TY - JOUR

T1 - Leveraging tensor kernels to reduce objective function mismatch in deep clustering

AU - Trosten, Daniel J.

AU - Løkse, Sigurd

AU - Jenssen, Robert

AU - Kampffmeyer, Michael

N1 - Publisher Copyright: © 2023 The Authors

PY - 2024

Y1 - 2024

N2 - Objective Function Mismatch (OFM) occurs when the optimization of one objective has a negative impact on the optimization of another objective. In this work we study OFM in deep clustering, and find that the popular autoencoder-based approach to deep clustering can lead to both reduced clustering performance, and a significant amount of OFM between the reconstruction and clustering objectives. To reduce the mismatch, while maintaining the structure-preserving property of an auxiliary objective, we propose a set of new auxiliary objectives for deep clustering, referred to as the Unsupervised Companion Objectives (UCOs). The UCOs rely on a kernel function to formulate a clustering objective on intermediate representations in the network. Generally, intermediate representations can include other dimensions, for instance spatial or temporal, in addition to the feature dimension. We therefore argue that the naïve approach of vectorizing and applying a vector kernel is suboptimal for such representations, as it ignores the information contained in the other dimensions. To address this drawback, we equip the UCOs with structure-exploiting tensor kernels, designed for tensors of arbitrary rank. The UCOs can thus be adapted to a broad class of network architectures. We also propose a novel, regression-based measure of OFM, allowing us to accurately quantify the amount of OFM observed during training. Our experiments show that the OFM between the UCOs and the main clustering objective is lower, compared to a similar autoencoder-based model. Further, we illustrate that the UCOs improve the clustering performance of the model, in contrast to the autoencoder-based approach. The code for our experiments is available at https://github.com/danieltrosten/tk-uco.

AB - Objective Function Mismatch (OFM) occurs when the optimization of one objective has a negative impact on the optimization of another objective. In this work we study OFM in deep clustering, and find that the popular autoencoder-based approach to deep clustering can lead to both reduced clustering performance, and a significant amount of OFM between the reconstruction and clustering objectives. To reduce the mismatch, while maintaining the structure-preserving property of an auxiliary objective, we propose a set of new auxiliary objectives for deep clustering, referred to as the Unsupervised Companion Objectives (UCOs). The UCOs rely on a kernel function to formulate a clustering objective on intermediate representations in the network. Generally, intermediate representations can include other dimensions, for instance spatial or temporal, in addition to the feature dimension. We therefore argue that the naïve approach of vectorizing and applying a vector kernel is suboptimal for such representations, as it ignores the information contained in the other dimensions. To address this drawback, we equip the UCOs with structure-exploiting tensor kernels, designed for tensors of arbitrary rank. The UCOs can thus be adapted to a broad class of network architectures. We also propose a novel, regression-based measure of OFM, allowing us to accurately quantify the amount of OFM observed during training. Our experiments show that the OFM between the UCOs and the main clustering objective is lower, compared to a similar autoencoder-based model. Further, we illustrate that the UCOs improve the clustering performance of the model, in contrast to the autoencoder-based approach. The code for our experiments is available at https://github.com/danieltrosten/tk-uco.

KW - Deep clustering

KW - Objective function mismatch

KW - Tensor kernels

KW - Unsupervised companion objectives

U2 - 10.1016/j.patcog.2023.110229

DO - 10.1016/j.patcog.2023.110229

M3 - Journal article

AN - SCOPUS:85182404100

VL - 149

JO - Pattern Recognition

JF - Pattern Recognition

SN - 0031-3203

M1 - 110229

ER -