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Hierarchical Matrix Factorization
Matrix decomposition technique that captures data structures at multiple levels of abstraction, organizing factors according to a hierarchy to model complex relationships.
Hierarchical Singular Value Decomposition (HSVD)
Extension of traditional SVD that operates on hierarchical data structures, producing singular vectors organized in a tree to represent multi-scale dependencies.
Hierarchical Non-Negative Matrix Factorization (HNMF)
Variant of NMF that imposes non-negativity constraints while discovering hierarchical structure in factors, often used for topic analysis with sub-topic relationships.
Factor Tree
Tree data structure where each node represents a latent factor, and parent-child relationships encode hierarchical dependencies between underlying data concepts.
Hierarchical Kernel Matrix
Similarity matrix constructed by integrating hierarchical relationships between instances, where similarity is calculated considering paths in the hierarchy.
Multi-Scale Representation Learning
Learning process of simultaneous latent vectors at different granularities, from most general to most specific, to capture information at multiple detail levels.
Hierarchical Regularization
Penalty term added to the loss function to encourage factors to follow a predefined or learned hierarchical structure, promoting consistency between levels.
Hierarchical Tensor Factorization
Generalization of matrix factorization to tensors (multi-dimensional arrays) that respects and reveals hierarchical structures inherent in multi-axis data.
Hierarchical Matrix Clustering
Method that combines matrix factorization with hierarchical clustering, where latent factors are used to define clusters at each level of the hierarchy.
Hierarchical Mixture Model
Type of mixture model where the mixture components are themselves organized hierarchically, allowing for finer modeling of subpopulations within broader groups.
Factorization Depth
Parameter defining the number of levels in the factor hierarchy, controlling the granularity of the representation and the model's ability to capture nested structures.
Factor Propagation
Mechanism by which information or constraints are transmitted along the factor hierarchy, typically from parent nodes to child nodes to ensure consistency.
Hierarchical Incidence Matrix
Binary matrix that encodes the membership relationships between elements and different levels of the hierarchy, used to link factors between layers.
Hierarchical Component Factorization (HCF)
Method that decomposes a matrix into a set of hierarchically organized components (factors), where each component captures part of the variance at a specific abstraction level.
Hierarchical Bayesian Model for Factorization
Probabilistic framework that uses hierarchical priors on latent factors, allowing for rigorous inference of both factors and the underlying hierarchical structure.
Factor Aggregation by Level
Operation that combines factors from a given level of the hierarchy to produce a consolidated representation, often through weighted sum or averaging.
Hierarchical Gradient Descent
Optimization algorithm that updates model parameters while respecting the hierarchical structure, propagating gradients from the top to the base of the factor tree.