Weighted Group Sparsity-Constrained Tensor Factorization for Hyperspectral Unmixing

Recently, unmixing methods based on nonnegative tensor factorization have played an important role in the decomposition of hyperspectral mixed pixels. According to the spatial prior knowledge, there are many regularizations designed to improve the performance of unmixing algorithms, such as the total variation (TV) regularization. However, these methods mostly ignore the similar characteristics among different spectral bands. To solve this problem, this paper proposes a group sparse regularization that uses the weighted constraint of the L2,1 norm, which can not only explore the similar characteristics of the hyperspectral image in the spectral dimension, but also keep the data smooth characteristics in the spatial dimension. In summary, a non-negative tensor factorization framework based on weighted group sparsity constraint is proposed for hyperspectral images. In addition, an effective alternating direction method of multipliers (ADMM) algorithm is used to solve the algorithm proposed in this paper. Compared with the existing popular methods, experiments conducted on three real datasets fully demonstrate the effectiveness and advancement of the proposed method.

Reducing Parameters of Neural Networks via Recursive Tensor Approximation

Large-scale neural networks have attracted much attention for surprising results in various cognitive tasks such as object detection and image classification. However, the large number of weight parameters in the complex networks can be problematic when the models are deployed to embedded systems. In addition, the problems are exacerbated in emerging neuromorphic computers, where each weight parameter is stored within a synapse, the primary computational resource of the bio-inspired computers. We describe an effective way of reducing the parameters by a recursive tensor factorization method. Applying the singular value decomposition in a recursive manner decomposes a tensor that represents the weight parameters. Then, the tensor is approximated by algorithms minimizing the approximation error and the number of parameters. This process factorizes a given network, yielding a deeper, less dense, and weight-shared network with good initial weights, which can be fine-tuned by gradient descent.

Shared and Unshared Feature Extraction in Major Depression During Music Listening Using Constrained Tensor Factorization

Ongoing electroencephalography (EEG) signals are recorded as a mixture of stimulus-elicited EEG, spontaneous EEG and noises, which poses a huge challenge to current data analyzing techniques, especially when different groups of participants are expected to have common or highly correlated brain activities and some individual dynamics. In this study, we proposed a data-driven shared and unshared feature extraction framework based on nonnegative and coupled tensor factorization, which aims to conduct group-level analysis for the EEG signals from major depression disorder (MDD) patients and healthy controls (HC) when freely listening to music. Constrained tensor factorization not only preserves the multilinear structure of the data, but also considers the common and individual components between the data. The proposed framework, combined with music information retrieval, correlation analysis, and hierarchical clustering, facilitated the simultaneous extraction of shared and unshared spatio-temporal-spectral feature patterns between/in MDD and HC groups. Finally, we obtained two shared feature patterns between MDD and HC groups, and obtained totally three individual feature patterns from HC and MDD groups. The results showed that the MDD and HC groups triggered similar brain dynamics when listening to music, but at the same time, MDD patients also brought some changes in brain oscillatory network characteristics along with music perception. These changes may provide some basis for the clinical diagnosis and the treatment of MDD patients.

Higher-order tensor decomposition based scalp-to-intracranial EEG projection for detection of interictal epileptiform discharges

Objective. Interictal epileptiform discharges (IEDs) occur between two seizures onsets. IEDs are mainly captured by intracranial recordings and are often invisible over the scalp. This study proposes a model based on tensor factorization to map the time-frequency (TF) features of scalp EEG (sEEG) to the TF features of intracranial EEG (iEEG) in order to detect IEDs from over the scalp with high sensitivity. Approach. Continuous wavelet transform is employed to extract the TF features. Time, frequency, and channel modes of IED segments from iEEG recordings are concatenated into a four-way tensor. Tucker and CANDECOMP/PARAFAC decomposition techniques are employed to decompose the tensor into temporal, spectral, spatial, and segmental factors. Finally, TF features of both IED and non-IED segments from scalp recordings are projected onto the temporal components for classification. Main results. The model performance is obtained in two different approaches: within- and between-subject classification approaches. Our proposed method is compared with four other methods, namely a tensor-based spatial component analysis method, TF-based method, linear regression mapping model, and asymmetric-symmetric autoencoder mapping model followed by convolutional neural networks. Our proposed method outperforms all these methods in both within- and between-subject classification approaches by respectively achieving 84.2% and 72.6% accuracy values. Significance. The findings show that mapping sEEG to iEEG improves the performance of the scalp-based IED detection model. Furthermore, the tensor-based mapping model outperforms the autoencoder- and regression-based mapping models.