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We propose the Decomposer Networks (DecompNet), a semantic autoencoder that factorizes an input into multiple interpretable components. Unlike classical autoencoders that compress an input into a single latent representation, the Decomposer Network maintains N parallel branches, each assigned a residual input defined as the original signal minus the reconstructions of all other branches. By unrolling a Gauss--Seidel style block-coordinate descent into a differentiable network, DecompNet enforce explicit competition among components, yielding parsimonious, semantically meaningful representations. We situate our model relative to linear decomposition methods (PCA, NMF), deep unrolled optimization, and object-centric architectures (MONet, IODINE, Slot Attention), and highlight its novelty as the first semantic autoencoder to implement an all-but-one residual update rule.

Analysis of data from functional magnetic resonance imaging (fMRI) results in constructing functional brain networks. Principal component analysis (PCA) and independent component analysis (ICA) are widely used to generate functional brain networks. Moreover, dictionary learning and sparse representation provide some latent patterns that rules brain activities and they can be interpreted as brain networks. However, these methods lack modeling dependencies of the discovered networks. In this study an alternative to these conventional methods is presented in which dependencies of the networks are considered via correlated sparsity patterns. We formulate this challenge as a new dictionary learning problem and propose two approaches to solve the problem effectively.

Source localization and radio cartography using multi-way representation of spectrum is the subject of study in this paper. A joint matrix factorization and tensor decomposition problem is proposed and solved using an iterative algorithm. The multi-way measured spectrum is organized in a tensor and it is modeled by multiplication of a propagation tensor and a channel gain matrix. The tensor indicates the propagating power from each location and each frequency over time and the channel matrix links the propagating tensor to the sensed spectrum. We utilize sparsity and other intrinsic characteristics of spectrum to identify the solution of the proposed problem. Moreover, The online implementation of the proposed framework results in online radio cartography which is a powerful tool for efficient spectrum awareness and utilization. The simulation results show that our algorithm is a promising technique for dynamic primary user localization and online radio cartography.

In this paper I present a new approach for regression of time series using their own samples. This is a celebrated problem known as Auto-Regression. Dealing with outlier or missed samples in a time series makes the problem of estimation difficult, so it should be robust against them. Moreover for coding purposes I will show that it is desired the residual of auto-regression be sparse. To these aims, I first assume a multivariate Gaussian prior on the residual and then obtain the estimation. Two simple simulations have been done on spectrum estimation and speech coding.

Reliable and efficient spectrum sensing through dynamic selection of a subset of spectrum sensors is studied. The problem of selecting K sensor measurements from a set of M potential sensors is considered where K << M. In addition, K may be less than the dimension of the unknown variables of estimation. Through sensor selection, we reduce the problem to an under-determined system of equations with potentially infinite number of solutions. However, the sparsity of the underlying data facilitates limiting the set of solutions to a unique solution. Sparsity enables employing the emerging compressive sensing technique, where the compressed measurements are selected from a large number of potential sensors. This paper suggests selecting sensors in a way that the reduced system of equations constructs a well-conditioned measurement matrix. Our criterion for sensor selection is based on E-optimalily, which is highly related to the restricted isometry property that provides some guarantees for sparse solution obtained by L1 minimization. Moreover, the proposed framework exploits a feedback mechanism to evolve the selected sensors dynamically over time. The evolution aims to maximize the reliability of the sensed spectrum.

Text-to-Image (T2I) diffusion models have achieved remarkable success in synthesizing high-quality images conditioned on text prompts. Recent methods have tried to replicate the success by either training text-to-video (T2V) models on a very large number of text-video pairs or adapting T2I models on text-video pairs independently. Although the latter is computationally less expensive, it still takes a significant amount of time for per-video adaption. To address this issue, we propose SAVE, a novel spectral-shift-aware adaptation framework, in which we fine-tune the spectral shift of the parameter space instead of the parameters themselves. Specifically, we take the spectral decomposition of the pre-trained T2I weights and only update the singular values while freezing the corresponding singular vectors. In addition, we introduce a spectral shift regularizer aimed at placing tighter constraints on larger singular values compared to smaller ones. This form of regularization enables the model to grasp finer details within the video that align with the provided textual descriptions. We also offer theoretical justification for our proposed regularization technique. Since we are only dealing with spectral shifts, the proposed method reduces the adaptation time significantly (approx. 10 times) and has fewer resource constraints for training. Such attributes posit SAVE to be more suitable for real-world applications, e.g. editing undesirable content during video streaming. We validate the effectiveness of SAVE with an extensive experimental evaluation under different settings, e.g. style transfer, object replacement, privacy preservation, etc.

Meta-learning often referred to as learning-to-learn is a promising notion raised to mimic human learning by exploiting the knowledge of prior tasks but being able to adapt quickly to novel tasks. A plethora of models has emerged in this context and improved the learning efficiency, robustness, etc. The question that arises here is can we emulate other aspects of human learning and incorporate them into the existing meta learning algorithms? Inspired by the widely recognized finding in neuroscience that distinct parts of the brain are highly specialized for different types of tasks, we aim to improve the model performance of the current meta learning algorithms by selectively using only parts of the model conditioned on the input tasks. In this work, we describe an approach that investigates task-dependent dynamic neuron selection in deep convolutional neural networks (CNNs) by leveraging the scaling factor in the batch normalization (BN) layer associated with each convolutional layer. The problem is intriguing because the idea of helping different parts of the model to learn from different types of tasks may help us train better filters in CNNs, and improve the model generalization performance. We find that the proposed approach, neural routing in meta learning (NRML), outperforms one of the well-known existing meta learning baselines on few-shot classification tasks on the most widely used benchmark datasets.

In this paper, the problem of target localization in the presence of outlying sensors is tackled. This problem is important in practice because in many real-world applications the sensors might report irrelevant data unintentionally or maliciously. The problem is formulated by applying robust statistics techniques on squared range measurements and two different approaches to solve the problem are proposed. The first approach is computationally efficient; however, only the objective convergence is guaranteed theoretically. On the other hand, the whole-sequence convergence of the second approach is established. To enjoy the benefit of both approaches, they are integrated to develop a hybrid algorithm that offers computational efficiency and theoretical guarantees. The algorithms are evaluated for different simulated and real-world scenarios. The numerical results show that the proposed methods meet the Cr'amer-Rao lower bound (CRLB) for a sufficiently large number of measurements. When the number of the measurements is small, the proposed position estimator does not achieve CRLB though it still outperforms several existing localization methods.

A new deep learning-based electroencephalography (EEG) signal analysis framework is proposed. While deep neural networks, specifically convolutional neural networks (CNNs), have gained remarkable attention recently, they still suffer from high dimensionality of the training data. Two-dimensional input images of CNNs are more vulnerable to be redundant versus one-dimensional input time-series of conventional neural networks. In this study, we propose a new dimensionality reduction framework for reducing the dimension of CNN inputs based on the tensor decomposition of the time-frequency representation of EEG signals. The proposed tensor decomposition-based dimensionality reduction algorithm transforms a large set of slices of the input tensor to a concise set of slices which are called super-slices. Employing super-slices not only handles the artifacts and redundancies of the EEG data but also reduces the dimension of the CNNs training inputs. We also consider different time-frequency representation methods for EEG image generation and provide a comprehensive comparison among them. We test our proposed framework on HCB-MIT data and as results show our approach outperforms other previous studies.

The problem of simultaneous column and row subset selection is addressed in this paper. The column space and row space of a matrix are spanned by its left and right singular vectors, respectively. However, the singular vectors are not within actual columns/rows of the matrix. In this paper, an iterative approach is proposed to capture the most structural information of columns/rows via selecting a subset of actual columns/rows. This algorithm is referred to as two-way spectrum pursuit (TWSP) which provides us with an accurate solution for the CUR matrix decomposition. TWSP is applicable in a wide range of applications since it enjoys a linear complexity w.r.t. number of original columns/rows. We demonstrated the application of TWSP for joint channel and sensor selection in cognitive radio networks, informative users and contents detection, and efficient supervised data reduction.