When visualizing a high-dimensional dataset, dimension reduction techniques are commonly employed which provide a single 2 dimensional view of the data. We describe ENS-t-SNE: an algorithm for Embedding Neighborhoods Simultaneously that generalizes the t-Stochastic Neighborhood Embedding approach. By using different viewpoints in ENS-t-SNE's 3D embedding, one can visualize different types of clusters within the same high-dimensional dataset. This enables the viewer to see and keep track of the different types of clusters, which is harder to do when providing multiple 2D embeddings, where corresponding points cannot be easily identified. We illustrate the utility of ENS-t-SNE with real-world applications and provide an extensive quantitative evaluation with datasets of different types and sizes.

Single-microphone, speaker-independent speech separation is normally performed through two steps: (i) separating the specific speech sources, and (ii) determining the best output-label assignment to find the separation error. The second step is the main obstacle in training neural networks for speech separation. Recently proposed Permutation Invariant Training (PIT) addresses this problem by determining the output-label assignment which minimizes the separation error. In this study, we show that a major drawback of this technique is the overconfident choice of the output-label assignment, especially in the initial steps of training when the network generates unreliable outputs. To solve this problem, we propose Probabilistic PIT (Prob-PIT) which considers the output-label permutation as a discrete latent random variable with a uniform prior distribution. Prob-PIT defines a log-likelihood function based on the prior distributions and the separation errors of all permutations; it trains the speech separation networks by maximizing the log-likelihood function. Prob-PIT can be easily implemented by replacing the minimum function of PIT with a soft-minimum function. We evaluate our approach for speech separation on both TIMIT and CHiME datasets. The results show that the proposed method significantly outperforms PIT in terms of Signal to Distortion Ratio and Signal to Interference Ratio.

When applying unsupervised learning techniques like ICA or temporal decorrelation, a key question is whether the discovered projections are reliable. In other words: can we give error bars or can we assess the quality of our separation? We use resampling methods to tackle these questions and show experimentally that our proposed variance estimations are strongly correlated to the separation error. We demonstrate that this reliability estimation can be used to choose the appropriate ICA-model, to enhance significantly the separation performance, and, most important, to mark the components that have a actual physical meaning.

When applying unsupervised learning techniques like ICA or temporal decorrelation, a key question is whether the discovered projections are reliable. In other words: can we give error bars or can we assess the quality of our separation? We use resampling methods to tackle these questions and show experimentally that our proposed variance estimations are strongly correlated to the separation error. We demonstrate that this reliability estimation can be used to choose the appropriate ICA-model, to enhance significantly the separation performance, and, most important, to mark the components that have a actual physical meaning.

When applying unsupervised learning techniques like ICA or temporal decorrelation,a key question is whether the discovered projections arereliable. In other words: can we give error bars or can we assess the quality of our separation? We use resampling methods totackle these questions and show experimentally that our proposed variance estimations are strongly correlated to the separation error.We demonstrate that this reliability estimation can be used to choose the appropriate ICA-model, to enhance significantly theseparation performance, and, most important, to mark the components that have a actual physical meaning.