We address the problem of acoustic source separation in a deep learning framework we call "deep clustering". Rather than directly estimating signals or masking functions, we train a deep network to produce spectrogram embeddings that are discriminative for partition labels given in training data. Previous deep network approaches provide great advantages in terms of learning power and speed, but previously it has been unclear how to use them to separate signals in a classindependent way. In contrast, spectral clustering approaches are flexible with respect to the classes and number of items to be segmented, but it has been unclear how to leverage the learning power and speed of deep networks. To obtain the best of both worlds, we use an objective function that to train embeddings that yield a low-rank approximation to an ideal pairwise affinity matrix, in a classindependent way. This avoids the high cost of spectral factorization and instead produces compact clusters that are amenable to simple clustering methods. The segmentations are therefore implicitly encoded in the embeddings, and can be "decoded" by clustering. Preliminary experiments show that the proposed method can separate speech: when trained on spectrogram features containing mixtures of two speakers, and tested on mixtures of a held-out set of speakers, it can infer masking functions that improve signal quality by around 6dB. We show that the model can generalize to three-speaker mixtures despite training only on twospeaker mixtures. The framework can be used without class labels, and therefore has the potential to be trained on a diverse set of sound types, and to generalize to novel sources. We hope that future work will lead to segmentation of arbitrary sounds, with extensions to microphone array methods as well as image segmentation and other domains.

In speech enhancement and source separation, signal-to-noise ratio is a ubiquitous objective measure of denoising/separation quality. A decade ago, the BSS eval toolkit was developed to give researchers worldwide a way to evaluate the quality of their algorithms in a simple, fair, and hopefully insightful way: it attempted to account for channel variations, and to not only evaluate the total distortion in the estimated signal but also split it in terms of various factors such as remaining interference, newly added artifacts, and channel errors. In recent years, hundreds of papers have been relying on this toolkit to evaluate their proposed methods and compare them to previous works, often arguing that differences on the order of 0.1 dB proved the effectiveness of a method over others. We argue here that the signal-to-distortion ratio (SDR) implemented in the BSS eval toolkit has generally been improperly used and abused, especially in the case of single-channel separation, resulting in misleading results. We propose to use a slightly modified definition, resulting in a simpler, more robust measure, called scale-invariant SDR (SI-SDR). We present various examples of critical failure of the original SDR that SI-SDR overcomes.

The Kullback Leibler (KL) Divergence is a widely used tool in statistics and pattern recognition. The KL divergence between two Gaussian Mixture Models (GMMs) is frequently needed in the fields of speech and image recognition. Unfortunately the KL divergence between two GMMs is not analytically tractable, nor does any efficient computational algorithm exist. Some techniques cope with this problem by replacing the KL divergence with other functions that can be computed efficiently. We introduce two new methods, the variational approximation and the variational upper bound, and compare them to existing methods. We discuss seven different techniques in total and weigh the benefits of each one against the others. To conclude we evaluate the performance of each one through numerical experiments.Index Terms-Kullback Leibler divergence, variational methods, gaussian mixture models, unscented transformation.

Separation of speech embedded in non-stationary interference is a challenging problem that has recently seen dramatic improvements using deep network-based methods. Previous work has shown that estimating a masking function to be applied to the noisy spectrum is a viable approach that can be improved by using a signalapproximation based objective function. Better modeling of dynamics through deep recurrent networks has also been shown to improve performance. Here we pursue both of these directions. We develop a phase-sensitive objective function based on the signal-to-noise ratio (SNR) of the reconstructed signal, and show that in experiments it yields uniformly better results in terms of signal-to-distortion ratio (SDR). We also investigate improvements to the modeling of dynamics, using bidirectional recurrent networks, as well as by incorporating speech recognition outputs in the form of alignment vectors concatenated with the spectral input features. Both methods yield further improvements, pointing to tighter integration of recognition with separation as a promising future direction.

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