Deep Learning Inverse Multidimensional Projections

We present a new method for computing inverse projections from 2D spaces to arbitrary high-dimensional spaces. Given any projection technique, we train a deep neural network to learn a low-to-high dimensional mapping based on a projected training set, and next use this mapping to infer the mapping on arbitrary points. We compare our method with two recent inverse projection techniques on three datasets, and show that our method has similar or higher accuracy, is one to two orders of magnitude faster, and delivers result that match well known ground-truth information about the respective high-dimensional data. Visual analytics Unsupervised learning Dimensionality reduction and manifold learning CCS Concepts • Visualization → Visualization application domains; •Machine learning → Learning paradigms;

[1]  Alberto D. Pascual-Montano,et al.  A survey of dimensionality reduction techniques , 2014, ArXiv.

[2]  Jian Sun,et al.  Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification , 2015, 2015 IEEE International Conference on Computer Vision (ICCV).

[3]  Luiz Velho,et al.  Facing the high-dimensions: Inverse projection with radial basis functions , 2015, Comput. Graph..

[4]  Geoffrey E. Hinton,et al.  Visualizing Data using t-SNE , 2008 .

[5]  Roland Vollgraf,et al.  Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms , 2017, ArXiv.

[6]  Mario Costa Sousa,et al.  iLAMP: Exploring high-dimensional spacing through backward multidimensional projection , 2012, 2012 IEEE Conference on Visual Analytics Science and Technology (VAST).

[7]  Eric O. Postma,et al.  Dimensionality Reduction: A Comparative Review , 2008 .

[8]  Alexandru Telea,et al.  Visual Analytics of Multidimensional Projections for Constructing Classifier Decision Boundary Maps , 2019, VISIGRAPP.

[9]  Luis Gustavo Nonato,et al.  Multidimensional Projection for Visual Analytics: Linking Techniques with Distortions, Tasks, and Layout Enrichment , 2019, IEEE Transactions on Visualization and Computer Graphics.

[10]  Jie Li,et al.  A survey of dimensionality reduction techniques based on random projection , 2017, ArXiv.

[11]  Stefano Soatto,et al.  Empirical Study of the Topology and Geometry of Deep Networks , 2018, 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition.

[12]  Luis Gustavo Nonato,et al.  Local Affine Multidimensional Projection , 2011, IEEE Transactions on Visualization and Computer Graphics.

[13]  Leland McInnes,et al.  UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction , 2018, ArXiv.

[14]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[15]  Alexandru Cristian Telea,et al.  Image-Based Visualization of Classifier Decision Boundaries , 2018, 2018 31st SIBGRAPI Conference on Graphics, Patterns and Images (SIBGRAPI).

[16]  Zoubin Ghahramani,et al.  Unifying linear dimensionality reduction , 2014, 1406.0873.