Multivariate Convolutional Sparse Coding with Low Rank Tensor
This paper introduces a new multivariate convolutional sparse coding based on tensor algebra with a general model enforcing both element-wise sparsity and low-rankness of the activations tensors. By using the CP decomposition, this model achieves a significantly more efficient encoding of the multivariate signal-particularly in the high order/ dimension setting-resulting in better performance. We prove that our model is closely related to the Kruskal tensor regression problem, offering interesting theoretical guarantees to our setting. Furthermore, we provide an efficient optimization algorithm based on alternating optimization to solve this model. Finally, we evaluate our algorithm with a large range of experiments, highlighting its advantages and limitations.
Code (0)
등록된 구현이 없습니다.
Tasks
regressiontensor algebraSimilar Papers 제목 키워드 기반
Tensor Convolutional Sparse Coding with Low-Rank activations, an application to EEG analysis
Recently, there has been growing interest in the analysis of spectrograms of ElectroEncephaloGram (EEG), particularly to study the neural correlates of (un)-consciousness during General Anesthesia (GA). Indeed, it has be…
EEGElectroencephalogram (EEG)Tensor Completion via Convolutional Sparse Coding Regularization
Tensor data often suffer from missing value problem due to the complex high-dimensional structure while acquiring them. To complete the missing information, lots of Low-Rank Tensor Completion (LRTC) methods have been pro…
Multi-dimensional Signal Recovery using Low-rank Deconvolution
In this work we present Low-rank Deconvolution, a powerful framework for low-level feature-map learning for efficient signal representation with application to signal recovery. Its formulation in multi-linear algebra inh…
Hankel-structured Tensor Robust PCA for Multivariate Traffic Time Series Anomaly Detection
Spatiotemporal traffic data (e.g., link speed/flow) collected from sensor networks can be organized as multivariate time series with additional spatial attributes. A crucial task in analyzing such data is to identify and…
Anomaly DetectionTime SeriesTime Series AnalysisTime Series Anomaly DetectionQuaternion Tensor Train Rank Minimization with Sparse Regularization in a Transformed Domain for Quaternion Tensor Completion
The tensor train rank (TT-rank) has achieved promising results in tensor completion due to its ability to capture the global low-rankness of higher-order (>3) tensors. On the other hand, recently, quaternions have proven…