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PointHop: An Explainable Machine Learning Method for Point Cloud Classification

Min Zhang, Haoxuan You, Pranav Kadam, Shan Liu, C. -C. Jay Kuo

arXiv:1907.12766v2cs.CVcs.LG

TL;DR

Deep-learning point-cloud classifiers can be hard to interpret and costly to train, while extensive labeling adds burden. PointHop builds attributes through iterative one-hop exchanges and classifies aggregated features; its reported performance is comparable to state of the art, with substantially lower training complexity.

  • Problem

    Deep-learning point-cloud methods are difficult to interpret and computationally expensive, and extensive labeling adds burden.

    Source: §I · pp. 1–2

  • Method

    PointHop builds local-to-global attributes from one-hop neighbor descriptors, then classifies aggregated features using classifiers and ensembles.

    Source: §I · p. 2, A. Local-to-Global Attribute Building · p. 5

  • Results

    89.1% overall accuracy with ensemble; PointHop trails PointNet by 0.1% and DGCNN [18] by 3.1%, while outperforming LFD-GAN [44] and FoldingNet.

    Source: C. Comparison with State-of-the-Art… · p. 8

  • Takeaways & Limitations

    PointHop training takes less than 20 minutes on CPU, compared with several hours even with GPU for deep-learning methods.

    Source: §I · p. 2

Abstract

from arXiv · show

An explainable machine learning method for point cloud classification, called the PointHop method, is proposed in this work. The PointHop method consists of two stages: 1) local-to-global attribute building through iterative one-hop information exchange, and 2) classification and ensembles. In the attribute building stage, we address the problem of unordered point cloud data using a space partitioning procedure and developing a robust descriptor that characterizes the relationship between a point and its one-hop neighbor in a PointHop unit. When we put multiple PointHop units in cascade, the attributes of a point will grow by taking its relationship with one-hop neighbor points into account iteratively. Furthermore, to control the rapid dimension growth of the attribute vector associated with a point, we use the Saab transform to reduce the attribute dimension in each PointHop unit. In the classification and ensemble stage, we feed the feature vector obtained from multiple PointHop units to a classifier. We explore ensemble methods to improve the classification performance furthermore. It is shown by experimental results that the PointHop method offers classification performance that is comparable with state-of-the-art methods while demanding much lower training complexity.

I. INTRODUCTION

Deep-learning point-cloud classifiers are difficult to interpret and computationally costly, while extensive labeling adds burden. PointHop offers an explainable, lower-complexity alternative built from iterative one-hop attribute exchange and classification.

I. INTRODUCTION

  • Deep point-cloud learning methods are difficult to interpret, computationally expensive, and require extensive labeling, motivating an explainable alternative.The introduction identifies computational cost and labeling requirements as burdens on reliable and flexible 3D-vision applications.Source: §I · pp. 1–2
  • PointHop has two stages: local-to-global attribute building through iterative one-hop information exchange, followed by classification and ensembles.Its attribute-building stage uses space partitioning and a descriptor of each point's relationship to a one-hop neighbor.Source: §I · p. 2
  • PointHop achieves comparable ModelNet40 classification performance to state-of-the-art methods, with training under 20 minutes on CPU versus several hours even with GPU for deep-learning methods.The reported comparison describes PointHop's training complexity as much lower.Source: §I · p. 2
  • Cascaded PointHop units iteratively expand point attributes, while the Saab transform reduces each unit's attribute dimension before classification.The resulting features are fed to classifiers such as SVM or random forest, and ensemble methods are explored to improve performance.Source: §I · p. 2

II. REVIEW OF RELATED WORK

Prior work spans feedforward-designed transforms and methods tailored to point-cloud structure. PointHop applies cascaded processing to unordered, disturbance-affected inputs.

A. Feedforward-designed CNNs (FF-CNNs)

  • FF-CNN filters can be derived from PCA in unsupervised, feedforward stages without backpropagation; the cited FF-CNN work tested only MNIST and CIFAR-10.The Saab transform is described as having half as many filters as the Saak transform.Source: A. Feedforward-designed CNNs (FF-CNNs) · p. 3

B. Point Cloud Processing Methods

  • Point-cloud methods span handcrafted descriptors and deep models: PointNet++ [17] aggregates local sets hierarchically, while PointCNN uses χ-Conv within local pitches.Earlier work also combined multiple handcrafted features for different tasks.Source: B. Point Cloud Processing Methods · p. 3

III. PROPOSED POINTHOP SYSTEM

  • PointHop addresses unordered, disturbance-affected clouds with cascaded units for multi-hop attribute building and classification, using random sampling to reduce processing time.The system takes a point cloud as input and outputs its class label.Source: §III · pp. 3–4, Figure 3 · p. 4

A. Local-to-Global Attribute Building

PointHop builds point attributes by iteratively incorporating one-hop neighbors, then reduces their growing dimension with the Saab transform. It aggregates attributes from multiple units into a feature vector, with spatial sampling between units to reduce processing.

A. Local-to-Global Attribute Building

  • Each PointHop unit builds a local descriptor from one-hop neighbors and applies the Saab transform to reduce the expanded attribute dimension.The unit partitions a point’s local region into eight quadrants, averages attributes within each, and concatenates the centroids; this averaging is described as robust to point-position disturbance.Source: A. Local-to-Global Attribute Building · p. 4
  • Attributes grow iteratively across hops, expanding from 3D coordinates to 24 dimensions at one hop and 192 at two hops.The n-hop attributes characterize a point’s relationship with neighbors up to m hops away, where m ≤ n.Source: A. Local-to-Global Attribute Building · p. 5
  • The Saab transform reduces attribute dimension before the next hop, limiting rapid growth as attributes cover a wider region.L cascaded PointHop units use L-stage Saab transforms; the experiments set L = 4 and select AC filter counts at the PCA energy-curve knee.Source: A. Local-to-Global Attribute Building · p. 5
  • For each unit, the method pools each attribute across points using multiple schemes, then concatenates the pooled features across units.The pooling schemes include max, mean, l1-norm, and l2-norm aggregation.Source: A. Local-to-Global Attribute Building · p. 5
  • Farthest point sampling between units reduces the number of points processed and is used to capture point-cloud geometry.The selection starts with the point closest to the centroid, then iteratively adds the point farthest from the selected subset.Source: A. Local-to-Global Attribute Building · p. 5

B. Classification and Ensembles

PointHop classifies its aggregated feature vector with an SVM or random forest and explores decision- and feature-level ensembles. The method uses feature ensembles for their higher observed accuracy, while varying settings to enrich feature diversity.

B. Classification and Ensembles

  • The method uses SVM or random forest classifiers on the feature vector; the random forest averages outputs from its decision trees.The SVM classifies samples by mapping them to one side of separating gaps.Source: B. Classification and Ensembles · p. 5
  • Decision ensembles concatenate decision vectors from individual PointHop-unit classifiers, while feature ensembles cascade features from multiple units.Source: B. Classification and Ensembles · p. 6
  • Feature ensembles are selected for higher observed accuracy, with higher complexity when feature dimension is large.The paper reports that feature ensembles outperform decision ensembles in accuracy.Source: B. Classification and Ensembles · p. 6
  • Feature diversity is varied through input rotation, Saab-filter counts, KNN K values, and the number of points in PointHop units.Source: B. Classification and Ensembles · p. 6

IV. EXPERIMENTAL RESULTS

Experiments use ModelNet40 and a default four-unit PointHop configuration. The input is randomly sampled, while farthest point sampling is used between units.

IV. EXPERIMENTAL RESULTS

  • Experiments use ModelNet40, which has 40 object categories, 9,843 training samples, and 2,468 testing samples.Each initial point cloud contains 2,048 points with three Cartesian coordinates.Source: §IV · p. 6
  • The default setup samples 256 points randomly for the first unit and uses K = 64 with four PointHop units.The second, third, and fourth units use 128, 128, and 64 points, respectively.Source: §IV · pp. 6–7
  • Between units, the default setup uses farthest point sampling and Saab AC filter counts of 15, 25, 40, and 80 across the four units.The experimental default uses mean pooling, a random forest classifier, and no ensembles.Source: §IV · pp. 6–7

A. Ablation Study on PointHop Unit

In the 256-point ablation setting, PointHop reaches 86.1% accuracy with five minutes of training; across the point-count sweep, all-four pooling ensembles perform best.

A. Ablation Study on PointHop Unit

  • In Table I’s last row, the PointHop system reaches 86.1% classification accuracy using randomly selected 256 input points, and the whole training time is only 5 minutes.Source: A. Ablation Study on PointHop Unit · p. 7
  • 88.2% accuracy is reached with the all-four-pooling ensemble at either 768 or 1,024 sampled points.The ensemble of all pooling schemes performs best in all four point-count settings; max and mean pooling perform worst, while the remaining five schemes have a small performance gap at 1,024 points.Source: Figure 6 · p. 7, A. Ablation Study on PointHop Unit · p. 8

B. Ensembles of PointHop Systems

The ensemble tests vary rotation, filter counts, KNN neighborhood sizes, and input point counts across five PointHop systems. Rotating point clouds is reported as the simplest effective ensemble, reaching 88% test accuracy.

B. Ensembles of PointHop Systems

  • Rotating point clouds yields the simplest effective ensemble result, reaching 88% test accuracy.The default setting ensembles five PointHops with changed hyperparameters; later experiments focus on rotation.Source: B. Ensembles of PointHop Systems · p. 8
  • The ensemble variants change rotation, AC-filter counts, KNN K values, or input point counts across PointHop units.For HP-B, HP-C, and HP-D, the listed values correspond to the first through fourth units; other hyperparameters are held fixed when deriving each individual ensemble result.Source: B. Ensembles of PointHop Systems · p. 8

C. Comparison with State-of-the-Art Methods

On ModelNet40, PointHop’s ensemble reaches 89.1% overall accuracy, while training takes less time than deep-learning methods. Tests also report greater robustness under several point-count settings and train-test mismatches.

C. Comparison with State-of-the-Art Methods

D. Feature Visualization

First-stage PointHop features show geometric patterns across varied point clouds, while error analysis identifies difficult classes and shape-related confusions. The conclusion highlights lower training complexity and points to combining data-driven and rule-based approaches for further improvement.

D. Feature Visualization

  • First-stage PointHop channels respond to patterns such as tent and lamp corners and airplane and bed planes across six varied point clouds.The displayed channel responses are normalized to [0, 1], shown from blue to red.Source: D. Feature Visualization · p. 9, Figure 8 · p. 10

E. Error Analysis

  • PointHop is 1.8% below PointNet in average accuracy but equals or exceeds it in 18 classes; flower pots score 10%, cups 55%, radios 65%, and sinks 60%.Flower pots are the most challenging class; the error analysis reports shape- and function-related confusions for flower pots and cups.Source: E. Error Analysis · p. 9, Table V · p. 10, Figure 9 · p. 11

V. CONCLUSION

  • The conclusion reports significantly lower training complexity than state-of-the-art deep-learning methods with comparable classification performance, and proposes joint data-driven and rule-based approaches for hard classes as future work.PointHop builds attributes through iterative one-hop information exchange, uses space partitioning for unordered point clouds, and applies the Saab transform to reduce attribute dimension.Source: §V · pp. 9, 11

APPENDIX: SAAB TRANSFORM

The Saab transform uses multi-stage PCA, with a DC filter capturing the local mean and AC filters derived from the residual. Its bias choices keep filter responses non-negative, so nonlinear activation can be removed.

APPENDIX: SAAB TRANSFORM

  • The DC filter uses an all-ones weight vector, and projecting the input onto it gives the local mean.Source: APPENDIX: SAAB TRANSFORM · p. 11
  • The AC filters are the first K−1 principal components obtained by applying PCA to the AC component of the input.The AC component is derived by subtracting the DC component from the input.Source: APPENDIX: SAAB TRANSFORM · p. 11
  • Saab uses equal bias terms that are large enough to keep filter responses non-negative, allowing nonlinear activation to be removed.The output coefficient is defined using a filter weight and bias term.Source: APPENDIX: SAAB TRANSFORM · p. 11
  • Multi-stage PCA handles decaying spatial correlations across multiple resolutions, unlike single-stage PCA at one resolution.The transform first applies PCA in a local window, then applies PCA to the resulting joint spatial-spectral cuboid.Source: APPENDIX: SAAB TRANSFORM · p. 11

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