A-tSNEApproximated and user steerable for progressive visual analytics

Nicola Pezzotti et al.Presented by: Lovedeep Gondara

March 9, 2017

Nicola Pezzotti et al. Presented by: Lovedeep Gondara A-tSNE March 9, 2017 1 / 25

Outline

1 InroductionHigh dimensional data vistSNEBarnes-Hut SNE

2 A-tSNEIntroductionInteractive analysisCase studies

3 Critique

Nicola Pezzotti et al. Presented by: Lovedeep Gondara A-tSNE March 9, 2017 2 / 25

Outline

1 InroductionHigh dimensional data vistSNEBarnes-Hut SNE

2 A-tSNEIntroductionInteractive analysisCase studies

3 Critique

Nicola Pezzotti et al. Presented by: Lovedeep Gondara A-tSNE March 9, 2017 3 / 25

High dimensional data

Most real world datasets are high dimensional.

High dimensional data vis is hard.

Dimensionality reduction to the rescue.

Nicola Pezzotti et al. Presented by: Lovedeep Gondara A-tSNE March 9, 2017 4 / 25

Outline

1 InroductionHigh dimensional data vistSNEBarnes-Hut SNE

2 A-tSNEIntroductionInteractive analysisCase studies

3 Critique

Nicola Pezzotti et al. Presented by: Lovedeep Gondara A-tSNE March 9, 2017 5 / 25

tSNEIntroduction

A tool for dimensionality reduction/vis of high dimensional data.

Converts similarities between data points in high dimensional space tojoint probability distribution P.

Computes a joint probability distribution Q, describing similarity inlow dimensional space.

Goal: Represent P faithfully using Q.

Nicola Pezzotti et al. Presented by: Lovedeep Gondara A-tSNE March 9, 2017 6 / 25

tSNEIntroduction

Minimize Kullback-Leibler divergence between P and Q.

Use gradient descent for minimization.

Each point attracts or repels all other points with a force F .

Nicola Pezzotti et al. Presented by: Lovedeep Gondara A-tSNE March 9, 2017 7 / 25

Outline

1 InroductionHigh dimensional data vistSNEBarnes-Hut SNE

2 A-tSNEIntroductionInteractive analysisCase studies

3 Critique

Nicola Pezzotti et al. Presented by: Lovedeep Gondara A-tSNE March 9, 2017 8 / 25

Barnes-Hut SNE

Original tSNE uses brute force approach for F .

Computation and memory complexity of O(n2).

Barnes-Hut SNE is an evolution of tSNE.

Nicola Pezzotti et al. Presented by: Lovedeep Gondara A-tSNE March 9, 2017 9 / 25

Barnes-Hut SNE

Uses two approximations.

Approximation 1: Similarities between data points are computed byonly taking set of nearest neighbours N.

Approximation 2: Uses Barnes-Hut algorithm.

Reduces computational and memory complexity to O(N log(N))) andO(N) respectively.

Nicola Pezzotti et al. Presented by: Lovedeep Gondara A-tSNE March 9, 2017 10 / 25

Outline

1 InroductionHigh dimensional data vistSNEBarnes-Hut SNE

2 A-tSNEIntroductionInteractive analysisCase studies

3 Critique

Nicola Pezzotti et al. Presented by: Lovedeep Gondara A-tSNE March 9, 2017 11 / 25

A-tSNEIntroduction

Evolution of BH-SNE.

Uses approximations to generate useful intermediate results.

Approximation defined by user.

Nicola Pezzotti et al. Presented by: Lovedeep Gondara A-tSNE March 9, 2017 12 / 25

A-tSNEIntroduction

Figure: Progressive visual analytics using tSNE

Figure: Progressive visual analytics using A-tSNE

Nicola Pezzotti et al. Presented by: Lovedeep Gondara A-tSNE March 9, 2017 13 / 25

A-tSNEIntroduction

Improves BH-SNE using approximated KNN computations forapproximated P.

Using a precision parameter ρ, describe the average percentage ofpoints in approximated neighbourhood that belong to the exactneighbourhood.

ρ is user defined, large values of ρ means better approximations butmore computational overhead.

These approximations make A-tSNE computationally steerable.

Nicola Pezzotti et al. Presented by: Lovedeep Gondara A-tSNE March 9, 2017 14 / 25

A-tSNEIntroduction

Figure: BH-SNE: 3191.8 s

Figure: A-tSNE (ρ = 0.34): 30.1 s

Figure: A-tSNE (ρ = 0.23): 20.4 s

Figure: A-tSNE (ρ = 0.07): 13.0 s

Nicola Pezzotti et al. Presented by: Lovedeep Gondara A-tSNE March 9, 2017 15 / 25

Outline

1 InroductionHigh dimensional data vistSNEBarnes-Hut SNE

2 A-tSNEIntroductionInteractive analysisCase studies

3 Critique

Nicola Pezzotti et al. Presented by: Lovedeep Gondara A-tSNE March 9, 2017 16 / 25

A-tSNEUser driven refinement

User selection: Select a subset of points for immediate refinement.

Breadth first search: If only a few points are selected, include theneighbourhoods.

Density based refinement: Global overview, user defined selection orwhole dataset.

Nicola Pezzotti et al. Presented by: Lovedeep Gondara A-tSNE March 9, 2017 17 / 25

A-tSNEVisualization and interaction

Density based: Simple points increase clutter, use KDE.

Visualizing approximations: Precision of high dimensional similaritiesis gradually refined until exact, requested precision can be visualizedwhile refinement is ongoing.

Use magic lens to show approximations

Nicola Pezzotti et al. Presented by: Lovedeep Gondara A-tSNE March 9, 2017 18 / 25

A-tSNEData manipulation

Inserting points

Deleting points

Dimensionality modification

Nicola Pezzotti et al. Presented by: Lovedeep Gondara A-tSNE March 9, 2017 19 / 25

A-tSNEInterface

Figure: Interface

Nicola Pezzotti et al. Presented by: Lovedeep Gondara A-tSNE March 9, 2017 20 / 25

Outline

1 InroductionHigh dimensional data vistSNEBarnes-Hut SNE

2 A-tSNEIntroductionInteractive analysisCase studies

3 Critique

Nicola Pezzotti et al. Presented by: Lovedeep Gondara A-tSNE March 9, 2017 21 / 25

A-tSNEMouse brain gene expression

Figure: Analysis of the gene expression in the mouse brain using A-tSNE

Nicola Pezzotti et al. Presented by: Lovedeep Gondara A-tSNE March 9, 2017 22 / 25

A-tSNEReal-time analysis of high-dimensional streams

Figure: Initial embedding

Figure: New cluster indicates thecreation of a set of different readings

Figure: Evolution of (a)

Figure: The cluster that identifiesmiscalibrated readings is removed

Nicola Pezzotti et al. Presented by: Lovedeep Gondara A-tSNE March 9, 2017 23 / 25

Critique

Enhanced performance.

User selective refinement.

Too many moving parts.

Not sure if all are helpful.

Nicola Pezzotti et al. Presented by: Lovedeep Gondara A-tSNE March 9, 2017 24 / 25

For Further Reading I

Pezotti et al. 2016Approximated and user steerable tsne for progressive visual analytics.IEEE Transactions on Visualization and Computer Graphics, 2016.

Nicola Pezzotti et al. Presented by: Lovedeep Gondara A-tSNE March 9, 2017 25 / 25