Kernel alignment measures the degree of similarity between two kernels. In this paper, inspired from kernel alignment, we propose a new Linear Discriminant Analysis (LDA) formulation, kernel alignment LDA (kaLDA). We first define two kernels, data kernel and class indicator kernel. The problem is to find a subspace to maximize the alignment between subspace-transformed data kernel and class indicator kernel. Surprisingly, the kernel alignment induced kaLDA objective function is very similar to classical LDA and can be expressed using between-class and total scatter matrices. This can be extended to multi-label data. We use a Stiefel-manifold gradient descent algorithm to solve this problem. We perform experiments on 8 single-label and 6 multi-label data sets. Results show that kaLDA has very good performance on many single-label and multi-label problems.
The unsupervised task of aligning two or more distributions in a shared latent space has many applications including fair representations, batch effect mitigation, and unsupervised domain adaptation. Existing flow-based approaches estimate multiple flows independently, which is equivalent to learning multiple full generative models. Other approaches require adversarial learning, which can be computationally expensive and challenging to optimize. Thus, we aim to jointly align multiple distributions while avoiding adversarial learning. Inspired by efficient alignment algorithms from optimal tran…
Majority of the modern meta-learning methods for few-shot classification tasks operate in two phases: a meta-training phase where the meta-learner learns a generic representation by solving multiple few-shot tasks sampled from a large dataset and a testing phase, where the meta-learner leverages its learnt internal representation for a specific few-shot task involving classes which were not seen during the meta-training phase. To the best of our knowledge, all such meta-learning methods use a single base dataset for meta-training to sample tasks from and do not adapt the algorithm after meta-t…
Chongqing University（重庆大学）；School of Microelectronics and Communication Engineering（微电子与通信工程学院）
Unsupervised domain adaptation (UDA) aims to improve the classification performance on an unlabeled target domain by leveraging information from a fully labeled source domain. Recent approaches explore domain-invariant and class-discriminant representations to tackle this task. These methods, however, ignore the interaction between domain alignment learning and class discrimination learning. As a result, the missing or inadequate tradeoff between domain alignment and class discrimination are prone to the problem of negative transfer. In this paper, we propose Dynamic Weighted Learning (DWL) to…
Peking University（北京大学）；University of Oxford（牛津大学）；JD Explore Academy（京东探索研究院）；Wuhan University（武汉大学）；Peng Cheng Laboratory（鹏城实验室）
Few-shot class-incremental learning (FSCIL) has been a challenging problem as only a few training samples are accessible for each novel class in the new sessions. Finetuning the backbone or adjusting the classifier prototypes trained in the prior sessions would inevitably cause a misalignment between the feature and classifier of old classes, which explains the well-known catastrophic forgetting problem. In this paper, we deal with this misalignment dilemma in FSCIL inspired by the recently discovered phenomenon named neural collapse, which reveals that the last-layer features of the same clas…
Kernel Alignment for Unsupervised Transfer Learning
Laboratoire Hubert Curien, CNRS (UMR 5516) Universit\'e Jean Monnet F-42000, Saint-Etienne, France Email；Laboratoire d'Informatique de Paris-Nord, CNRS (UMR 7030) Universit\'e Paris 13, Sorbonne Paris Cit\'e F-93430, Villetaneuse, France Email
LIGM, Ecole des Ponts（巴黎桥路学院LIGM实验室）；Univ Gustave Eiffel（古斯塔夫·埃菲尔大学）；CNRS（法国国家科学研究中心）
Recent state-of-the-art methods for point cloud processing are based on the notion of point convolution, for which several approaches have been proposed. In this paper, inspired by discrete convolution in image processing, we provide a formulation to relate and analyze a number of point convolution methods. We also propose our own convolution variant, that separates the estimation of geometry-less kernel weights and their alignment to the spatial support of features. Additionally, we define a point sampling strategy for convolution that is both effective and fast. Finally, using our convolutio…
University of Washington（华盛顿大学）；Salesforce Research（赛富时研究院）
For protein sequence datasets, unlabeled data has greatly outpaced labeled data due to the high cost of wet-lab characterization. Recent deep-learning approaches to protein prediction have shown that pre-training on unlabeled data can yield useful representations for downstream tasks. However, the optimal pre-training strategy remains an open question. Instead of strictly borrowing from natural language processing (NLP) in the form of masked or autoregressive language modeling, we introduce a new pre-training task: directly predicting protein profiles derived from multiple sequence alignments.…
