131,039 research outputs found
Low-Multi-Rank High-Order Bayesian Robust Tensor Factorization
The recently proposed tensor robust principal component analysis (TRPCA)
methods based on tensor singular value decomposition (t-SVD) have achieved
numerous successes in many fields. However, most of these methods are only
applicable to third-order tensors, whereas the data obtained in practice are
often of higher order, such as fourth-order color videos, fourth-order
hyperspectral videos, and fifth-order light-field images. Additionally, in the
t-SVD framework, the multi-rank of a tensor can describe more fine-grained
low-rank structure in the tensor compared with the tubal rank. However,
determining the multi-rank of a tensor is a much more difficult problem than
determining the tubal rank. Moreover, most of the existing TRPCA methods do not
explicitly model the noises except the sparse noise, which may compromise the
accuracy of estimating the low-rank tensor. In this work, we propose a novel
high-order TRPCA method, named as Low-Multi-rank High-order Bayesian Robust
Tensor Factorization (LMH-BRTF), within the Bayesian framework. Specifically,
we decompose the observed corrupted tensor into three parts, i.e., the low-rank
component, the sparse component, and the noise component. By constructing a
low-rank model for the low-rank component based on the order- t-SVD and
introducing a proper prior for the model, LMH-BRTF can automatically determine
the tensor multi-rank. Meanwhile, benefiting from the explicit modeling of both
the sparse and noise components, the proposed method can leverage information
from the noises more effectivly, leading to an improved performance of TRPCA.
Then, an efficient variational inference algorithm is established for
parameters estimation. Empirical studies on synthetic and real-world datasets
demonstrate the effectiveness of the proposed method in terms of both
qualitative and quantitative results
Submodular Load Clustering with Robust Principal Component Analysis
Traditional load analysis is facing challenges with the new electricity usage
patterns due to demand response as well as increasing deployment of distributed
generations, including photovoltaics (PV), electric vehicles (EV), and energy
storage systems (ESS). At the transmission system, despite of irregular load
behaviors at different areas, highly aggregated load shapes still share similar
characteristics. Load clustering is to discover such intrinsic patterns and
provide useful information to other load applications, such as load forecasting
and load modeling. This paper proposes an efficient submodular load clustering
method for transmission-level load areas. Robust principal component analysis
(R-PCA) firstly decomposes the annual load profiles into low-rank components
and sparse components to extract key features. A novel submodular cluster
center selection technique is then applied to determine the optimal cluster
centers through constructed similarity graph. Following the selection results,
load areas are efficiently assigned to different clusters for further load
analysis and applications. Numerical results obtained from PJM load demonstrate
the effectiveness of the proposed approach.Comment: Accepted by 2019 IEEE PES General Meeting, Atlanta, G
Functional Linear Mixed Models for Irregularly or Sparsely Sampled Data
We propose an estimation approach to analyse correlated functional data which
are observed on unequal grids or even sparsely. The model we use is a
functional linear mixed model, a functional analogue of the linear mixed model.
Estimation is based on dimension reduction via functional principal component
analysis and on mixed model methodology. Our procedure allows the decomposition
of the variability in the data as well as the estimation of mean effects of
interest and borrows strength across curves. Confidence bands for mean effects
can be constructed conditional on estimated principal components. We provide
R-code implementing our approach. The method is motivated by and applied to
data from speech production research
Fast Robust PCA on Graphs
Mining useful clusters from high dimensional data has received significant
attention of the computer vision and pattern recognition community in the
recent years. Linear and non-linear dimensionality reduction has played an
important role to overcome the curse of dimensionality. However, often such
methods are accompanied with three different problems: high computational
complexity (usually associated with the nuclear norm minimization),
non-convexity (for matrix factorization methods) and susceptibility to gross
corruptions in the data. In this paper we propose a principal component
analysis (PCA) based solution that overcomes these three issues and
approximates a low-rank recovery method for high dimensional datasets. We
target the low-rank recovery by enforcing two types of graph smoothness
assumptions, one on the data samples and the other on the features by designing
a convex optimization problem. The resulting algorithm is fast, efficient and
scalable for huge datasets with O(nlog(n)) computational complexity in the
number of data samples. It is also robust to gross corruptions in the dataset
as well as to the model parameters. Clustering experiments on 7 benchmark
datasets with different types of corruptions and background separation
experiments on 3 video datasets show that our proposed model outperforms 10
state-of-the-art dimensionality reduction models. Our theoretical analysis
proves that the proposed model is able to recover approximate low-rank
representations with a bounded error for clusterable data
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