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ACEV: Unsupervised Intersecting Manifold Segmentation using Adaptation to Angular Change of Eigenvectors in Intrinsic Dimension
Machine Learning · Submitted 30 Sep 2024
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The proposed method performs better than 18 SOTA manifold segmentation methods in ARI and NMI scores over 14 real-world datasets with lesser time complexity and better stability.
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The abstract, sentence by sentence
Intersecting manifold segmentation has been a focus of research, where individual manifolds, that intersect with other manifolds, are separated to discover their distinct properties. The proposed method is based on the intuition that when a manifold in $D$ dimensional space with an intrinsic dimension of $d$ intersects with another manifold, the data variance grows in more than $d$ directions. The proposed method measures local data variances and determines their vector directions. It counts the number of vectors with non-zero variance, which determines the manifold's intrinsic dimension. For detection of the intersection region, the method adapts to the changes in the angular gaps between the corresponding direction vectors of the child and parent using exponential moving averages using a tree structure construction. Accordingly, it includes those data points in the same manifold whose neighborhood is within the adaptive angular difference and eventually identifies the data points in the intersection area of manifolds. Data points whose inclusion in the neighborhood-identified data points increases their intrinsic dimensionality are removed based on data variance and distance. The proposed method performs better than 18 SOTA manifold segmentation methods in ARI and NMI scores over 14 real-world datasets with lesser time complexity and better stability.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Intersecting manifold segmentation has been a focus of research, where individual manifolds, that intersect with other manifolds, are separated to discover their distinct properties. | background 1.00 | 0.04 | 0.03 | asserted 1.00 |
| s1 | The proposed method is based on the intuition that when a manifold in $D$ dimensional space with an intrinsic dimension of $d$ intersects with another manifold, the data variance grows in more than $d$ directions. | method 0.78 | 0.23 | 0.07 | asserted 0.93 |
| s2 | The proposed method measures local data variances and determines their vector directions. | method 1.00 | 0.91 | 0.02 | asserted 1.00 |
| s3 | It counts the number of vectors with non-zero variance, which determines the manifold's intrinsic dimension. | method 1.00 | 0.86 | 0.03 | asserted 1.00 |
| s4 | For detection of the intersection region, the method adapts to the changes in the angular gaps between the corresponding direction vectors of the child and parent using exponential moving averages using a tree structure construction. | method 1.00 | 0.90 | 0.04 | asserted 1.00 |
| s5 | Accordingly, it includes those data points in the same manifold whose neighborhood is within the adaptive angular difference and eventually identifies the data points in the intersection area of manifolds. | method 1.00 | 0.88 | 0.08 | asserted 1.00 |
| s6 | Data points whose inclusion in the neighborhood-identified data points increases their intrinsic dimensionality are removed based on data variance and distance. | method 1.00 | 0.87 | 0.04 | asserted 1.00 |
| s7 | The proposed method performs better than 18 SOTA manifold segmentation methods in ARI and NMI scores over 14 real-world datasets with lesser time complexity and better stability. | result 1.00 | 0.95 | 0.84 | asserted 1.00 |
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The paper
Original abstract
Intersecting manifold segmentation has been a focus of research, where individual manifolds, that intersect with other manifolds, are separated to discover their distinct properties. The proposed method is based on the intuition that when a manifold in $D$ dimensional space with an intrinsic dimension of $d$ intersects with another manifold, the data variance grows in more than $d$ directions. The proposed method measures local data variances and determines their vector directions. It counts the number of vectors with non-zero variance, which determines the manifold's intrinsic dimension. For detection of the intersection region, the method adapts to the changes in the angular gaps between the corresponding direction vectors of the child and parent using exponential moving averages using a tree structure construction. Accordingly, it includes those data points in the same manifold whose neighborhood is within the adaptive angular difference and eventually identifies the data points in the intersection area of manifolds. Data points whose inclusion in the neighborhood-identified data points increases their intrinsic dimensionality are removed based on data variance and distance. The proposed method performs better than 18 SOTA manifold segmentation methods in ARI and NMI scores over 14 real-world datasets with lesser time complexity and better stability.
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