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single-cell-analysis

single-cell and spatial omics quantification and analysis

10x Cell Ranger, Scanpy, Seurat

SystemTechniques · 11Primitives · 44 single-cell-analysis Graph community detectiongraphs · medium: Louvain/label propagation community detection for rings, fraud clusters and campaignsGeneralized linear models (GLMs)machine-learning · medium: Linear model for counts, rates, positive amounts and proportions: a linear score pushed through a link, fitted by iteratively reweighted least squares.›Image segmentationmachine-learning · medium: Pixel/instance segmentation networks and promptable segmentation (Mask R-CNN, SAM-style)Umap embeddingmachine-learning · medium: Nonlinear dimension reduction: build a fuzzy kNN graph and optimise a low-dimensional layout by cross-entropy with negative samplingImage alignment registrationmedia · medium: Align frames via feature matching or pyramidal optical flow for burst merging and stitchingVariational autoencodersml-training · medium: VAEs and latent autoencoders: ELBO, KL weighting, latent compression for diffusion modelsExternal merge sortsearch-sort · medium: Sort data larger than RAM: write memory-sized sorted runs, then k-way merge them with large sequential buffers; terabytes in one merge pass.›Sparse matrices (CSR)numerics · low: Compressed sparse row stores only nonzeros as row pointers, column indices and values; SpMV streams them once, so it is memory-bandwidth bound.›Swiss tabledata-structures · low: Open-addressing hash table that filters 8-16 slots at once with 1-byte hash tags and SIMD, giving fast lookups at 87.5 % load.›PCA and SVDmachine-learning · low: Find orthogonal directions of maximum variance by an SVD of the centred data; randomized SVD gets the top k components in a few passes.›Edit distancesearch-sort · low: Levenshtein/Damerau distance by DP, bit-parallel Myers variantSuffix arraysearch-sort · low: Sorted array of all suffix start positions of a text; finds every occurrence of any substring by binary search, at 4-5 bytes per text byte.›Robust statisticsstatistics · low: Location and scale estimates (median, MAD, trimmed mean, Huber M-estimator) that stay correct when a minority of the data is garbage.›Union-findgraphs · low: Disjoint-set forest with union by size and path compression; merges sets and answers same-set queries in effectively constant time.›PRNGs (PCG, xoshiro)numerics · low: Small, fast, statistically strong non-cryptographic generators: PCG32 and xoshiro256**, with seeding, parallel streams and unbiased ranges.›Linear and logistic regressionmachine-learning · low: Fit a weighted sum of features to a number (least squares) or a probability (logistic); the baseline every model must beat.›LU and Cholesky factorizationnumerics · low: Factor A = PLU (any square matrix, partial pivoting) or A = LLᵀ (SPD) once in O(n³), then solve each right-hand side in O(n²).›Newton root findingnumerics · low: Linearize at the guess and jump to the tangent root; quadratic convergence near a simple root, made robust by brackets (1D) or line search.›Loss functionsmachine-learning · low: The scalar a model minimizes: cross-entropy for classes and tokens, MSE or Huber for values, each with a stable form and simple gradient.›Non-maximum suppressionmachine-learning · low: Keep the best-scoring candidate in each neighbourhood and drop the rest; greedy NMS, Soft-NMS and 1-D peak picking share one loop.›Convolutional networksml-training · low: Layers that slide a small shared kernel over a grid, giving translation equivariance and few parameters; still the most compute-efficient choice for many vision tasks.›Homogeneous transformsgeometry · low: 4x4 affine and projective matrices, homogeneous coordinates, view and projection, normal matricesImage pyramidsgraphics · low: Gaussian/Laplacian pyramids and tiled multi-resolution images for zoom and blending+ 4 more techniques+ 28 more primitives

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