# Manifold-Aware Deep Clustering: Maximizing Angles between Embedding Vectors Based on Regular Simplex

arXiv: https://arxiv.org/abs/2106.02331 · HTML: https://mlsanity.com/paper/2106.02331/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 34 references that are in the map.
- First posted on arXiv 4 Jun 2021.

## Builds on (most cited first, 15 of 15)

- [SDR - half-baked or well done?](https://mlsanity.com/paper/1811.02508/) (2018)
- [Conv-TasNet: Surpassing Ideal Time-Frequency Magnitude Masking for Speech Separation](https://mlsanity.com/paper/1809.07454/) (2018)
- [Deep clustering: Discriminative embeddings for segmentation and separation](https://mlsanity.com/paper/1508.04306/) (2015)
- [Permutation Invariant Training of Deep Models for Speaker-Independent Multi-talker Speech Separation](https://mlsanity.com/paper/1607.00325/) (2016)
- [Dual-path RNN: efficient long sequence modeling for time-domain single-channel speech separation](https://mlsanity.com/paper/1910.06379/) (2019)
- [Multi-talker Speech Separation with Utterance-level Permutation Invariant Training of Deep Recurrent Neural Networks](https://mlsanity.com/paper/1703.06284/) (2017)
- [Wavesplit: End-to-End Speech Separation by Speaker Clustering](https://mlsanity.com/paper/2002.08933/) (2020)
- [Voice Separation with an Unknown Number of Multiple Speakers](https://mlsanity.com/paper/2003.01531/) (2020)
- [Single-Channel Multi-Speaker Separation using Deep Clustering](https://mlsanity.com/paper/1607.02173/) (2016)
- [Asteroid: the PyTorch-based audio source separation toolkit for researchers](https://mlsanity.com/paper/2005.04132/) (2020)
- [Deep attractor network for single-microphone speaker separation](https://mlsanity.com/paper/1611.08930/) (2016)
- [Simultaneous Separation and Transcription of Mixtures with Multiple Polyphonic and Percussive Instruments](https://mlsanity.com/paper/1910.12621/) (2019)
- [Speaker-independent Speech Separation with Deep Attractor Network](https://mlsanity.com/paper/1707.03634/) (2017)
- [Deep Clustering and Conventional Networks for Music Separation: Stronger Together](https://mlsanity.com/paper/1611.06265/) (2016)
- [Closing the Training/Inference Gap for Deep Attractor Networks](https://mlsanity.com/paper/1911.02091/) (2019)

## Abstract (arXiv)

This paper presents a new deep clustering (DC) method called manifold-aware DC (M-DC) that can enhance hyperspace utilization more effectively than the original DC. The original DC has a limitation in that a pair of two speakers has to be embedded having an orthogonal relationship due to its use of the one-hot vector-based loss function, while our method derives a unique loss function aimed at maximizing the target angle in the hyperspace based on the nature of a regular simplex. Our proposed loss imposes a higher penalty than the original DC when the speaker is assigned incorrectly. The change from DC to M-DC can be easily achieved by rewriting just one term in the loss function of DC, without any other modifications to the network architecture or model parameters. As such, our method has high practicability because it does not affect the original inference part. The experimental results show that the proposed method improves the performances of the original DC and its expansion method.