Learning Kernel for Conditional Moment-Matching Discrepancy-Based Image Classification

Abstract

Conditional Maximum Mean Discrepancy (CMMD) can capture the discrepancy between conditional distributions by drawing support from nonlinear kernel functions, thus it has been successfully used for pattern classification. However, CMMD does not work well on complex distributions, especially when the kernel function fails to correctly characterize the difference between intra-class similarity and inter-class similarity. In this paper, a new kernel learning method is proposed to improve the discrimination performance of CMMD. It can be operated with deep network features iteratively and thus denoted as KLN for abbreviation. The CMMD loss and an auto-encoder (AE) are used to learn an injective function. By considering the compound kernel, i.e., the injective function with a characteristic kernel, the effectiveness of CMMD for data category description is enhanced. KLN can simultaneously learn a more expressive kernel and label prediction distribution, thus, it can be used to improve the classification performance in both supervised and semi-supervised learning scenarios. In particular, the kernelbased similarities are iteratively learned on the deep network features, and the algorithm can be implemented in an endto-end manner. Extensive experiments are conducted on four benchmark datasets, including MNIST, SVHN, CIFAR-10 and CIFAR-100. The results indicate that KLN achieves state-of-theart classification performance.

Unsupervised Domain Adaptation via Discriminative Manifold Embedding and Alignment

“…The distribution alignment methods minimize the discrepancy of domains based on common statistics directly, e.g., the first-order statistic based on maximum mean discrepancies (MMD) (Sejdinovic et al 2013;Long et al 2015;Ren et al 2019) and the second-order statistic based on covariance matrices (Sun, Feng, and Saenko 2016;Chen et al 2019a). Inspired by the GANs (Goodfellow et al 2014), lots of adversarial approaches with different purposes are developed.…”

Cross-Site Severity Assessment of COVID-19 From CT Images via Domain Adaptation

“…Kernel-based pattern analysis has been validated in improving classification performance [48]. To make use of the kernel method for classification, one can directly map the input data onto a reproducing kernel Hilbert space (RKHS) and establish a classifier followed by a cross-entropy (CE) loss.…”

“…However, this manner relies on the selection of a suitable kernel function, which is expected to effectively capture the difference between intra-class similarity and inter-class one. To address this problem, Ren et al [48] propose a new kernel learning method for CMMD-based image classification. Motivated by its effectiveness in learning a representative kernel function through placing the CMMD loss in the representation learning phase, we design a CMMD loss in FLARE as follows.…”

“…Variables X b s and Ŷ b s are defined in a similar way on the dataset D b s . As [48], we apply the kernel functions on the latent features (Z a s and Z b s ) but the raw data (X a s and X b s ). The CMMD loss on the source domain is…”

“…The differences between our FLARE and some related works are as follows. 1) In [48], the CMMD loss is used on traditional classification tasks where training and testing data is subject to the same distribution, whereas we design a CMDD loss on the DA task. In addition, compared with [48], we consider both supervised and semi-supervised learning scenarios in a framework.…”