Optimizing graph layout by t-SNE perplexity estimation

AbstractPerplexity is one of the key parameters of dimensionality reduction algorithm of t-distributed stochastic neighbor embedding (t-SNE). In this paper, we investigated the relationship of t-SNE perplexity and graph layout evaluation metrics including graph stress, preserved neighborhood information and visual inspection. As we found that a small perplexity is correlated with a relative higher normalized stress while preserving neighborhood information with a higher precision but less global structure information, we proposed our method to estimate appropriate perplexity either based on a modified standard t-SNE or the sklearn Barnes–Hut TSNE. Experimental results demonstrate effectiveness and ease of use of our approach when tested on a set of benchmark datasets.</jats:p

Approximated and User Steerable tSNE for Progressive Visual Analytics

Progressive Visual Analytics aims at improving the interactivity in existing analytics techniques by means of visualization as well as interaction with intermediate results. One key method for data analysis is dimensionality reduction, for example, to produce 2D embeddings that can be visualized and analyzed efficiently. t-Distributed Stochastic Neighbor Embedding (tSNE) is a well-suited technique for the visualization of several high-dimensional data. tSNE can create meaningful intermediate results but suffers from a slow initialization that constrains its application in Progressive Visual Analytics. We introduce a controllable tSNE approximation (A-tSNE), which trades off speed and accuracy, to enable interactive data exploration. We offer real-time visualization techniques, including a density-based solution and a Magic Lens to inspect the degree of approximation. With this feedback, the user can decide on local refinements and steer the approximation level during the analysis. We demonstrate our technique with several datasets, in a real-world research scenario and for the real-time analysis of high-dimensional streams to illustrate its effectiveness for interactive data analysis

Deep Metric Learning via Lifted Structured Feature Embedding

Learning the distance metric between pairs of examples is of great importance for learning and visual recognition. With the remarkable success from the state of the art convolutional neural networks, recent works have shown promising results on discriminatively training the networks to learn semantic feature embeddings where similar examples are mapped close to each other and dissimilar examples are mapped farther apart. In this paper, we describe an algorithm for taking full advantage of the training batches in the neural network training by lifting the vector of pairwise distances within the batch to the matrix of pairwise distances. This step enables the algorithm to learn the state of the art feature embedding by optimizing a novel structured prediction objective on the lifted problem. Additionally, we collected Online Products dataset: 120k images of 23k classes of online products for metric learning. Our experiments on the CUB-200-2011, CARS196, and Online Products datasets demonstrate significant improvement over existing deep feature embedding methods on all experimented embedding sizes with the GoogLeNet network.Comment: 11 page

Conditional t-SNE: Complementary t-SNE embeddings through factoring out prior information

Dimensionality reduction and manifold learning methods such as t-Distributed Stochastic Neighbor Embedding (t-SNE) are routinely used to map high-dimensional data into a 2-dimensional space to visualize and explore the data. However, two dimensions are typically insufficient to capture all structure in the data, the salient structure is often already known, and it is not obvious how to extract the remaining information in a similarly effective manner. To fill this gap, we introduce \emph{conditional t-SNE} (ct-SNE), a generalization of t-SNE that discounts prior information from the embedding in the form of labels. To achieve this, we propose a conditioned version of the t-SNE objective, obtaining a single, integrated, and elegant method. ct-SNE has one extra parameter over t-SNE; we investigate its effects and show how to efficiently optimize the objective. Factoring out prior knowledge allows complementary structure to be captured in the embedding, providing new insights. Qualitative and quantitative empirical results on synthetic and (large) real data show ct-SNE is effective and achieves its goal

FAST: A Fully Asynchronous Split Time-Integrator for Self-Gravitating Fluid

We describe a new algorithm for the integration of self-gravitating fluid systems using SPH method. We split the Hamiltonian of a self-gravitating fluid system to the gravitational potential and others (kinetic and internal energies) and use different time-steps for their integrations. The time integration is done in the way similar to that used in the mixed variable or multiple stepsize symplectic schemes. We performed three test calculations. One was the spherical collapse and the other was an explosion. We also performed a realistic test, in which the initial model was taken from a simulation of merging galaxies. In all test calculations, we found that the number of time-steps for gravitational interaction were reduced by nearly an order of magnitude when we adopted our integration method. In the case of the realistic test, in which the dark matter potential dominates the total system, the total calculation time was significantly reduced. Simulation results were almost the same with those of simulations with the ordinary individual time-step method. Our new method achieves good performance without sacrificing the accuracy of the time integration.Comment: 14 pages, 8 figures, accepted for publication in PAS