Given a Delaunay decomposition of a compact hyperbolic surface, one may record the topological data of the decomposition, together with the intersection angles between the `empty disks' circumscribing the regions of the decomposition. The main result of this paper is a characterization of when a given topological decom…
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48 results for “Data decomposition”
The paper uses tensor decompositions to improve neural network models for tree data.
problem Encoding structural knowledge from tree-structured data efficiently.
method Introduces new aggregation functions using Canonical and Tensor-Train decompositions.
result Proposed models outperform traditional methods on tree classification tasks.
A new algorithm speeds up CP decomposition for large tensors.
problem Efficiently processing large-scale tensors in real-time.
method Randomized online CP decomposition (ROCP) algorithm.
result ROCP reduces computing time and memory usage significantly.
FunBaT extends Tucker decomposition to handle continuous-indexed tensor data.
problem Handling continuous-indexed tensor data that doesn't fit traditional Tucker decomposition.
method FunBaT treats continuous-indexed data as interactions between a core tensor and a group of latent functions modeled by Gaussian processes (GP). It converts each GP into a state-space prior and uses advanced message-passing techniques for scalable inference.
result FunBaT effectively handles real-world data with continuous indexes, demonstrating its advantage in synthetic and real-world applications.
D-CDLF: Decomposition of Common and Distinctive Latent Factors for Multi-view High-dimensional Datastat.ML
Proposes D-CDLF for multi-view data decomposition.
problem Uncorrelatedness between common and distinctive latent factors.
method Decomposes data into common, distinctive, and noise components.
result Effective uncorrelatedness between distinctive latent factors from different views.
New method uses random decompositions for high-dimensional Bayesian optimization.
problem Learning accurate decompositions for high-dimensional black-box functions.
method Data-independent random tree-based decomposition sampling.
result Random decomposition upper-confidence bound algorithm (RDUCB) yields significant empirical gains.
Scalable and robust TR decomposition for large-scale data with missing entries and outliers.
problem Handling large-scale tensor data with missing entries and outliers.
method Auto-weighted steepest descent method for missing entries and outliers identification, FGMC and RStS strategies.
result Outperforms existing TR decomposition methods in the presence of outliers and runs faster than robust tensor completion algorithms.
Proposes a Gaussian process for Koopman mode decomposition.
problem Estimating Koopman mode decomposition quantities and latent variables.
method Unsupervised Gaussian process for simultaneous estimation.
result Efficient parameter estimation through low-rank approximations.
Tensor decomposition recovers Gaussian mixtures from moments.
problem Recovering Gaussian mixture models from datasets.
method Symmetric tensor decomposition of moment tensors built from empirical moments.
result Identifiable tensors with interpolation degree less than half their order.
Tensor decompositions are powerful tools for large data analytics as they jointly model multiple aspects of data into one framework and enable the discovery of the latent structures and higher-order correlations within the data. One of the most widely studied and used decompositions, especially in data mining and machi…
We present an approach for penalized tensor decomposition (PTD) that estimates smoothly varying latent factors in multi-way data. This generalizes existing work on sparse tensor decomposition and penalized matrix decompositions, in a manner parallel to the generalized lasso for regression and smoothing problems. Our ap…
NACT improves tensor regression predictions with regularization.
problem Improving tensor regression predictions with structural information.
method Noise-Augmented regularization on Tucker decomposition.
result Achieves exact regularization on core tensor in linear and generalized linear tensor regression.
SRMD uses random features for efficient time-frequency analysis.
problem Efficiently analyzing time-series data with low computational cost.
method Sparse Random Mode Decomposition (SRMD) constructs a sparse approximation to the spectrogram.
result SRMD outperforms other methods in signal representation, outlier removal, and mode decomposition.
The paper studies batch decompositions of random datasets with probabilistic similarity constraints.
problem Understanding how to optimally split large datasets into batches for better model learning.
method Assumes independent data points from a space, defines similarity, and uses probabilistic and martingale methods to find bounds on batch sizes.
result Demonstrates an inherent tradeoff between relaxing similarity constraints and batch size, and provides bounds for maximum similarity subsets.
Anomaly Detection has several important applications. In this paper, our focus is on detecting anomalies in seller-reviewer data using tensor decomposition. While tensor-decomposition is mostly unsupervised, we formulate Bayesian semi-supervised tensor decomposition to take advantage of sparse labeled data. In addition…
Bayesian tensor train method recovers streaming data with high accuracy.
problem Recovering high-order, incomplete, and noisy streaming data.
method Bayesian tensor train decomposition using streaming variational Bayes method.
result The proposed SPTT algorithm excels in recovering streaming data compared to state-of-the-art methods.
ALCORE tensor decomposition reduces computational cost for sparse count data.
problem Efficiently decompose sparse count data matrices.
method Probabilistic Tucker decomposition with -norm constraint.
result ALCORE achieves similar results to full Tucker decomposition at a fraction of the cost.
The paper explores tensor decompositions in deep learning models.
problem Compressing parameter space and creating richer representations.
method Tensor decompositions applied to deep learning models.
result Tensor methods can yield richer adaptive representations of complex data.
Develops a tensor decomposition method with side information.
problem Identifying the relationship between a high-dimensional tensor and side information.
method Supervised tensor decomposition incorporating multiple feature matrices.
result Captures effective dimension reduction of the data tensor in feature space.
Develops SymGCP for tensor decompositions with general symmetry.
problem Handling symmetry in tensor decompositions for better model accuracy.
method Introduces SymGCP, a generalized CP decomposition that accounts for any subset of tensor modes' symmetry.
result SymGCP enables efficient and scalable tensor decomposition with improved model robustness and accuracy.
Tensor decomposition is an important technique for capturing the high-order interactions among multiway data. Multi-linear tensor composition methods, such as the Tucker decomposition and the CANDECOMP/PARAFAC (CP), assume that the complex interactions among objects are multi-linear, and are thus insufficient to repres…
Tensor decomposition methods allow us to learn the parameters of latent variable models through decomposition of low-order moments of data. A significant limitation of these algorithms is that there exists no general method to regularize them, and in the past regularization has mostly been performed using bespoke modif…
Paper characterizes optimization landscape of Tucker decomposition.
problem Finding exact Tucker decomposition is a nonconvex optimization problem.
method Characterized the optimization landscape and provided a local search algorithm.
result All local minima are globally optimal if tensor has an exact Tucker decomposition.
To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new formulation of sparse coding is proposed which enables high dimensional tensors dictiona…
IKD uses eigen-decomposition for nonlinear dimensionality reduction.
problem Lack of sophisticated and nonlinear dimensionality reduction methods.
method Inverse Kernel Decomposition (IKD) based on eigen-decomposition of sample covariance matrix.
result IKD achieves comparable performance to optimization-based methods with faster running speeds.
Tree Ensemble Explainability through the Hoeffding Functional Decomposition and TreeHFD Algorithmstat.ML
TreeHFD algorithm explains tree ensemble models through hierarchical orthogonality.
problem Difficulty in explaining black-box tree ensemble models.
method TreeHFD algorithm using hierarchical orthogonality constraints.
result TreeHFD estimates Hoeffding decomposition from data samples.
Adaptive tensor modeling preserves continuity in multidimensional data.
problem Discretization of continuous multidimensional data loses important information.
method Functional Tucker decomposition (FTD) with RKHS modeling.
result FTD enables adaptive and expressive tensor modeling.
Proposes FOAGP for efficient orthogonal effect decomposition of black-box computer experiments.
problem Challenges in sensitivity analysis of black-box computer experiments with complex, nonlinear functional outputs.
method Functional-output orthogonal additive Gaussian process (FOAGP) with conditional orthogonality constraint.
result Demonstrates effectiveness in orthogonal effect decomposition and variance decomposition through simulations and real-world application.
Paper studies nonnegative Tucker decomposition identifiability with sparsity conditions.
problem Identify nonnegative Tucker decomposition factors uniquely.
method Adapting NMF identifiability results, derive procedures using tensor unfoldings or slices.
result Nonnegative Tucker decomposition factors are identifiable under certain sparsity conditions.
DiPCA algorithm improves scalability and solution quality for time-dependent data.
problem Analyzing time-dependent multivariate data with dynamic latent variables.
method Solves a large-scale, dense, nonconvex NLP using a scalable decomposition algorithm.
result The decomposition algorithm is a specialized coordinate maximization algorithm, explaining its performance and guiding improvements.
Study shows OAT decomposition generates unexplained profit and loss, while SU decompositions depend on risk factor order.
problem Understanding profit and loss attribution in financial markets.
method Used financial market data from 2003 to 2022 to compare OAT, SU, and ASU decompositions.
result SU decompositions are sensitive to risk factor order and cannot identify all relevant risk factors.
Matrix decomposition is a popular and fundamental approach in machine learning and data mining. It has been successfully applied into various fields. Most matrix decomposition methods focus on decomposing a data matrix from one single source. However, it is common that data are from different sources with heterogeneous…
Shape Constrained Tensor Decompositions using Sparse Representations in Over-Complete Librariesstat.ML
We consider -way data arrays and low-rank tensor factorizations where the time mode is coded as a sparse linear combination of temporal elements from an over-complete library. Our method, Shape Constrained Tensor Decomposition (SCTD) is based upon the CANDECOMP/PARAFAC (CP) decomposition which produces -rank appr…
Paper bounds tensor decomposition's RLCT, aiding Bayesian inference.
problem Unclear mathematical property of tensor decomposition.
method Algebraic geometrical method for upper bound derivation.
result Upper bound of real log canonical threshold (RLCT) derived.
A general framework for solving the subspace clustering problem using the CUR decomposition is presented. The CUR decomposition provides a natural way to construct similarity matrices for data that come from a union of unknown subspaces . The similarity matrices thus c…
Proves Kato manifolds satisfy Hodge decomposition.
problem Proving Hodge decomposition for Kato manifolds.
method Relating cohomology to modification data and studying Bott-Chern and Aeppli cohomology.
result Kato manifolds satisfy Hodge decomposition.
A new probabilistic BTD method for tensor data.
problem Modeling higher-order tensors with robust inference.
method Probabilistic Block-Term Decomposition using variational Bayesian inference and von-Mises Fisher distribution.
result The proposed pBTD can quantify multi-linear structures robustly.
Paper proposes ONTD for nonnegative tensor data.
problem Handling nonnegative tensor data efficiently.
method Orthogonal Nonnegative Tucker Decomposition (ONTD) with convex relaxation algorithm.
result Demonstrates effectiveness on real-world image data applications.
Tensor decomposition is a well-known tool for multiway data analysis. This work proposes using stochastic gradients for efficient generalized canonical polyadic (GCP) tensor decomposition of large-scale tensors. GCP tensor decomposition is a recently proposed version of tensor decomposition that allows for a variety of…
Pattern Decomposition with Complex Combinatorial Constraints: Application to Materials Discoverycs.AI
Identifying important components or factors in large amounts of noisy data is a key problem in machine learning and data mining. Motivated by a pattern decomposition problem in materials discovery, aimed at discovering new materials for renewable energy, e.g. for fuel and solar cells, we introduce CombiFD, a framework …
Variables in many massive high-dimensional data sets are structured, arising for example from measurements on a regular grid as in imaging and time series or from spatial-temporal measurements as in climate studies. Classical multivariate techniques ignore these structural relationships often resulting in poor performa…
The report analyzes Legendre decomposition for tensor data.
problem Finding effective lower dimensional representations of tensors.
method Theoretical analysis of dual parameters and dually flat manifold properties, followed by experimental verification and clustering.
result Parameters on submanifold cannot be directly used as low-rank representations.
New method extracts joint and individual signals from multi-view data.
problem Extract joint and individual signals from multi-view data.
method Double-matched matrix decomposition with optimization and iterative algorithm.
result Superior signal estimation performance compared to single-matching methods.
We provide a unified view of additive explanations for dependent inputs.
problem Challenges in obtaining a tractable representation and estimating the decomposition for dependent inputs.
method Combining Hilbert space methods with generalized functional ANOVA, we build an explicit decomposition Riesz Basis.
result Proposed a simple yet powerful algorithm to estimate the decomposition from data.
Paper tackles tensor decomposition for unaligned observations using RKHS and novel loss functions.
problem Tackles tensor decomposition for unaligned observations.
method Uses functions in RKHS to represent mode with unaligned observations, introduces versatile loss function, proposes optimization algorithm and stochastic gradient method.
result Demonstrates improved tensor decomposition efficiency and effectiveness with synthetic and real data.
SWoTTeD discovers hidden temporal patterns in EHR data.
problem Complex temporal patterns in EHR data.
method Sliding Window for Temporal Tensor Decomposition (SWoTTeD) with constraints and regularizations.
result SWoTTeD achieves at least as accurate reconstruction as state-of-the-art models and extracts meaningful temporal phenotypes.
Paper applies ANOVA decomposition for interpretable data approximation.
problem High-dimensional data interpretation and dimensionality reduction.
method ANOVA decomposition and Grouped Transformations for interpretability.
result Ability to rank variable interactions and unimportant variables.
We provide the proof that the space of time series data is a Kolmogorov space with -separation axiom using the loop space of time series data. In our approach we define a cyclic coordinate of intrinsic time scale of time series data after empirical mode decomposition. A spinor field of time series data comes fro…