinates for dimensionality reduction, visualization, and outlier detection.
- How deep it goes
- Explains coordinate transformation, variance ordering, component independence, and practical weighting, without deriving the underlying mathematics.
- Examples
- Demonstrates correlated synthetic data, two contrasting outliers, component scatterplots, and detector comparisons using selected components.
- What you can do after
- Apply it via scikit-learn to transform features, inspect explained variance, and prepare component scores for univariate outlier tests.
Read how Outlier Detection in Python explains principal component →
Natural Language Processing in Action, Second Edition
A principal component is an orthonormal direction in transformed data space along which variance is maximized subject to the preceding components.
- How it is used
- Reduces high-dimensional data to compact coordinates for preserving dominant variation, analysis, clustering, and visualization.
- How deep it goes
- Explains geometric intuition, variance ordering, projection, sign ambiguity, and transformation of new points, while deferring deeper SVD applications.
- Examples
- Uses a 3D point cloud reduced to two plotted coordinates with scikit-learn.
- What you can do after
- Apply it via scikit-learn to transform point clouds and inspect lower-dimensional representations.
Read how Natural Language Processing in Action, Second Edition explains principal component →
Cyber Threat Hunting
A principal component is a derived feature formed by combining original features and representing a direction of variation in the data.
- How it is used
- Reduces correlated feature sets before applying supervised machine-learning models.
- How deep it goes
- Defines component formation and demonstrates scaling, variance inspection, transformation, and visualization without deriving the underlying mathematics.
- Examples
- Uses X_train_scaled, four transformed columns, cumulative-variance plots, and class-colored PC1–PC2 and PC3–PC4 plots.
- What you can do after
- Apply PCA via scikit-learn after scaling features and choose a component count using cumulative explained variance.
Read how Cyber Threat Hunting explains principal component →
Related concepts
- principal component analysisproduced by · Principal component analysis is a linear dimensionality-reduction technique that transforms data into orthogonal components ordered by the variance they capture.
- covariance matrixproduced by · A covariance matrix is a square matrix whose diagonal entries are variances and whose off-diagonal entries are pairwise covariances among variables.
- weighted sumkind of · A weighted sum is an expression formed by multiplying terms by corresponding scalar coefficients and adding the resulting products.
- dimensionkind of · A dimension is an independent coordinate, measurable axis, or descriptive attribute used to represent, locate, or analyze something.
- eigenvectorequivalent to · An eigenvector is a nonzero vector that a linear transformation maps to a scalar multiple of itself.
These guides are generated from the text of Manning books by Manning's knowledge graph and link to the sections they draw on. The full books are available on liveBook and at manning.com.