Related papers: Constant rank factorizations of smooth maps
In a previous paper [1] it was discussed the viability of functional analysis using as a basis a couple of generic functions, and hence vectorial decomposition. Here we complete the paradigm exploiting one of the analysis methodologies…
We generalize Newton-type methods for minimizing smooth functions to handle a sum of two convex functions: a smooth function and a nonsmooth function with a simple proximal mapping. We show that the resulting proximal Newton-type methods…
We propose a completely unsupervised method to understand audio scenes observed with random microphone arrangements by decomposing the scene into its constituent sources and their relative presence in each microphone. To this end, we…
Source-tract decomposition (or glottal flow estimation) is one of the basic problems of speech processing. For this, several techniques have been proposed in the literature. However studies comparing different approaches are almost…
In this work we study orbit recovery over $SO(3)$, where the goal is to recover a function on the sphere from noisy, randomly rotated copies of it. We assume that the function is a linear combination of low-degree spherical harmonics. This…
A tensor network is a type of decomposition used to express and approximate large arrays of data. A given data-set, quantum state or higher dimensional multi-linear map is factored and approximated by a composition of smaller multi-linear…
The last decade has seen a revolution in the theory and application of machine learning and pattern recognition. Through these advancements, variable ranking has emerged as an active and growing research area and it is now beginning to be…
Localization and mapping with heterogeneous multi-sensor fusion have been prevalent in recent years. To adequately fuse multi-modal sensor measurements received at different time instants and different frequencies, we estimate the…
Practical tensor data is often along with time information. Most existing temporal decomposition approaches estimate a set of fixed factors for the objects in each tensor mode, and hence cannot capture the temporal evolution of the objects'…
The singular value decomposition (SVD) is not only a classical theory in matrix computation and analysis, but also is a powerful tool in machine learning and modern data analysis. In this tutorial we first study the basic notion of SVD and…
In this paper, we consider a regularization strategy for the factorization method when there is noise added to the data operator. The factorization method is a qualitative method used in shape reconstruction problems. These methods are…
In this article, we describe a new method of extracting information from signals, called functional dissipation, that proves to be very effective for enhancing classification of high resolution, texture-rich data. Our algorithm bypasses to…
Disentangling and recovering physical attributes, such as shape and material, from a few waveform examples is a challenging inverse problem in audio signal processing, with numerous applications in musical acoustics as well as structural…
Physical systems and signals are often characterized by complex functions of frequency in the harmonic-domain. The extension of such functions to the complex frequency plane has been a topic of growing interest as it was shown that specific…
Embedding acoustic information into fixed length representations is of interest for a whole range of applications in speech and audio technology. Two novel unsupervised approaches to generate acoustic embeddings by modelling of acoustic…
The problem of decomposing a given covariance matrix as the sum of a positive semi-definite matrix of given rank and a positive semi-definite diagonal matrix, is considered. We present a projection-type algorithm to address this problem.…
Tensor rank and low-rank tensor decompositions have many applications in learning and complexity theory. Most known algorithms use unfoldings of tensors and can only handle rank up to $n^{\lfloor p/2 \rfloor}$ for a $p$-th order tensor in…
Sorting algorithms are fundamental to computer science, and their correctness criteria are well understood as rearranging elements of a list according to a specified total order on the underlying set of elements. As mathematical functions,…
While convolutional neural networks (CNNs) have become the de facto standard for most image processing and computer vision applications, their deployment on edge devices remains challenging. Tensor decomposition methods provide a means of…
Manipulation tasks often require robots to be continuously in contact with an object. Therefore tactile perception systems need to handle continuous contact data. Shear deformation causes the tactile sensor to output path-dependent readings…