Multimodal Signal Restoration with Signed Twofold Graph Learning

Multimodal signals on sensor networks are commonly modeled under the twofold graph assumption (TGA), which represents spatial structure and inter-modality relations as two separate graphs. Existing TGA-based signal restoration methods, however, either assume the graphs are known or restrict edge weights to be non-negative, preventing them from capturing negative inter-modal correlations. We address both limitations by formulating joint signal restoration and twofold graph learning as MAP estimation under a matrix normal prior, where the spatial and modality graph Laplacians appear directly as precision matrices. The resulting non-convex objective is solved by alternating minimization: The signal is updated via conjugate gradient applied to the arising Sylvester-type linear system; the graphs are updated via primal-dual hybrid gradient (PDHG). We further propose a method to estimate the signed structure of the modality graph from the dominant eigenspace of a complementary kernel matrix, which is then used in PDHG to update edge magnitudes. These iterative solvers are then unrolled into a feedforward network, with regularization weights and step sizes as layer-wise trainable parameters. Experiments on synthetic multimodal graph signals and a real Japan meteorological dataset confirm that the proposed method outperforms existing baselines across a range of noise levels and missing-data patterns.

Auditory Attention Decoding without Spatial Information: A Diotic EEG Study

Auditory attention decoding (AAD) identifies the attended speech stream in multi-speaker environments by decoding brain signals such as electroencephalography (EEG). This technology is essential for realizing smart hearing aids that address the cocktail party problem and for facilitating objective audiometry systems. Existing AAD research mainly utilizes dichotic environments where different speech signals are presented to the left and right ears, enabling models to classify directional attention rather than speech content. However, this spatial reliance limits applicability to real-world scenarios, such as the "cocktail party" situation, where speakers overlap or move dynamically. To address this challenge, we propose an AAD framework for diotic environments where identical speech mixtures are presented to both ears, eliminating spatial cues. Our approach maps EEG and speech signals into a shared latent space using independent encoders. We extract speech features using wav2vec 2.0 and encode them with a 2-layer 1D convolutional neural network (CNN), while employing the BrainNetwork architecture for EEG encoding. The model identifies the attended speech by calculating the cosine similarity between EEG and speech representations. We evaluate our method on a diotic EEG dataset and achieve 72.70% accuracy, which is 22.58% higher than the state-of-the-art direction-based AAD method.

Efficient Learning of Balanced Signed Graphs via Iterative Linear Programming

Signed graphs are equipped with both positive and negative edge weights, encoding pairwise correlations as well as anti-correlations in data. A balanced signed graph has no cycles of odd number of negative edges. Laplacian of a balanced signed graph has eigenvectors that map simply to ones in a similarity-transformed positive graph Laplacian, thus enabling reuse of well-studied spectral filters designed for positive graphs. We propose a fast method to learn a balanced signed graph Laplacian directly from data. Specifically, for each node $i$, to determine its polarity $\beta_i \in \{-1,1\}$ and edge weights $\{w_{i,j}\}_{j=1}^N$, we extend a sparse inverse covariance formulation based on linear programming (LP) called CLIME, by adding linear constraints to enforce ``consistent" signs of edge weights $\{w_{i,j}\}_{j=1}^N$ with the polarities of connected nodes -- i.e., positive/negative edges connect nodes of same/opposing polarities. For each LP, we adapt projections on convex set (POCS) to determine a suitable CLIME parameter $\rho > 0$ that guarantees LP feasibility. We solve the resulting LP via an off-the-shelf LP solver in $\mathcal{O}(N^{2.055})$. Experiments on synthetic and real-world datasets show that our balanced graph learning method outperforms competing methods and enables the use of spectral filters and graph convolutional networks (GCNs) designed for positive graphs on signed graphs.