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Register a new userQuadric hypersurface intersection for manifold learning in feature space
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The knowledge that data lies close to a particular submanifold of the ambient Euclidean space may be useful in a number of ways. For instance, one may want to automatically mark any point far away from the submanifold as an outlier, or to use its geodesic distance to measure similarity between points. Classical problems for manifold learning are often posed in a very high dimension, e.g. for spaces of images or spaces of representations of words. Today, with deep representation learning on the rise in areas such as computer vision and natural language processing, many problems of this kind may be transformed into problems of moderately high dimension, typically of the order of hundreds. Motivated by this, we propose a manifold learning technique suitable for moderately high dimension and large datasets. The manifold is learned from the training data in the form of an intersection of quadric hypersurfaces -- simple but expressive objects. At test time, this manifold can be used to introduce an outlier score for arbitrary new points and to improve a given similarity metric by incorporating learned geometric structure into it.
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Recently proposed adversarial training methods show the robustness to both adversarial and original examples and achieve state-of-the-art results in supervised and semi-supervised learning. All the existing adversarial training methods consider only how the worst perturbed examples (i.e., adversarial examples) could affect the model output. Despite their success, we argue that such setting may be in lack of generalization, since the output space (or label space) is apparently less informative.In this paper, we propose a novel method, called Manifold Adversarial Training (MAT). MAT manages to build an adversarial framework based on how the worst perturbation could affect the distributional manifold rather than the output space. Particularly, a latent data space with the Gaussian Mixture Model (GMM) will be first derived.On one hand, MAT tries to perturb the input samples in the way that would rough the distributional manifold the worst. On the other hand, the deep learning model is trained trying to promote in the latent space the manifold smoothness, measured by the variation of Gaussian mixtures (given the local perturbation around the data point). Importantly, since the latent space is more informative than the output space, the proposed MAT can learn better a robust and compact data representation, leading to further performance improvement. The proposed MAT is important in that it can be considered as a superset of one recently-proposed discriminative feature learning approach called center loss. We conducted a series of experiments in both supervised and semi-supervised learning on three benchmark data sets, showing that the proposed MAT can achieve remarkable performance, much better than those of the state-of-the-art adversarial approaches. We also present a series of visualization which could generate further understanding or explanation on adversarial examples.
Manifold learning methods play a prominent role in nonlinear dimensionality reduction and other tasks involving high-dimensional data sets with low intrinsic dimensionality. Many of these methods are graph-based: they associate a vertex with each data point and a weighted edge with each pair. Existing theory shows that the Laplacian matrix of the graph converges to the Laplace-Beltrami operator of the data manifold, under the assumption that the pairwise affinities are based on the Euclidean norm. In this paper, we determine the limiting differential operator for graph Laplacians constructed using $textit{any}$ norm. Our proof involves an interplay between the second fundamental form of the manifold and the convex geometry of the given norms unit ball. To demonstrate the potential benefits of non-Euclidean norms in manifold learning, we consider the task of mapping the motion of large molecules with continuous variability. In a numerical simulation we show that a modified Laplacian eigenmaps algorithm, based on the Earthmovers distance, outperforms the classic Euclidean Laplacian eigenmaps, both in terms of computational cost and the sample size needed to recover the intrinsic geometry.
Messenger advertisements (ads) give direct and personal user experience yielding high conversion rates and sales. However, people are skeptical about ads and sometimes perceive them as spam, which eventually leads to a decrease in user satisfaction. Targeted advertising, which serves ads to individuals who may exhibit interest in a particular advertising message, is strongly required. The key to the success of precise user targeting lies in learning the accurate user and ad representation in the embedding space. Most of the previous studies have limited the representation learning in the Euclidean space, but recent studies have suggested hyperbolic manifold learning for the distinct projection of complex network properties emerging from real-world datasets such as social networks, recommender systems, and advertising. We propose a framework that can effectively learn the hierarchical structure in users and ads on the hyperbolic space, and extend to the Multi-Manifold Learning. Our method constructs multiple hyperbolic manifolds with learnable curvatures and maps the representation of user and ad to each manifold. The origin of each manifold is set as the centroid of each user cluster. The user preference for each ad is estimated using the distance between two entities in the hyperbolic space, and the final prediction is determined by aggregating the values calculated from the learned multiple manifolds. We evaluate our method on public benchmark datasets and a large-scale commercial messenger system LINE, and demonstrate its effectiveness through improved performance.
Data augmentation is usually used by supervised learning approaches for offline writer identification, but such approaches require extra training data and potentially lead to overfitting errors. In this study, a semi-supervised feature learning pipeline was proposed to improve the performance of writer identification by training with extra unlabeled data and the original labeled data simultaneously. Specifically, we proposed a weighted label smoothing regularization (WLSR) method for data augmentation, which assigned the weighted uniform label distribution to the extra unlabeled data. The WLSR method could regularize the convolutional neural network (CNN) baseline to allow more discriminative features to be learned to represent the properties of different writing styles. The experimental results on well-known benchmark datasets (ICDAR2013 and CVL) showed that our proposed semi-supervised feature learning approach could significantly improve the baseline measurement and perform competitively with existing writer identification approaches. Our findings provide new insights into offline write identification.
We study the problem of balancing effectiveness and efficiency in automated feature selection. After exploring many feature selection methods, we observe a computational dilemma: 1) traditional feature selection is mostly efficient, but difficult to identify the best subset; 2) the emerging reinforced feature selection automatically navigates to the best subset, but is usually inefficient. Can we bridge the gap between effectiveness and efficiency under automation? Motivated by this dilemma, we aim to develop a novel feature space navigation method. In our preliminary work, we leveraged interactive reinforcement learning to accelerate feature selection by external trainer-agent interaction. In this journal version, we propose a novel interactive and closed-loop architecture to simultaneously model interactive reinforcement learning (IRL) and decision tree feedback (DTF). Specifically, IRL is to create an interactive feature selection loop and DTF is to feed structured feature knowledge back to the loop. First, the tree-structured feature hierarchy from decision tree is leveraged to improve state representation. In particular, we represent the selected feature subset as an undirected graph of feature-feature correlations and a directed tree of decision features. We propose a new embedding method capable of empowering graph convolutional network to jointly learn state representation from both the graph and the tree. Second, the tree-structured feature hierarchy is exploited to develop a new reward scheme. In particular, we personalize reward assignment of agents based on decision tree feature importance. In addition, observing agents actions can be feedback, we devise another reward scheme, to weigh and assign reward based on the feature selected frequency ratio in historical action records. Finally, we present extensive experiments on real-world datasets to show the improved performance.
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