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Added by
Dong Wang
Publication date
2015
fields
Informatics Engineering
and research's language is
English
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T-SNE is a well-known approach to embedding high-dimensional data and has been widely used in data visualization. The basic assumption of t-SNE is that the data are non-constrained in the Euclidean space and the local proximity can be modelled by Gaussian distributions. This assumption does not hold for a wide range of data types in practical applications, for instance spherical data for which the local proximity is better modelled by the von Mises-Fisher (vMF) distribution instead of the Gaussian. This paper presents a vMF-SNE embedding algorithm to embed spherical data. An iterative process is derived to produce an efficient embedding. The results on a simulation data set demonstrated that vMF-SNE produces better embeddings than t-SNE for spherical data.
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Modern datasets and models are notoriously difficult to explore and analyze due to their inherent high dimensionality and massive numbers of samples. Existing visualization methods which employ dimensionality reduction to two or three dimensions are often inefficient and/or ineffective for these datasets. This paper introduces t-SNE-CUDA, a GPU-accelerated implementation of t-distributed Symmetric Neighbor Embedding (t-SNE) for visualizing datasets and models. t-SNE-CUDA significantly outperforms current implementations with 50-700x speedups on the CIFAR-10 and MNIST datasets. These speedups enable, for the first time, visualization of the neural network activations on the entire ImageNet dataset - a feat that was previously computationally intractable. We also demonstrate visualization performance in the NLP domain by visualizing the GloVe embedding vectors. From these visualizations, we can draw interesting conclusions about using the L2 metric in these embedding spaces. t-SNE-CUDA is publicly available athttps://github.com/CannyLab/tsne-cuda
A first line of attack in exploratory data analysis is data visualization, i.e., generating a 2-dimensional representation of data that makes clusters of similar points visually identifiable. Standard Johnson-Lindenstrauss dimensionality reduction does not produce data visualizations. The t-SNE heuristic of van der Maaten and Hinton, which is based on non-convex optimization, has become the de facto standard for visualization in a wide range of applications. This work gives a formal framework for the problem of data visualization - finding a 2-dimensional embedding of clusterable data that correctly separates individual clusters to make them visually identifiable. We then give a rigorous analysis of the performance of t-SNE under a natural, deterministic condition on the ground-truth clusters (similar to conditions assumed in earlier analyses of clustering) in the underlying data. These are the first provable guarantees on t-SNE for constructing good data visualizations. We show that our deterministic condition is satisfied by considerably general probabilistic generative models for clusterable data such as mixtures of well-separated log-concave distributions. Finally, we give theoretical evidence that t-SNE provably succeeds in partially recovering cluster structure even when the above deterministic condition is not met.
We introduce an improved unsupervised clustering protocol specially suited for large-scale structured data. The protocol follows three steps: a dimensionality reduction of the data, a density estimation over the low dimensional representation of the data, and a final segmentation of the density landscape. For the dimensionality reduction step we introduce a parallelized implementation of the well-known t-Stochastic Neighbouring Embedding (t-SNE) algorithm that significantly alleviates some inherent limitations, while improving its suitability for large datasets. We also introduce a new adaptive Kernel Density Estimation particularly coupled with the t-SNE framework in order to get accurate density estimates out of the embedded data, and a variant of the rainfalling watershed algorithm to identify clusters within the density landscape. The whole mapping protocol is wrapped in the bigMap R package, together with visualization and analysis tools to ease the qualitative and quantitative assessment of the clustering.
spectral-based subspace learning is a common data preprocessing step in many machine learning pipelines. The main aim is to learn a meaningful low dimensional embedding of the data. However, most subspace learning methods do not take into consideration possible measurement inaccuracies or artifacts that can lead to data with high uncertainty. Thus, learning directly from raw data can be misleading and can negatively impact the accuracy. In this paper, we propose to model artifacts in training data using probability distributions; each data point is represented by a Gaussian distribution centered at the original data point and having a variance modeling its uncertainty. We reformulate the Graph Embedding framework to make it suitable for learning from distributions and we study as special cases the Linear Discriminant Analysis and the Marginal Fisher Analysis techniques. Furthermore, we propose two schemes for modeling data uncertainty based on pair-wise distances in an unsupervised and a supervised contexts.
Knowledge graph embedding (KGE) is a technique for learning continuous embeddings for entities and relations in the knowledge graph.Due to its benefit to a variety of downstream tasks such as knowledge graph completion, question answering and recommendation, KGE has gained significant attention recently. Despite its effectiveness in a benign environment, KGE robustness to adversarial attacks is not well-studied. Existing attack methods on graph data cannot be directly applied to attack the embeddings of knowledge graph due to its heterogeneity. To fill this gap, we propose a collection of data poisoning attack strategies, which can effectively manipulate the plausibility of arbitrary targeted facts in a knowledge graph by adding or deleting facts on the graph. The effectiveness and efficiency of the proposed attack strategies are verified by extensive evaluations on two widely-used benchmarks.
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