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Unsupervised approaches to learning in neural networks are of substantial interest for furthering artificial intelligence, both because they would enable the training of networks without the need for large numbers of expensive annotations,…

Manifold learning now plays a very important role in machine learning and many relevant applications. Although its superior performance in dealing with nonlinear data distribution, data sparsity is always a thorny knot. There are few…

The multiscale simulation of heterogeneous materials is a popular and important subject in solid mechanics and materials science due to the wide application of composite materials. However, the classical FE2 (finite element2) scheme can be…

Graph embedding has been widely applied in areas such as network analysis, social network mining, recommendation systems, and bioinformatics. However, current graph construction methods often require the prior definition of neighborhood…

In forecasting multiple time series, accounting for the individual features of each sequence can be challenging. To address this, modern deep learning methods for time series analysis combine a shared (global) model with local layers,…

The objective of this paper is to design an embedding method that maps local features describing an image (e.g. SIFT) to a higher dimensional representation useful for the image retrieval problem. First, motivated by the relationship…

When dealing with continuous numeric features, we usually adopt feature discretization. In this work, to find the best way to conduct feature discretization, we present some theoretical analysis, in which we focus on analyzing correctness…

$t$-SNE is an embedding method that the data science community has widely Two interesting characteristics of t-SNE are the structure preservation property and the answer to the crowding problem, where all neighbors in high dimensional space…

Majority of the current dimensionality reduction or retrieval techniques rely on embedding the learned feature representations onto a computable metric space. Once the learned features are mapped, a distance metric aids the bridging of gaps…

There has been an intense recent activity in embedding of very high dimensional and nonlinear data structures, much of it in the data science and machine learning literature. We survey this activity in four parts. In the first part we cover…

We present Regularized Linear Embedding (RLE), a novel method that projects a collection of linked documents (e.g. citation network) into a pretrained word embedding space. In addition to the textual content, we leverage a matrix of…

Manifold structure learning is often used to exploit geometric information among data in semi-supervised feature learning algorithms. In this paper, we find that local discriminative information is also of importance for semi-supervised…

In deep neural nets, lower level embedding layers account for a large portion of the total number of parameters. Tikhonov regularization, graph-based regularization, and hard parameter sharing are approaches that introduce explicit biases…

We present a method for balancing between the Local and Global Structures (LGS) in graph embedding, via a tunable parameter. Some embedding methods aim to capture global structures, while others attempt to preserve local neighborhoods. Few…

Automatic head frontal-view identification is challenging due to appearance variations caused by pose changes, especially without any training samples. In this paper, we present an unsupervised algorithm for identifying frontal view among…

Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…

Existing manifold learning methods are not appropriate for image retrieval task, because most of them are unable to process query image and they have much additional computational cost especially for large scale database. Therefore, we…

Embedding high-dimensional data onto a low-dimensional manifold is of both theoretical and practical value. In this paper, we propose to combine deep neural networks (DNN) with mathematics-guided embedding rules for high-dimensional data…

Existing network embedding approaches tackle the problem of learning low-dimensional node representations. However, networks can also be seen in the light of edges interlinking pairs of nodes. The broad goal of this paper is to introduce…

The proposed method extends upon the representational output of semantic instance segmentation by explicitly including both visible and occluded parts. A fully convolutional network is trained to produce consistent pixel-level embedding…