Principal component analysis

Q: How deeply does Evolutionary Deep Learning: Genetic algorithms and neural networks cover principal component analysis?

Explains projection, variance-based components, and implementation, but defers detailed algorithmic treatment to documentation or other resources.

As explained in Evolutionary Deep Learning: Genetic algorithms and neural networks

Principal component analysis is a dimensionality-reduction technique that transforms correlated multidimensional data into a smaller set of components capturing variation in the data.

Principal component analysis (PCA) reduces multidimensional vector data to fewer dimensions, making otherwise high-dimensional hyperparameter results easier to visualize in two or three dimensions. section 5.5.2

PCA works by:

Projecting higher-dimensional data into a lower-dimensional space. section 5.5.2
Calculating components from variance, with each axis representing relative distances between elements in vector space. section 5.5.2
Supporting visualization while additional hyperparameters vary during automated optimization. section 5.5.2 section 5.7

Reducing four dimensions to two

Create a scikit-learn PCA object with n_components=2, call fit_transform on four-dimensional population data, transpose the result, and scatter-plot its two component axes. section 5.5.2

Listing 5.27 EDL_5_5_ES_HPO_PCA.ipynb: Adding PCA

pop = np.array([[-.5, .75, -.1, .8], 
                [-.5, -.3, -.5, .8],
                [-.5, 1, -.5, -.8],
                [ 1, -.3, -.5, .8]])      #1
pca = PCA(n_components=2)                 #2
reduced = pca.fit_transform(pop)          #3
 
t = reduced.transpose()                   #4
 
plt.scatter(t[0], t[1])                   #5
plt.show()

The runnable listing demonstrates PCA setup, transformation, and plotting on contrived four-dimensional data. section 5.5.2

How Evolutionary Deep Learning: Genetic algorithms and neural networks covers it

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Related concepts

dimensionality reductionkind of · Dimensionality reduction is the transformation of data into a representation with fewer dimensions while retaining selected information, structure, or relationships.
covariance matrixuses · A covariance matrix is a square matrix whose diagonal entries are variances and whose off-diagonal entries are pairwise covariances among variables.
varianceuses · Variance is the expected squared deviation of a random variable from its mean, measuring the spread of its distribution.
principal componentproduces · A principal component is an orthogonal direction in transformed data space that captures a ranked amount of variation in the data.
embeddinguses · A numerical vector representation of an item or input that encodes features or relationships useful for computational tasks.

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