Nonnegative matrix factorization (NMF) has become a ubiquitous tool for data analysis. An important variant is the sparse NMF problem which arises when we explicitly require the learnt features to be sparse. A natural measure of sparsity is the L @math norm, however its optimization is NP-hard. Mixed norms, such as L @math L @math measure, have been shown to model sparsity robustly, based on intuitive attributes that such measures need to satisfy. This is in contrast to computationally cheaper alternatives such as the plain L @math norm. However, present algorithms designed for optimizing the mixed norm L @math L @math are slow and other formulations for sparse NMF have been proposed such as those based on L @math and L @math norms. Our proposed algorithm allows us to solve the mixed norm sparsity constraints while not sacrificing computation time. We present experimental evidence on real-world datasets that shows our new algorithm performs an order of magnitude faster compared to the current state-of-the-art solvers optimizing the mixed norm and is suitable for large-scale datasets.
Other SNMF formulations have been considered by Hoyer2002 @cite_4 , Morupl0 @cite_5 , Kim2007 @cite_21 , Pascual06 @cite_6 (nsNMF) and Peharz2011 @cite_17 . SNMF formulations using similar sparsity measures as used in this paper have been considered for applications in speech and audio recordings @cite_15 @cite_22 .
@cite_4 @cite_22 @cite_21 @cite_6 @cite_5 @cite_15 @cite_17
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Several parametric representations of the acoustic signal were compared with regard to word recognition performance in a syllable-oriented continuous speech recognition system. The vocabulary included many phonetically similar monosyllabic words, therefore the emphasis was on the ability to retain phonetically significant acoustic information in the face of syntactic and duration variations. For each parameter set (based on a mel-frequency cepstrum, a linear frequency cepstrum, a linear prediction cepstrum, a linear prediction spectrum, or a set of reflection coefficients), word templates were generated using an efficient dynamic warping method, and test data were time registered with the templates. A set of ten mel-frequency cepstrum coefficients computed every 6.4 ms resulted in the best performance, namely 96.5 percent and 95.0 percent recognition with each of two speakers. The superior performance of the mel-frequency cepstrum coefficients may be attributed to the fact that they better represent the perceptually relevant aspects of the short-term speech spectrum. Acoustic models based on long short-term memory recurrent neural networks (LSTM-RNNs) were applied to statistical parametric speech synthesis (SPSS) and showed significant improvements in naturalness and latency over those based on hidden Markov models (HMMs). This paper describes further optimizations of LSTM-RNN-based SPSS for deployment on mobile devices; weight quantization, multi-frame inference, and robust inference using an -contaminated Gaussian loss function. Experimental results in subjective listening tests show that these optimizations can make LSTM-RNN-based SPSS comparable to HMM-based SPSS in runtime speed while maintaining naturalness. Evaluations between LSTM-RNN- based SPSS and HMM-driven unit selection speech synthesis are also presented. Several different parametric representations of speech derived from the linear prediction model are examined for their effectiveness for automatic recognition of speakers from their voices. Twelve predictor coefficients were determined approximately once every 50 msec from speech sampled at 10 kHz. The predictor coefficients and other speech parameters derived from them, such as the impulse response function, the autocorrelation function, the area function, and the cepstrum function were used as input to an automatic speaker‐recognition system. The speech data consisted of 60 utterances, consisting of six repetitions of the same sentence spoken by 10 speakers. The identification decision was based on the distance of the test sample vector from the reference vector for different speakers in the population; the speaker corresponding to the reference vector with the smallest distance was judged to be the unknown speaker. In verification, the speaker was verified if the distance between the test sample vector and the reference vector for the claimed speaker was less than a fixed threshold. Among all the parameters investigated, the cepstrum was found to be the most effective, providing an identification accuracy of 70 for speech 50 msec in duration, which increased to more than 98 for a duration of 0.5 sec. Using the same speech data, the verification accuracy was found to be approximately 83 for a duration of 50 msec, increasing to 98 for a duration of 1 sec. In a separate study to determine the feasibility of text‐independent speaker identification, an identification accuracy of 93 was achieved for speech 2 sec in duration even though the texts of the test and reference samples were different. Monaural source separation is important for many real world applications. It is challenging because, with only a single channel of information available, without any constraints, an infinite number of solutions are possible. In this paper, we explore joint optimization of masking functions and deep recurrent neural networks for monaural source separation tasks, including speech separation, singing voice separation, and speech denoising. The joint optimization of the deep recurrent neural networks with an extra masking layer enforces a reconstruction constraint. Moreover, we explore a discriminative criterion for training neural networks to further enhance the separation performance. We evaluate the proposed system on the TSP, MIR-1K, and TIMIT datasets for speech separation, singing voice separation, and speech denoising tasks, respectively. Our approaches achieve 2.30-4.98 dB SDR gain compared to NMF models in the speech separation task, 2.30-2.48 dB GNSDR gain and 4.32-5.42 dB GSIR gain compared to existing models in the singing voice separation task, and outperform NMF and DNN baselines in the speech denoising task.