Equal Graph Partitioning on Estimated Infection Network as an Effective Epidemic Mitigation Measure

Controlling severe outbreaks remains the most important problem in infectious disease area. With time, this problem will only become more severe as population density in urban centers grows. Social interactions play a very important role in determining how infectious diseases spread, and organization of people along social lines gives rise to non-spatial networks in which the infections spread. Infection networks are different for diseases with different transmission modes, but are likely to be identical or highly similar for diseases that spread the same way. Hence, infection networks estimated from common infections can be useful to contain epidemics of a more severe disease with the same transmission mode. Here we present a proof-of-concept study demonstrating the effectiveness of epidemic mitigation based on such estimated infection networks. We first generate artificial social networks of different sizes and average degrees, but with roughly the same clustering characteristic. We then start SIR epidemics on these networks, censor the simulated incidences, and use them to reconstruct the infection network. We then efficiently fragment the estimated network by removing the smallest number of nodes identified by a graph partitioning algorithm. Finally, we demonstrate the effectiveness of this targeted strategy, by comparing it against traditional untargeted strategies, in slowing down and reducing the size of advancing epidemics

Incorporating Prior Information in Nonnegative Matrix Factorization for Audio Source Separation

In this work, we propose solutions to the problem of audio source separation from a single recording. The audio source signals can be speech, music or any other audio signals. We assume training data for the individual source signals that are present in the mixed signal are available. The training data are used to build a representative model for each source. In most cases, these models are sets of basis vectors in magnitude or power spectral domain. The proposed algorithms basically depend on decomposing the spectrogram of the mixed signal with the trained basis models for all observed sources in the mixed signal. Nonnegative matrix factorization (NMF) is used to train the basis models for the source signals. NMF is then used to decompose the mixed signal spectrogram as a weighted linear combination of the trained basis vectors for each observed source in the mixed signal. After decomposing the mixed signal, spectral masks are built and used to reconstruct the source signals. In this thesis, we improve the performance of NMF for source separation by incorporating more constraints and prior information related to the source signals to the NMF decomposition results. The NMF decomposition weights are encouraged to satisfy some prior information that is related to the nature of the source signals. The priors are modeled using Gaussian mixture models or hidden Markov models. These priors basically represent valid weight combination sequences that the basis vectors can receive for a certain type of source signal. The prior models are incorporated with the NMF cost function using either log-likelihood or minimum mean squared error estimation (MMSE). We also incorporate the prior information as a post processing. We incorporate the smoothness prior on the NMF solutions by using post smoothing processing. We also introduce post enhancement using MMSE estimation to obtain better separation for the source signals. In this thesis, we also improve the NMF training for the basis models. In cases when enough training data are not available, we introduce two different adaptation methods for the trained basis to better fit the sources in the mixed signal. We also improve the training procedures for the sources by learning more discriminative dictionaries for the source signals. In addition, to consider a larger context in the models, we concatenate neighboring spectra together and train basis sets from them instead of a single frame which makes it possible to directly model the relation between consequent spectral frames. Experimental results show that the proposed approaches improve the performance of using NMF in source separation application

Source separation using regularized NMF with MMSE estimates under GMM priors with online learning for the uncertainties

We propose a new method to incorporate priors on the solution of nonnegative matrix factorization (NMF). The NMF solution is guided to follow the minimum mean square error (MMSE) estimates of the weight combinations under a Gaussian mixture model (GMM) prior. The proposed algorithm can be used for denoising or single-channel source separation (SCSS) applications. NMF is used in SCSS in two main stages, the training stage and the separation stage. In the training stage, NMF is used to decompose the training data spectrogram for each source into a multiplication of a trained basis and gains matrices. In the separation stage, the mixed signal spectrogram is decomposed as a weighted linear combination of the trained basis matrices for the source signals. In this work, to improve the separation performance of NMF, the trained gains matrices are used to guide the solution of the NMF weights during the separation stage. The trained gains matrix is used to train a prior GMM that captures the statistics of the valid weight combinations that the columns of the basis matrix can receive for a given source signal. In the separation stage, the prior GMMs are used to guide the NMF solution of the gains/weights matrices using MMSE estimation. The NMF decomposition weights matrix is treated as a distorted image by a distortion operator, which is learned directly from the observed signals. The MMSE estimate of the weights matrix under the trained GMM prior and log-normal distribution for the distortion is then found to improve the NMF decomposition results. The MMSE estimate is embedded within the optimization objective to form a novel regularized NMF cost function. The corresponding update rules for the new objectives are derived in this paper. The proposed MMSE estimates based regularization avoids the problem of computing the hyper-parameters and the regularization parameters. MMSE also provides a better estimate for the valid gains matrix. Experimental results show that the proposed regularized NMF algorithm improves the source separation performance compared with using NMF without a prior or with other prior models. © 2014 Elsevier Inc

Regularized nonnegative matrix factorization using Gaussian mixture priors for supervised single channel source separation

© 2012 Elsevier Ltd.We introduce a new regularized nonnegative matrix factorization (NMF) method for supervised single-channel source separation (SCSS). We propose a new multi-objective cost function which includes the conventional divergence term for the NMF together with a prior likelihood term. The first term measures the divergence between the observed data and the multiplication of basis and gains matrices. The novel second term encourages the log-normalized gain vectors of the NMF solution to increase their likelihood under a prior Gaussian mixture model (GMM) which is used to encourage the gains to follow certain patterns. In this model, the parameters to be estimated are the basis vectors, the gain vectors and the parameters of the GMM prior. We introduce two different ways to train the model parameters, sequential training and joint training. In sequential training, after finding the basis and gains matrices, the gains matrix is then used to train the prior GMM in a separate step. In joint training, within each NMF iteration the basis matrix, the gains matrix and the prior GMM parameters are updated jointly using the proposed regularized NMF. The normalization of the gains makes the prior models energy independent, which is an advantage as compared to earlier proposals. In addition, GMM is a much richer prior than the previously considered alternatives such as conjugate priors which may not represent the distribution of the gains in the best possible way. In the separation stage after observing the mixed signal, we use the proposed regularized cost function with a combined basis and the GMM priors for all sources that were learned from training data for each source. Only the gain vectors are estimated from the mixed data by minimizing the joint cost function. We introduce novel update rules that solve the optimization problem efficiently for the new regularized NMF problem. This optimization is challenging due to using energy normalization and GMM for prior modeling, which makes the problem highly nonlinear and non-convex. The experimental results show that the introduced methods improve the performance of single channel source separation for speech separation and speech-music separation with different NMF divergence functions. The experimental results also show that, using the GMM prior gives better separation results than using the conjugate prior

Single channel speech music separation using nonnegative matrix factorization and spectral masks

A single channel speech-music separation algorithm based on nonnegative matrix factorization (NMF) with spectral masks is proposed in this work. The proposed algorithm uses training data of speech and music signals with nonnegative matrix factorization followed by masking to separate the mixed signal. In the training stage, NMF uses the training data to train a set of basis vectors for each source. These bases are trained using NMF in the magnitude spectrum domain. After observing the mixed signal, NMF is used to decompose its magnitude spectra into a linear combination of the trained bases for both sources. The decomposition results are used to build a mask, which explains the contribution of each source in the mixed signal. Experimental results show that using masks after NMF improves the separation process even when calculating NMF with fewer iterations, which yields a faster separation process. © 2011 IEEE

Hidden Mmarkov models as priors for regularized nonnegative matrix factorization in single-channel source separation

We propose a new method to incorporate rich statistical priors, modeling temporal gain sequences in the solutions of nonnegative matrix factorization (NMF). The proposed method can be used for single-channel source separation (SCSS) applications. In NMF based SCSS, NMF is used to decompose the spectra of the observed mixed signal as a weighted linear combination of a set of trained basis vectors. In this work, the NMF decomposition weights are enforced to consider statistical and temporal prior information on the weight combination patterns that the trained basis vectors can jointly receive for each source in the observed mixed signal. The Hidden Markov Model (HMM) is used as a log-normalized gains (weights) prior model for the NMF solution. The normalization makes the prior models energy independent. HMM is used as a rich model that characterizes the statistics of sequential data. The NMF solutions for the weights are encouraged to increase the log-likelihood with the trained gain prior HMMs while reducing the NMF reconstruction error at the same time

Semi-blind speech-music separation using sparsity and continuity priors

In this paper we propose an approach for the problem of single channel source separation of speech and music signals. Our approach is based on representing each source's power spectral density using dictionaries and nonlinearly projecting the mixture signal spectrum onto the combined span of the dictionary entries. We encourage sparsity and continuity of the dictionary coefficients using penalty terms (or log-priors) in an optimization framework. We propose to use a novel coordinate descent technique for ..

Initialization of nonnegative matrix factorization dictionaries for single channel source separation

In this work, we study different initialization methods for the nonnegative matrix factorization (NMF) dictionaries or bases. There is a need for good initializations for NMF dictionary because NMF decomposition is a non-convex problem which has many local minima. The effect of the initialization of NMF is evaluated in this work on audio source separation applications. In supervised audio source separation, NMF is used to train a set of basis vectors (basis matrix) for each source in an iterative fashion. Then NMF is used to decompose the mixed signal spectrogram as a weighted linear combination of the trained basis vectors for all sources in the mixed signal. The estimate for each source is computed by summing the decomposition terms that include its corresponding trained bases. In this work, we use principal component analysis (PCA), spherical K-means, and fuzzy C-means (FCM) to initialize the NMF basis matrices during the training procedures. Experimental results show that, better initialization for NMF bases gives better audio separation performance than using NMF with random initialization. © 2013 IEEE

Single channel speech music separation using nonnegative matrix factorization with sliding windows and spectral masks

A single channel speech-music separation algorithm based on nonnegative matrix factorization (NMF) with sliding windows and spectral masks is proposed in this work. We train a set of basis vectors for each source signal using NMF in the magnitude spectral domain. Rather than forming the columns of the matrices to be decomposed by NMF of a single spectral frame, we build them with multiple spectral frames stacked in one column. After observing the mixed signal, NMF is used to decompose its magnitude spectra into a weighted linear combination of the trained basis vectors for both sources. An initial spectrogram estimate for each source is found, and a spectral mask is built using these initial estimates. This mask is used to weight the mixed signal spectrogram to find the contributions of each source signal in the mixed signal. The method is shown to perform better than the conventional NMF approach. Copyright © 2011 ISCA

Single channel speech-music separation using matching pursuit and spectral masks

A single-channel speech music separation algorithm based on matching pursuit (MP) with multiple dictionaries and spectral masks is proposed in this work. A training data for speech and music signals is used to build two sets of magnitude spectral vectors of each source signal. These vectors' sets are called dictionaries, and the vectors are called atoms. Matching pursuit is used to sparsely decompose the magnitude spectrum of the observed mixed signal as a nonnegative weighted linear combination of the best atoms in the two dictionaries that match the mixed signal structure. The weighted sum of the resulting decomposition terms that include atoms from the speech dictionary is used as an initial estimate of the speech signal contribution in the mixed signal, and the weighted sum of the remaining terms for the music signal contribution. The initial estimate of each source is used to build a spectral mask that is used to reconstruct the source signals. Experimental results show that integrating MP with spectral mask gives good separation results. © 2011 IEEE