Fast Multiscale Neighbor Embedding

Bodt, Cyril de; Mulders, Dounia; Verleysen, Michel; Lee, John A.

doi:10.1109/tnnls.2020.3042807

Cited by 9 publications

(18 citation statements)

References 40 publications

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“…The t-distributed version of the algorithm is used and the target dimension P is 2 for all experiments. Each optimization consists of 30 iterations of the L-BFGS algorithm and uses a BH threshold θ = 0.75, as these values tend to produce good DR quality in reasonable time for the original f-ms-NE [7].…”

Section: Resultsmentioning

confidence: 99%

“…Figure 1 shows the quality of the resulting embeddings. As in [7], their quality is measured by the area under the curve (AUC) of the relative neighborhood preservation R NX [13], with a logarithmic scale for the neighborhood size. The AUC of R NX reaches 1 when the preservation is perfect for all data scales.…”

Section: Resultsmentioning

confidence: 99%

“…For this reason, reducing the time complexity of multi-scale NE requires a different approach for the HD side. In [7], the authors tackle this problem by defining small multi-scale neighbor sets I i for i ∈ I.…”

Section: Fast Multi-scale Neighbor Embeddingmentioning

confidence: 99%

“…However, multi-scale NE methods have a time complexity of O(N 2 log N ) with N data points, restricting their use to data sets of moderate size. A fast version of multi-scale NE (f-ms-NE) [7] has a time complexity of O(N log 2 N ), with a slight decrease in neighbor preservation as a trade-off. To achieve such an acceleration, f-ms-NE relies on random data subsamplings to capture both the local and global structures in the HD data.…”

Section: Introductionmentioning

confidence: 99%

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Impact of data subsamplings in Fast Multi-Scale Neighbor Embedding.

Lambert¹,

Lee²,

Verleysen³

et al. 2021

ESANN 2021 Proceedings

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Fast multi-scale neighbor embedding (f-ms-NE) is an algorithm that maps high-dimensional data to a low-dimensional space by preserving the multi-scale data neighborhoods. To lower its time complexity, f-ms-NE uses random subsamplings to estimate the data properties at multiple scales. To improve this estimation and study the f-ms-NE sensitivity to randomness, this paper generalizes the f-ms-NE cost function by averaging several subsamplings. Experiments reveal that this can slightly improve the quality of the embeddings while maintaining reasonable computation times. Codes are available at https://github.com/cdebodt/ Fast_Multi-scale_NE.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Fast Multi-scale Neighbor Embeddingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Impact of data subsamplings in Fast Multi-Scale Neighbor Embedding.

Lambert¹,

Lee²,

Verleysen³

et al. 2021

ESANN 2021 Proceedings

Self Cite

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“…This feature hinders the ability to analyze whether the neighborhoods are reproduced at different data scales and does not highlight the local and global properties of the mapping. For these reasons, some studies developed dimensionality reduction (DR) quality criteria which measure the high-dimensional neighborhood preservation in the projection [43], becoming generally adopted in several publications [44][45][46]. This neighborhood preservation principle is indeed considered as the driving factor in the DR quality [47].…”

Section: Neighborhood Preservation Assessmentmentioning

confidence: 99%

Tuning Database-Friendly Random Projection Matrices for Improved Distance Preservation on Specific Data

López-Sánchez

Bodt

Lee³

et al. 2021

Appl Intell

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Random Projection is one of the most popular and successful dimensionality reduction algorithms for large volumes of data. However, given its stochastic nature, different initializations of the projection matrix can lead to very different levels of performance. This paper presents a guided random search algorithm to mitigate this problem. The proposed method uses a small number of training data samples to iteratively adjust a projection matrix, improving its performance on similarly distributed data. Experimental results show that projection matrices generated with the proposed method result in a better preservation of distances between data samples. Conveniently, this is achieved while preserving the database-friendliness of the projection matrix, as it remains sparse and comprised exclusively of integers after being tuned with our algorithm. Moreover, running the proposed algorithm on a consumer-grade CPU requires only a few seconds.

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