Visualizing the quality of dimensionality reduction

Novel non-parametric dimensionality reduction techniques such as t-distributed stochastic neighbor embedding (t-SNE) lead to a powerful and flexible visualization of high-dimensional data. One drawback of non-parametric techniques is their lack of an explicit out-of-sample extension. In this contribution, we propose an efficient extension of t-SNE to a parametric framework, kernel t-SNE, which preserves the flexibility of basic t-SNE, but enables explicit out-of-sample extensions. We test the ability of kernel t-SNE in comparison to standard t-SNE for benchmark data sets, in particular addressing the generalization ability of the mapping for novel data. In the context of large data sets, this procedure enables us to train a mapping for a fixed size subset only, mapping all data afterwards in linear time. We demonstrate that this technique yields satisfactory results also for large data sets provided missing information due to the small size of the subset is accounted for by auxiliary information such as class labels, which can be integrated into kernel t-SNE based on the Fisher information.

show abstract

“…Albeit there are intuitive possibilities to extend this proposal [20], we will stick to this measure in this contribution.…”

Section: Evaluation Measuresmentioning

confidence: 99%

Parametric nonlinear dimensionality reduction using kernel t-SNE

2015

Self Cite

View full text Add to dashboard Cite

show abstract

“…Mokbel et al [20] extend the rank-based framework by introducing pointwise measures that follow directly from individual co-ranking matrices. These can be mapped directly to the point cloud visualization, enriching the information and enhancing interpretability.…”

Section: ð1þmentioning

confidence: 99%

“…We compare assessments of neighborhood preservation obtained with measures based on the co-ranking matrix and with our Neighborhood Validation, taking as example t-SNE projections of the Coil-20 data set 5 (with perplexity set to 15, as in [20]). This consists of 1440 images (128 Â 128 bitmaps) of 20 objects: each object characterizes a class, and has been photographed at 72 distinct rotations, at 5 degree increments.…”

Section: Comparing With Other Measures Of Neighborhood Preservationmentioning

confidence: 99%

Graph-based measures to assist user assessment of multidimensional projections

et al. 2015

View full text Add to dashboard Cite

“…all K-neighborhoods corresponds to the value Q NX (K) approaching 1. Interestingly, this framework can be linked to an information theoretic point of view as specified in [33] and it subsumes several previous evaluation criteria, see [14,20]. It is possible to extend this framework to a point-wise evaluation as introduced in [20].…”

Section: The Co-ranking Frameworkmentioning

confidence: 99%

“…7 demonstrates our proposed framework for the pointwise comparison of dissimilarity measures on the same data scenario. The coloring in 7c and 7d refers to Q xi NX (20), which is the agreement of the 20-neighborhood for every point x i as compared to the other dissimilarity measure. To link the coloring scheme to the evaluation curves, K = 20 is highlighted on the graphs in Fig.…”

Section: Java Programsmentioning

confidence: 99%

How to Quantitatively Compare Data Dissimilarities for Unsupervised Machine Learning?

Mokbel

Groß

Lux

et al. 2012

Artificial Neural Networks in Pattern Recognition

Self Cite

View full text Add to dashboard Cite

For complex data sets, the pairwise similarity or dissimilarity of data often serves as the interface of the application scenario to the machine learning tool. Hence, the final result of training is severely influenced by the choice of the dissimilarity measure. While dissimilarity measures for supervised settings can eventually be compared by the classification error, the situation is less clear in unsupervised domains where a clear objective is lacking. The question occurs, how to compare dissimilarity measures and their influence on the final result in such cases. In this contribution, we propose to use a recent quantitative measure introduced in the context of unsupervised dimensionality reduction, to compare whether and on which scale dissimilarities coincide for an unsupervised learning task. Essentially, the measure evaluates in how far neighborhood relations are preserved if evaluated based on rankings, this way achieving a robustness of the measure against scaling of data. Apart from a global comparison, local versions allow to highlight regions of the data where two dissimilarity measures induce the same results.

show abstract

Visualizing the quality of dimensionality reduction

Cited by 72 publications

References 20 publications

Parametric nonlinear dimensionality reduction using kernel t-SNE

Parametric nonlinear dimensionality reduction using kernel t-SNE

Graph-based measures to assist user assessment of multidimensional projections

How to Quantitatively Compare Data Dissimilarities for Unsupervised Machine Learning?

Contact Info

Product

Resources

About