In this letter, we propose a new approach to speech enhancement based on a complex Laplacian probability density function (pdf). With a use of a goodness-of-fit (GOF) test, we discover that the complex Laplacian pdf is more desirable to describe noisy speech distribution than the conventional Gaussian pdf for speech enhancement. The likelihood ratio (LR) is computed and then applied to computat...

This work presents a fusion of Log Gabor Wavelet (LGW) and Maximum a Posteriori (MAP) estimator as a speech enhancement tool for acoustical background noise reduction. The probability density function (pdf) of the speech spectral amplitude is approximated by a Generalized Laplacian Distribution (GLD). Compared to earlier estimators the proposed method estimates the underlying statistical model ...

The heat-kernel of a graph is computed by exponentiating the Laplacian eigen-system with time. In this paper, we study the heat kernel mapping of the nodes of a graph into a vector-space. Specifically, we investigate whether the resulting point distribution can be used for the purposes of graphclustering. Our characterisation is based on the covariance matrix of the point distribution. We explo...

In recommendation systems, probabilistic matrix factorization (PMF) is a state-of-the-art collaborative filtering method by determining the latent features to represent users and items. However, two major issues limiting the usefulness of PMF are the sparsity problem and long-tail distribution. Sparsity refers to the situation that the observed rating data are sparse, which results in that only...

Multi-scale manipulations are central to image editing but they are also prone to halos. Achieving artifact-free results requires sophisticated edge-aware techniques and careful parameter tuning. These shortcomings were recently addressed by the local Laplacian filters, which can achieve a broad range of effects using standard Laplacian pyramids. However, these filters are slow to evaluate and ...

Copyright q 2012 X. Pai and S. Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Let Φ G, λ det λIn − L G ∑n k 0 −1 ck G λn−k be the characteristic polynomial of the Laplacian matrix of a graph G of order n. In this paper, we g...

We study random graphs with possibly different edge probabilities in the challenging sparse regime of bounded expected degrees. Unlike in the dense case, neither the graph adjacency matrix nor its Laplacian concentrate around their expectations due to the highly irregular distribution of node degrees. It has been empirically observed that simply adding a constant of order 1/n to each entry of t...

We first analyze the limits of learning in high dimension. Hence, we stress the difference between high dimensional ambient space and intrinsic geometry associated to the marginal distribution. We observe that, in the semi-supervised setting, unlabeled data could be used to exploit low dimensionality of the intrinsic geometry. In order to formalize these intuitions we briefly introduce the mani...

for a simple digraph $g$ of order $n$ with vertex set${v_1,v_2,ldots, v_n}$, let $d_i^+$ and $d_i^-$ denote theout-degree and in-degree of a vertex $v_i$ in $g$, respectively. let$d^+(g)=diag(d_1^+,d_2^+,ldots,d_n^+)$ and$d^-(g)=diag(d_1^-,d_2^-,ldots,d_n^-)$. in this paper we introduce$widetilde{sl}(g)=widetilde{d}(g)-s(g)$ to be a new kind of skewlaplacian matrix of $g$, where $widetilde{d}(g...

Let G^s be a signed graph, where G = (V;E) is the underlying simple graph and s : E(G) to {+, -} is the sign function on E(G). In this paper, we obtain k-th signed spectral moment and k-th signed Laplacian spectral moment of Gs together with coefficients of their signed characteristic polynomial and signed Laplacian characteristic polynomial are calculated.