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Auto-Tuning Spectral Clustering for Speaker Diarization Using Normalized Maximum Eigengap

Tae Jin Park, Kyu J. Han, Manoj Kumar, Shrikanth Narayanan

arXiv:2003.02405v1eess.AScs.LG

TL;DR

Noisy affinity values and development-set tuning are challenges for spectral clustering in speaker diarization. This paper uses normalized maximum eigengap values to tune clustering parameters without development data, with performance reported as comparable to or better than tuned methods across evaluation settings.

Abstract

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In this study, we propose a new spectral clustering framework that can auto-tune the parameters of the clustering algorithm in the context of speaker diarization. The proposed framework uses normalized maximum eigengap (NME) values to estimate the number of clusters and the parameters for the threshold of the elements of each row in an affinity matrix during spectral clustering, without the use of parameter tuning on the development set. Even through this hands-off approach, we achieve a comparable or better performance across various evaluation sets than the results found using traditional clustering methods that apply careful parameter tuning and development data. A relative improvement of 17% in the speaker error rate on the well-known CALLHOME evaluation set shows the effectiveness of our proposed spectral clustering with auto-tuning.

I. INTRODUCTION

Speaker diarization groups speech segments by speaker, and spectral clustering is widely used for that task. The paper proposes an NME-based framework to tune clustering parameters without development data, against the background of the NJW algorithm.

I. INTRODUCTION

  • Speaker diarization systems segment speech, extract speaker embeddings, and cluster embeddings from the same speakers together.The task is to identify who spoke when and assign speaker identity labels in an audio stream.Source: §I · p. 1
  • Spectral clustering is widely used in speaker diarization, but noisy affinity-matrix entries can degrade clustering and parameter tuning on development data may hinder generalization to unseen conditions.Existing approaches use scaling or row-wise thresholding parameters that require development-set optimization.Source: §I · p. 1
  • The proposed framework uses normalized maximum eigengap (NME) values to estimate both the row-wise threshold p and the number of clusters k without development-set tuning.The paper hypothesizes that p/gp is a proxy for diarization error rate (DER) and uses the ratio to select p.Source: §I · p. 1

A. Ng-Jordan-Weiss (NJW) Algorithm

  • The NJW algorithm creates an affinity matrix, computes a Laplacian, and clusters a spectral embedding formed from its k largest eigenvectors using k-means.Its affinity matrix is based on pairwise speaker-embedding cosine similarity and uses a scaling factor.Source: A. Ng-Jordan-Weiss (NJW) Algorithm · pp. 1–2

B. Limitations of the Traditional Spectral Clustering

Traditional spectral clustering has limitations in speaker diarization because affinity values can be noisy and parameter choices may depend on development data. That dependence can make performance reliant on development-data selection and burden generalization to unseen conditions.

B. Limitations of the Traditional Spectral Clustering

  • Traditional spectral clustering has inherent limitations in speaker diarization.The section identifies sensitivity to affinity-matrix quality and adaptivity to data variability as concerns.Source: B. Limitations of the Traditional… · p. 2

1) Sensitivity to the Quality of an Affinity Matrix:

  • Noisy similarity values in the affinity matrix can degrade clustering when speaker embeddings do not represent speaker characteristics well.The values are estimated from distance measures such as cosine similarity.Source: 1) Sensitivity to the Quality of an… · p. 2

2) Adaptivity to the Variability in Data:

  • Scaling and thresholding parameters require development-data tuning, making clustering performance dependent on development-data selection and burdening generalization to unseen conditions.Prior work either retains each row's p-percentile entries or uses scaling factors to weight affinity-matrix elements.Source: 2) Adaptivity to the Variability in Data · p. 2

III. NORMALIZED MAXIMUM EIGENGAP ANALYSIS

The NME analysis is the basis of the proposed spectral-clustering procedure. Algorithm 1 takes an affinity matrix, produces a cluster vector, and computes a normalized maximum eigengap and a ratio for each p considered.

III. NORMALIZED MAXIMUM EIGENGAP ANALYSIS

  • Algorithm 1 takes an affinity matrix as input and returns a cluster vector.The procedure is presented as the NME-SC algorithm.Source: §III · p. 2
  • For each p, the algorithm applies SVD to Lp, computes the eigengap ep, and obtains gp as max(ep)/max(Σp).These operations are listed in the algorithm pseudocode.Source: §III · p. 2
  • For each p, the algorithm computes r[p] as p/gp.The listed computation follows the normalized maximum eigengap calculation.Source: §III · p. 2

1) Affinity Matrix:

The proposed affinity matrix uses raw cosine similarities, binarizes each row by its p largest values, and symmetrizes the result. The unnormalized matrix is then used for Laplacian computations.

1) Affinity Matrix:

  • The proposed affinity matrix uses raw cosine similarity values between speech segments, without a kernel or scaling parameter.The text specifies N^2 similarity values for N speech segments.Source: 1) Affinity Matrix · p. 2
  • p-neighbor binarization sets each row's p largest similarity values to 1 and the remaining values to 0 to mitigate unreliable similarities.The integer p is determined by the NME analysis.Source: 2) p-Neighbor Binarization · p. 2

3) Symmetrization:

5) Singular Value Decomposition (SVD):

The method computes eigenvalue gaps for each binarization threshold, uses normalized maximum eigengap values to select a threshold, and then estimates the number of clusters.

5) Singular Value Decomposition (SVD):

6) Eigengap Vector:

  • The eigengap vector e_p contains differences between consecutive eigenvalues sorted in ascending order for the selected p.Source: 6) Eigengap Vector · p. 3

7) Normalized Maximum Eigengap (NME):

10) k-means Clustering:

The section describes k-means clustering and examines how eigengap purity and the pruning threshold relate to cluster quality and diarization error rate.

10) k-means Clustering:

  • The smallest k eigenvalues and corresponding eigenvectors form k-dimensional spectral embeddings, which k-means groups into k clusters.Source: 10) k-means Clustering · p. 3

IV. VALIDATION OF NME ANALYSIS

  • The pruning analysis examines the relationship between the NME value g_p and parameter p because graph pruning depends strongly on p.Source: §IV · p. 3

A. Eigengap and the Purity of Clusters

  • Excessive affinity-matrix connections can raise g_p while reducing the estimated cluster count, so a high eigengap alone may coincide with poor diarization.The described example shows this reversal after p=50.Source: B. p Versus gp · p. 3
  • The ratio r(p)=p/g_p is presented as a proxy for diarization error rate, balancing a smaller pruning threshold against higher cluster purity.The section relates the ratio trend to the DER plot in Fig. 1.Source: C. r(p) = p/gp as a Good Proxy for DER · p. 3, Figure 1 · p. 3

V. EXPERIMENTAL RESULTS

The test setup holds the speaker embedding extractor constant and compares three clustering baselines described here; the supplied passages do not report their performance values.

A. Test Setup

  • All experiments use the same speaker embedding extractor, follow the evaluation method and metrics in, and limit estimated speakers to at most eight.Table I and Table II are identified as results with oracle and system SAD, respectively.Source: A. Test Setup · p. 3, Table I · p. 4, Table II · p. 4

1) COS+NJW-SC:

  • COS+NJW-SC uses cosine similarity with the NJW algorithm, and estimates cluster count using the method in.Source: 1) COS+NJW-SC · p. 4

2) COS+AHC:

  • COS+AHC follows the setup in, but uses cosine similarity instead of PLDA.Source: 2) COS+AHC · p. 4

3) PLDA+AHC:

  • PLDA+AHC couples AHC with PLDA, adapting the PLDA model on each development set.Source: 3) PLDA+AHC · p. 4

4) COS+B-SC:

The section contrasts a development-set-tuned binarization method with NME-based auto-tuning and describes the evaluation datasets and their speaker-count conditions.

4) COS+B-SC:

  • COS+B-SC uses the proposed p-neighbor binarization scheme but optimizes p on each development set instead of using the NME-selected threshold.Source: 4) COS+B-SC · p. 4

5) COS+NME-SC:

  • COS+NME-SC applies the proposed auto-tuning without hyperparameter optimization, searching p from 1 to floor(N/4) for each input utterance.N is the total number of segments in the utterance.Source: 5) COS+NME-SC · p. 4

1) NIST SRE 2000 (LDC2001S97):

2) CALLHOME American English Speech (CHAES) (LDC97S42):

  • CHAES contains English utterances with two to four speakers; CH109 provides the speaker count to systems, while its remaining utterances serve as development data.CHAES train and development sets are used for parameter tuning, and results are reported on its evaluation set.Source: 2) CALLHOME American English Speech… · p. 4

3) RT03 (LDC2007S10):

  • RT03 contains English utterances with two to four speakers, and this evaluation uses only Switchboard utterances from the split in.Source: 3) RT03 (LDC2007S10) · p. 4

C. Experiments

NME-SC is competitive without parameter tuning under oracle and system SAD, outperforming other methods in the system-SAD setting except on RT03. The discussion attributes gains to p-neighbor binarization and auto-tuning, while the conclusion identifies theoretical analysis and broader generalization as future work.

1) Oracle SAD:

  • With oracle SAD, NME-SC is very competitive without parameter tuning, except on RT03; the authors especially highlight CALLHOME, where utterances vary in speaker count.The authors describe the auto-tuning approach as advantageous on CALLHOME.Source: 1) Oracle SAD · p. 4

2) System SAD:

  • With system SAD, NME-SC outperforms all other methods except on RT03, where it is very close to dev-set-optimized COS+B-SC.System SAD uses the publicly available ASpIRE model and is described as closer to real-world scenarios.Source: 2) System SAD · p. 4

D. Discussions

  • The reported gains from NJW-SC to B-SC and from B-SC to NME-SC support the effectiveness of p-neighbor binarization and development-free tuning, respectively.The authors also report improvement over PLDA+AHC, suggesting competitive diarization without PLDA as a distance measure.Source: D. Discussions · p. 4

VI. CONCLUSIONS

  • The conclusion presents NME-based spectral clustering as competitive without hyper-parameter tuning and promising against PLDA-based AHC.Further work is proposed to analyze theoretically why p/gp proxies for DER and how the approach generalizes to varied data in real production systems.Source: §VI · p. 4
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