Related papers: Introducing Block-Toeplitz Covariance Matrices to …
Source enumeration typically relies on subspace-based techniques that require accurate separation of signal and noise subspaces. However, prior works do not address coherent sources in small uniform linear arrays, where ambiguities arise in…
We revisit Deep Linear Discriminant Analysis (Deep LDA) from a likelihood-based perspective. While classical LDA is a simple Gaussian model with linear decision boundaries, attaching an LDA head to a neural encoder raises the question of…
The emergence of large-margin softmax cross-entropy losses in training deep speaker embedding neural networks has triggered a gradual shift from parametric back-ends to a simpler cosine similarity measure for speaker verification. Popular…
In recent years, deep learning (DL) has contributed significantly to the improvement of motor-imagery brain-machine interfaces (MI-BMIs) based on electroencephalography(EEG). While achieving high classification accuracy, DL models have also…
Linear discriminant analysis (LDA) is a typical method for classification problems with large dimensions and small samples. There are various types of LDA methods that are based on the different types of estimators for the covariance…
This paper considers the problem of robustly estimating a structured covariance matrix with an elliptical underlying distribution with known mean. In applications where the covariance matrix naturally possesses a certain structure, taking…
This paper tackles the problem of Lipschitz regularization of Convolutional Neural Networks. Lipschitz regularity is now established as a key property of modern deep learning with implications in training stability, generalization,…
In the internet era there has been an explosion in the amount of digital text information available, leading to difficulties of scale for traditional inference algorithms for topic models. Recent advances in stochastic variational inference…
Quadratic discriminant analysis (QDA) is a widely used classification technique that generalizes the linear discriminant analysis (LDA) classifier to the case of distinct covariance matrices among classes. For the QDA classifier to yield…
The attention mechanism has gained significant recognition in the field of computer vision due to its ability to effectively enhance the performance of deep neural networks. However, existing methods often struggle to effectively utilize…
We develop a framework for analyzing multivariate time series using topological data analysis (TDA) methods. The proposed methodology involves converting the multivariate time series to point cloud data, calculating Wasserstein distances…
In time series analysis, when fitting an autoregressive model, one must solve a Toeplitz ordinary least squares problem numerous times to find an appropriate model, which can severely affect computational times with large data sets. Two…
Equalizer parameter optimization is critical for signal integrity in high-speed memory systems operating at multi-gigabit data rates. However, existing methods suffer from computationally expensive eye diagram evaluation, optimization of…
The problem of estimating the covariance matrix $\Sigma$ of a $p$-variate distribution based on its $n$ observations arises in many data analysis contexts. While for $n>p$, the classical sample covariance matrix $\hat{\Sigma}_n$ is a good…
The use of quadratic discriminant analysis (QDA) or its regularized version (R-QDA) for classification is often not recommended, due to its well-acknowledged high sensitivity to the estimation noise of the covariance matrix. This becomes…
Background: Topological data analysis (TDA) has exploded as a tool for analyzing and making sense of high dimensional datasets across a variety of fields. Mapper is a tool from TDA that captures low-dimensional structure from…
This paper addresses the problem of estimating the Hermitian Toeplitz covariance matrix under practical hardware constraints of sparse observations and coarse quantization. Within the triangular-dithered quantization framework, we propose…
Linear and Quadratic Discriminant analysis (LDA/QDA) are common tools for classification problems. For these methods we assume observations are normally distributed within group. We estimate a mean and covariance matrix for each group and…
Electroencephalography (EEG)-based wearable brain-computer interfaces (BCIs) face challenges due to low signal-to-noise ratio (SNR) and non-stationary neural activity. We introduce in this manuscript a mathematically rigorous framework that…
Advances in the motor imagery (MI)-based brain-computer interfaces (BCIs) allow control of several applications by decoding neurophysiological phenomena, which are usually recorded by electroencephalography (EEG) using a non-invasive…