In this paper, we take a topological view of unsupervised learning. From this point of view, clustering may be interpreted as trying to find the number of connected components of an underlying geometrically structured probability distribution in a certain sense that we will make precise. We construct a geometrically structured probability distribution that seems appropriate for modeling data in...

‎Let $G$ be a graph without an isolated vertex‎, ‎the normalized Laplacian matrix $tilde{mathcal{L}}(G)$‎ ‎is defined as $tilde{mathcal{L}}(G)=mathcal{D}^{-frac{1}{2}}mathcal{L}(G)mathcal{D}^{-frac{1}{2}}$‎, where ‎$mathcal{D}$ ‎is a‎ diagonal matrix whose entries are degree of ‎vertices ‎‎of ‎$‎G‎$‎‎. ‎The eigenvalues of‎ $tilde{mathcal{L}}(G)$ are ‎called as ‎the ‎normalized Laplacian eigenva...

liquid-liquid equilibria for the (water + lactic acid + benzyl alcohol or p-xylene) ternary systems were investigated at atmospheric pressure and in the temperature range from 298.15-318.15 k. the studied systems exhibit two types of liquid-liquid equilibrium (lle) behavior. the system consisting of benzyl alcohol displays type-1 lle behavior, while a type-2 behavior is exhibited by the other s...

The research on robust principal component analysis (RPCA) has been attracting much attention recently. The original RPCA model assumes sparse noise, and use the L1-norm to characterize the error term. In practice, however, the noise is much more complex and it is not appropriate to simply use a certain Lp-norm for noise modeling. We propose a generative RPCA model under the Bayesian framework ...

The stochastic blockmodel (SBM) models the connectivity within and between disjoint subsets of nodes in networks. Prior work demonstrated that rows an SBM’s adjacency spectral embedding (ASE) Laplacian (LSE) both converge law to Gaussian mixtures where components are curved exponential families. Maximum likelihood estimation via Expectation-Maximization (EM) algorithm for a full mixture model (...

This paper investigates the problem of verifying the pronunciations of phonemes from continuous utterances collected from impaired children speakers engaged in a speech therapy session. A new pronunciation verification (PV) approach based on the subspace Gaussian mixture model (SGMM) is presented. A single SGMM is trained from test utterances collected from impaired and unimpaired speakers. PV ...

‎let $g$ be a graph without an isolated vertex‎, ‎the normalized laplacian matrix $tilde{mathcal{l}}(g)$‎‎is defined as $tilde{mathcal{l}}(g)=mathcal{d}^{-frac{1}{2}}mathcal{l}(g) mathcal{d}^{-frac{1}{2}}$‎, where ‎$‎mathcal{‎d}‎$ ‎is a‎ diagonal matrix whose entries are degree of ‎vertices ‎‎of ‎$‎g‎$‎‎. ‎the eigenvalues of‎‎$tilde{mathcal{l}}(g)$ are ‎called ‎ ‎ as ‎the ‎normalized laplacian ...

A mathematical model has been introduced for the transmission dynamics of cholera disease by GQ Sun et al. recently. In this study, we add Laplacian and Triangular random effects to this model and analyze the variation of results for both cases. The expectations  and coefficients of variation are compared for the random models and the results are used to comment on the differences and similarit...

The Laplacian Distribution has been widely used to characterize the distribution of DCT coefficients in a great deal of research on statistical attributes of DCT for the reason that Laplacian distribution can achieve a good balance between the simplification of the model and fidelity to the real empirical data. But in our research, we found that there is a large discrepancy between the real dat...

in this paper, a new method is presented for the detection of defects in random textures. in the training stage, the feature vectors of the normal textures’ images are extracted by using the optimal response of gabor wavelet filters, and their probability density is estimated by means of the gaussian mixture model (gmm). in the testing stage, similar to the previous stage,at  first, the feature...