Related papers: Manifold Partition Discriminant Analysis
When modeling multivariate data, one might have an extra parameter of contextual information that could be used to treat some observations as more similar to others. For example, images of faces can vary by age, and one would expect the…
Recent attention has been devoted to the pursuit of learning semantic segmentation models exclusively from image tags, a paradigm known as image-level Weakly Supervised Semantic Segmentation (WSSS). Existing attempts adopt the Class…
We study the problem of supervised linear dimensionality reduction, taking an information-theoretic viewpoint. The linear projection matrix is designed by maximizing the mutual information between the projected signal and the class label…
In this paper, we explore the task of mapping spoken language utterances to one of thousands of natural language understanding domains in intelligent personal digital assistants (IPDAs). This scenario is observed for many mainstream IPDAs…
We introduce a new method of performing high dimensional discriminant analysis, which we call multiDA. We achieve this by constructing a hybrid model that seamlessly integrates a multiclass diagonal discriminant analysis model and feature…
Network embedding is an effective technique to learn the low-dimensional representations of nodes in networks. Real-world networks are usually with multiplex or having multi-view representations from different relations. Recently, there has…
While the existence of low-dimensional embedding manifolds has been shown in patterns of collective motion, the current battery of nonlinear dimensionality reduction methods are not amenable to the analysis of such manifolds. This is mainly…
We consider the problem of simultaneously clustering and learning a linear representation of data lying close to a union of low-dimensional manifolds, a fundamental task in machine learning and computer vision. When the manifolds are…
Understanding low-dimensional structures within high-dimensional data is crucial for visualization, interpretation, and denoising in complex datasets. Despite the advancements in manifold learning techniques, key challenges-such as limited…
Linear discriminant analysis (LDA) is a popular technique to learn the most discriminative features for multi-class classification. A vast majority of existing LDA algorithms are prone to be dominated by the class with very large deviation…
As one of the most popular linear subspace learning methods, the Linear Discriminant Analysis (LDA) method has been widely studied in machine learning community and applied to many scientific applications. Traditional LDA minimizes the…
Monocular depth estimation (MDE) has attracted intense study due to its low cost and critical functions for robotic tasks such as localization, mapping and obstacle detection. Supervised approaches have led to great success with the advance…
Unsupervised dimensionality reduction is one of the commonly used techniques in the field of high dimensional data recognition problems. The deep autoencoder network which constrains the weights to be non-negative, can learn a low…
Based on an idea in [4] we propose a new iterative multiplicative filtering algorithm for label assignment matrices which can be used for the supervised partitioning of data. Starting with a row-normalized matrix containing the averaged…
Topological Data Analysis (TDA) is a novel statistical technique, particularly powerful for the analysis of large and high dimensional data sets. Much of TDA is based on the tool of persistent homology, represented visually via persistence…
Manifold learning (ML) aims to seek low-dimensional embedding from high-dimensional data. The problem is challenging on real-world datasets, especially with under-sampling data, and we find that previous methods perform poorly in this case.…
Despite the popularity of the manifold hypothesis, current manifold-learning methods do not support machine learning directly on the latent $d$-dimensional data manifold, as they primarily aim to perform dimensionality reduction into…
Transfer learning under domain shift remains a fundamental challenge due to the divergence between source and target data manifolds. In this paper, we propose MAADA (Manifold-Aware Adversarial Data Augmentation), a novel framework that…
Principal component analysis (PCA), along with its extensions to manifolds and outlier contaminated data, have been indispensable in computer vision and machine learning. In this work, we present a unifying formalism for PCA and its…
We propose an unsupervised technique for implicit parameterization of data manifolds. In our approach, the data is assumed to belong to a lower dimensional manifold in a higher dimensional space, and the data points are viewed as the…