Guided Stable Dynamic Projections

Projections aim to convey the relationships and similarity of high‐dimensional data in a low‐dimensional representation. Most such techniques are designed for static data. When used for time‐dependent data, they usually fail to create a stable and suitable low dimensional representation. We propose two dynamic projection methods (PCD‐tSNE and LD‐tSNE) that use global guides to steer projection points. This avoids unstable movement that does not encode data dynamics while keeping t‐SNE's neighborhood preservation ability. PCD‐tSNE scores a good balance between stability, neighborhood preservation, and distance preservation, while LD‐tSNE allows creating stable and customizable projections. We compare our methods to 11 other techniques using quality metrics and datasets provided by a recent benchmark for dynamic projections.

[1]  Tobias Schreck,et al.  TimeSeriesPaths : Projection-Based Explorative Analysis of Multivariate Time Series Data , 2012, WSCG 2012.

[2]  Xiaohui Yu,et al.  A Perception-Driven Approach to Supervised Dimensionality Reduction for Visualization , 2018, IEEE Transactions on Visualization and Computer Graphics.

[3]  Ben J. A. Kröse,et al.  Learning from delayed rewards , 1995, Robotics Auton. Syst..

[4]  Joshua B. Tenenbaum,et al.  Sparse multidimensional scaling using land-mark points , 2004 .

[5]  Fernando Vieira Paulovich,et al.  UPDis: A user-assisted projection technique for distance information , 2018, Inf. Vis..

[6]  Paulo E. Rauber,et al.  Visualizing Time-Dependent Data Using Dynamic t-SNE , 2016, EuroVis.

[7]  Laurens van der Maaten,et al.  Accelerating t-SNE using tree-based algorithms , 2014, J. Mach. Learn. Res..

[8]  Ming-Hsuan Yang,et al.  Incremental Learning for Robust Visual Tracking , 2008, International Journal of Computer Vision.

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

[10]  Alex Krizhevsky,et al.  Learning Multiple Layers of Features from Tiny Images , 2009 .

[11]  Miguel Á. Carreira-Perpiñán,et al.  Locally Linear Landmarks for Large-Scale Manifold Learning , 2013, ECML/PKDD.

[12]  A. K. Cline,et al.  Computation of the Singular Value Decomposition , 2006 .

[13]  Haim Levkowitz,et al.  Least Square Projection: A Fast High-Precision Multidimensional Projection Technique and Its Application to Document Mapping , 2008, IEEE Transactions on Visualization and Computer Graphics.

[14]  Heng Tao Shen,et al.  Principal Component Analysis , 2009, Encyclopedia of Biometrics.

[15]  Stefan Steinerberger,et al.  Fast Interpolation-based t-SNE for Improved Visualization of Single-Cell RNA-Seq Data , 2017, Nature Methods.

[16]  Alfred Inselberg,et al.  Parallel coordinates: a tool for visualizing multi-dimensional geometry , 1990, Proceedings of the First IEEE Conference on Visualization: Visualization `90.

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

[18]  Alexandru Telea,et al.  Deep learning multidimensional projections , 2019, Inf. Vis..

[19]  Daniel A. Keim,et al.  Visual quality metrics and human perception: an initial study on 2D projections of large multidimensional data , 2010, AVI.

[20]  Daniel A. Keim,et al.  Temporal MDS Plots for Analysis of Multivariate Data , 2016, IEEE Transactions on Visualization and Computer Graphics.

[21]  John P. Lewis,et al.  Eurographics/ Ieee-vgtc Symposium on Visualization 2009 Selecting Good Views of High-dimensional Data Using Class Consistency , 2022 .

[22]  Jarkko Venna,et al.  Visualizing gene interaction graphs with local multidimensional scaling , 2006, ESANN.

[23]  Yves Le Traon,et al.  Visualizing and Exploring Dynamic High-Dimensional Datasets with LION-tSNE , 2017, ArXiv.

[24]  Rosane Minghim,et al.  Visual analysis of dimensionality reduction quality for parameterized projections , 2014, Comput. Graph..

[25]  Michael Krone,et al.  Visual Analysis of Multivariate Intensive Care Surveillance Data , 2020, VCBM.

[26]  Nicolas Le Roux,et al.  Out-of-Sample Extensions for LLE, Isomap, MDS, Eigenmaps, and Spectral Clustering , 2003, NIPS.

[27]  Andreas Kerren,et al.  Toward a Quantitative Survey of Dimension Reduction Techniques , 2019, IEEE Transactions on Visualization and Computer Graphics.

[28]  Richard A. Becker,et al.  The Visual Design and Control of Trellis Display , 1996 .

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

[30]  Valerio Pascucci,et al.  Visualizing High-Dimensional Data: Advances in the Past Decade , 2017, IEEE Transactions on Visualization and Computer Graphics.

[31]  Ramana Rao,et al.  The table lens: merging graphical and symbolic representations in an interactive focus + context visualization for tabular information , 1994, CHI '94.

[32]  Karol J. Piczak ESC: Dataset for Environmental Sound Classification , 2015, ACM Multimedia.

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

[34]  Paulo E. Rauber,et al.  Visualizing the Hidden Activity of Artificial Neural Networks , 2017, IEEE Transactions on Visualization and Computer Graphics.

[35]  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.

[36]  Christophe Hurter,et al.  Projection Navigation In Extremely Large Datasets (PNIELD) , 2017, EuroVis.

[37]  Wei Chen,et al.  Motion track: Visualizing variations of human motion data , 2010, 2010 IEEE Pacific Visualization Symposium (PacificVis).

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

[39]  Joshua B. Tenenbaum,et al.  Global Versus Local Methods in Nonlinear Dimensionality Reduction , 2002, NIPS.

[40]  Robert B. Ross,et al.  A visual analytics system for optimizing the performance of large-scale networks in supercomputing systems , 2018, Vis. Informatics.

[41]  Fernando V. Paulovich,et al.  Xtreaming: an incremental multidimensional projection technique and its application to streaming data , 2020, ArXiv.

[42]  Steven Franconeri,et al.  The Connected Scatterplot for Presenting Paired Time Series , 2016, IEEE Transactions on Visualization and Computer Graphics.

[43]  Kwan-Liu Ma,et al.  A Visual Analytics Framework for Reviewing Multivariate Time-Series Data with Dimensionality Reduction , 2021, IEEE Transactions on Visualization and Computer Graphics.

[44]  Bettina Speckmann,et al.  Quantitative Comparison of Time‐Dependent Treemaps , 2019, Comput. Graph. Forum.

[45]  Jorge S. Marques,et al.  Selecting Landmark Points for Sparse Manifold Learning , 2005, NIPS.

[46]  Alexandru Telea,et al.  Quantitative Comparison of Dynamic Treemaps for Software Evolution Visualization , 2018, 2018 IEEE Working Conference on Software Visualization (VISSOFT).

[47]  Pierre Dragicevic,et al.  Time Curves: Folding Time to Visualize Patterns of Temporal Evolution in Data , 2016, IEEE Transactions on Visualization and Computer Graphics.

[48]  Elmar Eisemann,et al.  Hierarchical Stochastic Neighbor Embedding , 2016, Comput. Graph. Forum.

[49]  Rosane Minghim,et al.  Explaining Neighborhood Preservation for Multidimensional Projections , 2015, CGVC.

[50]  E. F. Vernier,et al.  Quantitative Evaluation of Time‐Dependent Multidimensional Projection Techniques , 2020, Comput. Graph. Forum.

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

[52]  Christophe Hurter,et al.  Multidimensional Data Exploration by Explicitly Controlled Animation , 2017, Informatics.

[53]  I K Fodor,et al.  A Survey of Dimension Reduction Techniques , 2002 .

[54]  B. Zupan,et al.  Embedding to reference t-SNE space addresses batch effects in single-cell classification , 2019, bioRxiv.

[55]  Stefan Steinerberger,et al.  Clustering with t-SNE, provably , 2017, SIAM J. Math. Data Sci..

[56]  Daniel Kressner,et al.  Numerical Methods for General and Structured Eigenvalue Problems , 2005, Lecture Notes in Computational Science and Engineering.