# Dimension Reduction > [!quote] Linear vs Non-Linear Reductions > Intuitively, you can think about linear transformations as shifting and stretching the data, meanwhile non-linear transformations will make more dramatic changes on data, such as making it “inside out”. https://en.wikipedia.org/wiki/Curse_of_dimensionality ## Types of Dimension Reduction Techniques ### Supervised vs Unsupervised > See also: > - [[Machine Learning]] **Supervised:** - LDA **Unsupervised:** - PCA ### Linear vs Non-Linear #### Linear Transformations > See also: > - [[Linear Algebra]] ![[Pasted image 20240124164440.png|275]] [[Principal Component Analysis (PCA)]] - Can reduce data to a lower dimension while keeping the information (variance) in our data. - Converts data into an eigenvector and eigenvalue - Tries to reduce dimensionality by maximizing variance in the data #### Non-Linear Transformations ![[Pasted image 20240124164628.png|327]] **Kernal PCA (kPCA)** - An extension of PCA by introducing a **t-distributed Stochastic Neighbor Embedding (t-SNE)** - Tries to do the same as PCA by keeping similar data points together (and dissimilar data points apart) in both higher and lower dimensions - [StatQuest: t-SNE, Clearly Explained](https://www.youtube.com/watch?v=NEaUSP4YerM) **Uniform Manifold Approximation and Projection (UMAP)** - Supposedly very similar to t-SNE (considered a subset by some) - [ ] autoencoders ## Applications of Dimension Reduction ### Differential Gene Expression A gene is declared as differentially expressed (DE) if an observed difference or change in read counts or expression levels between two experimental conditions is statistically significant. - [NIH Paper on an Approach to DE](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4827276/) Cells can be clustered based on their PCA scores, with each PC essentially representing a ‘metafeature’ that combines information across a correlated feature set. ## Visualizing Dimension Reduction --- https://www.reddit.com/r/datascience/comments/wy1rmk/pca_vs_umap_vs_tsne_on_a_very_layman_level_what/ PCA is very useful