Conventional principal component analysis (PCA) finds a principal vector that maximizes the sum of second powers of principal components. We consider a generalized PCA that aims at maximizing the sum of an arbitrary convex function of principal components. We present a gradient ascent algorithm to solve the problem. Fo…
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48 results for “Principal Component Networks”
GT-PCA improves PCA for image and time series data.
problem Lack of robustness to transformations in PCA.
method GT-PCA is a neural network that estimates components invariant to specific transformations.
result GT-PCA outperforms alternative methods in synthetic and real data experiments.
We propose a new method for supervised learning, especially suited to wide data where the number of features is much greater than the number of observations. The method combines the lasso () sparsity penalty with a quadratic penalty that shrinks the coefficient vector toward the leading principal components of …
A new method reduces data movement in neural network training.
problem Large data movement during neural network training.
method Streaming batch principal component analysis for low-rank updates.
result Effective training of convolutional neural networks with low overhead.
Deep Neural Networks for image classification have been found to be vulnerable to adversarial samples, which consist of sub-perceptual noise added to a benign image that can easily fool trained neural networks, posing a significant risk to their commercial deployment. In this work, we analyze adversarial samples throug…
Two novel clustering methods improve community detection in networks.
problem Community detection in networks using principal components.
method Principal Component Clustering (PCC) and Normalized Principal Component Clustering (NPCC).
result NPCC provides significant improvement over PCC and RSC methods.
This paper develops GPCA for probability distributions using Otto-Wasserstein geometry.
problem Analyzing modes of variation in datasets of probability measures.
method Geodesic Principal Component Analysis (GPCA) on Wasserstein space with neural networks.
result Identification of geodesic curves that capture modes of variation in probability distributions.
Study on dynamics of non-linear autoencoders learning principal components.
problem Technical difficulty in studying non-linear autoencoders due to non-trivial correlations.
method Derive asymptotically exact equations for SGD training of shallow, non-linear autoencoders.
result Autoencoders learn principal components sequentially and tie weights are ineffective.
New simulations advise caution in choosing principal components for multivariate functional data.
problem Inaccurate selection of principal components in multivariate functional data.
method Extensive simulations investigating the reliability of percentage of variance explained thresholds.
result Conventional threshold methods may fail to accurately explain overall variance in multivariate functional data.
Designing and modifying complex hull forms for optimal vessel performances have been a major challenge for naval architects. In the present study, Principal Component Analysis (PCA) is introduced to compress the geometric representation of a group of existing vessels, and the resulting principal scores are manipulated …
Principal component regression (PCR) is a two-stage procedure that selects some principal components and then constructs a regression model regarding them as new explanatory variables. Note that the principal components are obtained from only explanatory variables and not considered with the response variable. To addre…
A new GNN architecture called coVariance neural network (VNN) improves stability and transferability of covariance matrix analysis.
problem Stability and transferability issues in covariance matrix analysis.
method Developed coVariance neural network (VNN) that operates on sample covariance matrices.
result VNN is more stable and transferable than PCA-based approaches.
Localized Sparse Principal Component Analysis of Multivariate Time Series in Frequency Domainstat.ME
The paper introduces a method for interpretable principal component analysis of high-dimensional time series.
problem Inconsistent and difficult-to-interpret principal component estimates in high-dimensional regimes.
method Localized sparse principal component analysis of spectral density matrices in frequency domain.
result Efficient algorithm for sparse-localized estimates of principal subspaces.
PCHAL and PCHAR use principal components to speed up HAL and HAR methods.
problem Computational infeasibility in high dimensions for HAL and HAR.
method Outcome-blind principal component reduction of HAL basis.
result Empirical performance comparable to HAL and HAR, with computational gains.
Efficient private matrix analysis algorithms for recent variants.
problem Private analysis of recent matrix updates.
method Identifying sufficient conditions on positive semidefinite matrices.
result First efficient differentially private algorithms for various matrix analysis tasks.
We consider principal component analysis (PCA) in decomposable Gaussian graphical models. We exploit the prior information in these models in order to distribute its computation. For this purpose, we reformulate the problem in the sparse inverse covariance (concentration) domain and solve the global eigenvalue problem …
We show how to efficiently project a vector onto the top principal components of a matrix, without explicitly computing these components. Specifically, we introduce an iterative algorithm that provably computes the projection using few calls to any black-box routine for ridge regression. By avoiding explicit principal …
A new PCR method using SVD with sparse regularization.
problem Lack of response variable information in traditional PCR.
method One-stage SVD approach with two loss functions and sparse regularization.
result Obtains principal component loadings with response variable information.
Study evaluates financial anomaly detection methods on Canadian stock market.
problem Detecting financial anomalies in the Canadian stock market.
method Topological data analysis (TDA), principal component analysis (PCA), and neural network-based approaches.
result Neural network-based methods achieve the strongest performance in detecting financial anomalies.
Essential principal components simplify spectral analysis with minimal training data.
problem Accurate spectral quantification from complex mixtures.
method Identifying essential principal components and using molar extinction coefficients.
result Near one-to-one projection from principal components to mixture constituents.
KPCA improves OoD detection by separating InD and OoD data.
problem Insufficiency of PCA in detecting OoD data from InD data.
method Kernel PCA (KPCA) with task-specific kernels.
result KPCA achieves superior OoD detection performance.
New method finds smaller networks with similar performance to large models in fewer epochs.
problem Training large neural networks is computationally expensive and energy-intensive.
method Use PCA to identify a basis of hidden layer activations and reduce network parameters.
result Principal Component Networks (PCNs) can train faster and use less energy than overparameterized models without accuracy loss.
A new method for sparse PCA using orthogonal rotations and soft-thresholding.
problem Sparse PCA with a new basis using orthogonal rotations.
method Initialize with leading principal components, apply orthogonal rotation, and soft-threshold the rotated components.
result The proposed method is more stable and explains more variance compared to alternatives.
Principal component regression (PCR) is a widely used two-stage procedure: principal component analysis (PCA), followed by regression in which the selected principal components are regarded as new explanatory variables in the model. Note that PCA is based only on the explanatory variables, so the principal components a…
QAPCA uses quantum annealing for robust PCA.
problem Outliers in data skew L2-norm principal components.
method Quantum annealing for L1-norm optimization.
result QAPCA's reconstruction error is comparable to L1-BF.
New supervised and unsupervised NFLTs for elliptical distributions.
problem Understanding unsupervised No Free Lunch Theorems for elliptical distributions.
method Proved two equally optimal strategies for elliptical distributions, inspired PRIM-based bump-hunting algorithms.
result Optimal strategies for selecting principal components based on variance or volume.
Deep equilibrium models estimate latent variables from data.
problem Estimating latent variables from data.
method Generalized exponential family models, deep equilibrium networks.
result Deep equilibrium models solve MAP estimates for latent and transformation parameters.
Two new PCA variants improve financial data analysis.
problem Numerical instability and nonstationarity in PCA for finance.
method Iterated and exponentially weighted moving PCA variants using Ogita-Aishima iteration.
result Improved stability and adaptability in financial data analysis.
Anomaly Detection on Financial Time Series by Principal Component Analysis and Neural Networksq-fin.ST
Proposes a method to detect anomalies in financial time series using PCA and neural networks.
problem Anomalies in financial time series lead to miscalibrated risk models.
method Extract features using PCA, define anomaly score with neural network, calibrate cutoff value.
result The proposed PCA NN approach outperforms other anomaly detection methods.
This paper analyses the Chinese Sovereign bond yield to find out the principal factors affecting the term structure of interest rate changes. We apply Principal Component Analysis (PCA) on our data consisting of the Chinese Sovereign bond from January 2002 till May 2018 with the different yield to maturity. Then we wil…
CPCR mitigates bias in PCR for overparameterized models.
problem Bias in Principal Component Regression (PCR) for overparameterized models.
method Calibrated Principal Component Regression (CPCR) learns a low-variance prior in the PC subspace and calibrates the model in the original feature space.
result CPCR outperforms standard PCR in overparameterized settings, improving prediction across multiple problems.
A new algorithm identifies interpretable network representations via subgraph count statistics.
problem Interpreting network-valued data samples.
method Principal Component Analysis for Networks (PCAN) and its fast sampling-based version (sPCAN).
result The PCAN and sPCAN methods provide informative and discriminatory features for network samples.
This paper analyzes how errors accumulate in PCA's deflation method.
problem Error accumulation in PCA's deflation method.
method Mathematical analysis of inexact Hotelling's deflation method in two scenarios.
result Characterization of error propagation in PCA's deflation method.
Paper presents a faster classical algorithm for principal component regression.
problem Efficiently solving principal component regression problems.
method Uses quantum-inspired linear algebra techniques.
result Achieves polylogarithmic runtime, significantly faster than state-of-the-art.
Bayesian SPCA method tackles orthogonality constraint with spike and slab prior.
problem Bayesian SPCA method for high-dimensional data with orthogonality constraint.
method Parameter-expanded coordinate ascent variational inference (PX-CAVI) with spike and slab prior.
result PX-CAVI algorithm outperforms existing SPCA approaches in performance.
We study sparse principal component analysis for high dimensional vector autoregressive time series under a doubly asymptotic framework, which allows the dimension to scale with the series length . We treat the transition matrix of time series as a nuisance parameter and directly apply sparse principal component…
Principal component analysis (PCA) is recognised as a quintessential data analysis technique when it comes to describing linear relationships between the features of a dataset. However, the well-known sensitivity of PCA to non-Gaussian samples and/or outliers often makes it unreliable in practice. To this end, a robust…
The computation of the sparse principal component of a matrix is equivalent to the identification of its principal submatrix with the largest maximum eigenvalue. Finding this optimal submatrix is what renders the problem -hard. In this work, we prove that, if the matrix is positive semidefinite and its …
Dynamic Principal Component Analysis: Identifying the Relationship between Multiple Air Pollutantsstat.AP
The dynamic nature of air quality chemistry and transport makes it difficult to identify the mixture of air pollutants for a region. In this study of air quality in the Houston metropolitan area we apply dynamic principal component analysis (DPCA) to a normalized multivariate time series of daily concentration measurem…
In this dissertation, the main goal is visualisation of financial time series. We expect that visualisation of financial time series will be a useful auxiliary for technical analysis. Firstly, we review the technical analysis methods and test our trading rules, which are built by the essential concepts of technical ana…
The paper uses PCA and HMM to forecast stock returns outperforming buy-and-hold.
problem Predicting stock returns accurately.
method Applied PCA to covariance matrix of S&P 500 stocks, used HMM on principal components, and forecasted stock returns.
result The model outperforms buy-and-hold strategy in terms of annualized Sharpe ratio.
Study explores K-means clustering of variables and its relation to PCA.
problem Exploring the relationship between K-means clustering of variables and PCA.
method Apply PCA to original data and K-means to transposed data, quantify variable contributions to principal components.
result Identifies how variable clusters contribute to principal components identified by PCA.
Paper proposes SDDP for improving time series forecasting with high-dimensional predictors.
problem Improving time series forecasting with high-dimensional predictors.
method SDDP framework that incorporates target variable and lagged observations into factor extraction process.
result SDDP improves predictive accuracy in time series forecasting.
We introduce a variant of (sparse) PCA in which the set of feasible support sets is determined by a graph. In particular, we consider the following setting: given a directed acyclic graph on vertices corresponding to variables, the non-zero entries of the extracted principal component must coincide with vertice…
Develops a new tensor PCA method for analyzing multiple network data.
problem Analyzing multiple large networks for dimensionality reduction.
method Semi-Symmetric Tensor PCA (SS-TPCA) for principal components analysis.
result SS-TPCA achieves the same estimation accuracy as classical matrix PCA, with error proportional to the square root of the number of vertices.
Paper develops a dual formulation for PCA in Hilbert spaces.
problem Characterizing probabilistic PCA in Hilbert spaces.
method Dual formulation for probabilistic PCA in Hilbert spaces.
result Generative framework for kernel methods developed.
Principal component analysis (PCA) has been a prominent tool for high-dimensional data analysis. Online algorithms that estimate the principal component by processing streaming data are of tremendous practical and theoretical interests. Despite its rich applications, theoretical convergence analysis remains largely ope…
A new method uses Gram matrix for efficient multivariate functional principal components.
problem Efficiently estimating eigencomponents of multidimensional functional datasets.
method Proposes using inner-product matrix to estimate eigenelements of multivariate and multidimensional functional datasets.
result Established relationship between eigenelements of covariance operator and inner-product matrix.