What is Optimal Transport? | What is a Tensor? | The Problem OTT Solves | The Key Concept: the f Parameter | Quick Start Example | Step 1: Create two tensors | Step 2: Choose the f parameter | Step 3: Run OTT | Step 4: Inspect the results | Parameter Reference | What's Next? | Session Information | References

Introduction | OTT_1 (OT) | OTT_12 (Co-OT) | OTT_11 (GW) | OTT_111 (triplets) | OTT_123 (triCo-OT) | OTT_112 (GW Collection) | Session Information | References

Introduction | NMF | NMTF | siNMF | jNMF | NTF | NTD | Session Information | References

What is Optimal Transport? | What is a Tensor? | The Problem OTT Solves | The Key Concept: the f Parameter | Quick Start Example | Step 1: Create two tensors | Step 2: Choose the f parameter | Step 3: Run OTT | Step 4: Inspect the results | Parameter Reference | What's Next? | Session Information | References

Introduction | OTT_1 (OT) | OTT_12 (Co-OT) | OTT_11 (GW) | OTT_111 (triplets) | OTT_123 (triCo-OT) | OTT_112 (GW Collection) | Session Information | References

Overview | 1. Single Tensor Decomposition with MWCA | Choosing different algorithms per mode | 2. Coupled Tensor Decomposition with CoupledMWCA | Toy data | Setting up the model | Running with default parameters | Customizing algorithms and dimensions | 3. Validating Parameters with checkCoupledMWCA | 4. Reproducible Initialization with initCoupledMWCA | Initialization policies | Using initialized values for optimization | 5. Factor Refinement with refineFactor (Experimental) | Mathematical interpretation | Refinement on CoupledMWCA results | 6. Factorization Programs with MWCAProgram (Experimental) | Defining a program | Validation | Compiling to solver parameters | Programs with refinement | Factor status: decomposed, fixed, frozen | Session Info

Specification change of LRBase and scTensor from BioC 3.14 (Nov. 2021) | Introduction | About Cell-Cell Interaction (CCI) databases | LRBase and scTensor framework | Usage | LRBase objects (ligand-receptor database for 134 organisms) | Data retrieval from AnnotationHub | columns, keytypes, keys, and select | Other functions | scTensor (CCI-tensor construction, decomposition, and HTML reporting) | Creating a SingleCellExperiment object | Parameter setting: cellCellSetting | CCI-tensor construction and decomposition: cellCellDecomp | HTML Report: cellCellReport | Session Information

Introduction | Step.1: Create a gene-level expression matrix | Case I: Gene-level quantification | Case II: Transcript-level quantification | Case III: UMI-count | Step.2: Convert the row names of a matrix as NCBI Gene ID (ENTREZID) | Case I: Ensembl Gene ID to NCBI Gene ID | Case II: Gene Symbol to NCBI Gene ID | Step.3: Normalize the count matrix | Session information

Summary of the output objects of scTensor | Execution of scTensor with the different options | Session information

Introduction | Semi-Ternary Matrix Factorization (STMF) | Basic Usage | Session Information | References

Introduction | Binary Simultaneous Matrix Factorization (BSMF) | Basic Usage | Semi-Binary Simultaneous Matrix Factorization (SBSMF) | Session Information | References

Introduction | Semi-Binary Simultaneous Matrix Factorization (SBSMF) | Basic Usage | Session Information | References

Introduction | Semi-Ternary Simultaneous Matrix Factorization (STSMF) | Basic Usage | Session Information | References

Introduction | Binary Tensor Factorization (BTF) | Basic Usage | Semi-Binary Tensor Factorization (SBTF) | Session Information | References

Introduction | Binary Tensor Factorization (BTF) | Basic Usage | Semi-Binary Tensor Factorization (SBTF) | Session Information | References

Introduction | Binary Matrix Tri-Factorization (BMTF) | Basic Usage | Semi-Binary Matrix Tri-Factorization (SBMTF) | Semi-Ternary Matrix Tri-Factorization (STMTF) | Session Information | References

Introduction | Binary Matrix Factorization (BMF) | Basic Usage | Semi-Binary Matrix Factorization (SBMF) | Semi-Ternary Matrix Factorization (STMF) | Session Information | References

Introduction | 1. ICA with time-independent sub-Gaussian data | 2. ICA with time-independent super-Gaussian data | 3. ICA with data mixed with signals having no time dependence and different kurtosis | 4. ICA with time-dependent data | 5. IPCA in N < P systems | Session Information | References

Introduction | Multimodal Independent Component Analysis (MICA) | Group Independent Component Analysis (GroupICA) | Session Information | References

Introduction | Multilinear Independent Component Analysis (MultilinearICA) | Session Information | References

Introduction | 2D Embedding | 3D Embedding | Session Information | References

Introduction | Guided Partial Least Squares (guided-PLS) | Basic Usage | Session Information | References

Introduction | Partial Least Squares by Singular Value Decomposition (PLS-SVD) | Basic Usage | Partial Least Squares Discriminant Analysis (PLS-DA) | Sparse Partial Least Squares Discriminant Analysis (sPLS-DA) | Comparison with unsupervised learning | Session Information | References

Introduction | NMF | Basic Usage | Rank Estimation of NMF | NMTF | Session Information | References

Introduction | siNMF | jNMF | Session Information | References

Introduction | NTF | NTD | NTD-2 | NTD-1 | Higher-order tensor decomposition | Session Information | References

What is MeSH? | What is MeSH ORA Framework? | Specification change of MeSH ORA Framework from BioC 3.14 (Nov. 2021) | Access to MeSH data on AnnotationHub | MeSH Enrichment Analysis | Session Information

Setting | Tensor Arithmetic Operations | Unfold/Fold Operations | Vectorization | Norm Operations | Outer Product | Diagonal Operations | Mode-wise Operations | Tensor Product Operations | Hadamard Product | Kronecker Product | Khatri-Rao Product | Utilities Functions | Bind Operations | Session information

Setting | Tensor Decomposition | Tucker Decomposition | CANDECOMP/PARAFAC (CP) Decomposition | Multilinear Principal Component Analysis (MPCA) | Population Value Decomposition (PVD) | Session information

Introduction | Heterogenous Biological Data | What is Tensor | What is Tensor Decomposition | Concept of DelayedTensor: Block Processing-enabled Tensor Operations | Session information

What is einsum | Einsum of DelayedTensor | Typical operations of einsum | No Operation | print, show | diag | Multiplication | Hadamard Product | Outer Product | Summation | Row-wise / Column-wise Summation | Mode-wise Vectorization | Mode-wise Summation | Trace | Permutation | Multiplication + Summation | Inner Product (Squared Frobenius Norm) | Contracted Product | Matrix Multiplication | Multiplication + Permutation | Summation + Permutation | Multiplication + Summation + Permutation | Create your original function by einsum | Session information

Introduction | Interpretation of "1. About scTensor Algorithm" | Interpretation of "2. Global statistics and plots" | Interpretation of "3. Ligand-Cell Patterns" | Interpretation of "4. Receptor-Cell Patterns" | Interpretation of "5. CCI-wise Hypergraph" | Interpretation of "6. Gene-wise Hypergraph" | Interpretation of "7. (Ligand-Cell, Receptor-Cell, LR-pair) Patterns" | Session information

Introduction | Session information

Introduction | About scTGIF | Usage | Test data | Parameter setting : settingTGIF | Calculate attention maps and map-related gene functions: calcTGIF | HTML Report : reportTGIF | Session information