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Dimensionality Reduction Methods
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Linear Discriminant Analysis (LDA)
LDA attempts to model the difference between the classes of data. It finds the axes that maximize the separation between multiple classes.
Multidimensional Scaling (MDS)
MDS is a technique for analyzing similarity or dissimilarity data. It aims to place each object in N-dimensional space such that the between-object distances are preserved as well as possible.
Principal Component Analysis (PCA)
PCA works by calculating the eigenvectors and eigenvalues of the covariance matrix to find the principal components. Benefits include noise reduction and finding the underlying structure of the data.
Autoencoders
Autoencoders are neural networks designed to learn an encoding for the data. They work by compressing the input into a latent-space representation and then reconstructing the output from this representation.
Truncated Singular Value Decomposition (SVD)
Truncated SVD, also known as Latent Semantic Analysis in text processing, reduces dimensionality by transforming data to a lower-dimensional space, preserving only the most significant singular values.
t-Distributed Stochastic Neighbor Embedding (t-SNE)
t-SNE converts similarities between data points to joint probabilities and minimizes the Kullback-Leibler divergence between the joint probabilities of the low-dimensional embedding and the high-dimensional data.
Uniform Manifold Approximation and Projection (UMAP)
UMAP is a manifold learning technique that approximates a high-dimensional manifold. It works well even with large datasets, preserving more of the local and global data structure than t-SNE.
Isomap
Isomap extends PCA to non-linear dimension reduction by incorporating geodesic distances among all points on the manifold.
Independent Component Analysis (ICA)
ICA aims to represent a multivariate signal as a combination of independent non-Gaussian signals. It is commonly used for blind source separation.
Factor Analysis
Factor analysis is a model-based technique that attempts to describe variables as influenced by several latent factors. It reduces dimensionality by modeling the observed variables as linear combinations of potential factors plus noise.
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