As the basic task of point cloud analysis, classification is fundamental but always challenging. To address some unsolved problems of existing methods, we propose a network that captures geometric features of point clouds for better representations. To achieve this, on the one hand, we enrich the geometric information of points in low-level 3D space explicitly. On the other hand, we apply CNN-based structures in high-level feature spaces to learn local geometric context implicitly. Specifically, we leverage an idea of error-correcting feedback structure to capture the local features of point clouds comprehensively. Furthermore, an attention module based on channel affinity assists the feature map to avoid possible redundancy by emphasizing its distinct channels. The performance on both synthetic and real-world point clouds datasets demonstrate the superiority and applicability of our network. Comparing with other state-of-the-art methods, our approach balances accuracy and efficiency.

Geometric Back-projection Network for Point Cloud Classification

PixelHop: A Successive Subspace Learning (SSL) Method for Object Recognition

Thanks to the exponential growth in computing power and vast amounts of data, artificial intelligence (AI) has witnessed remarkable developments in recent years, enabling it to be ubiquitously adopted in our daily lives. Even though AI-powered systems have brought competitive advantages, the black-box nature makes them lack transparency and prevents them from explaining their decisions. This issue has motivated the introduction of explainable artificial intelligence (XAI), which promotes AI algorithms that can show their internal process and explain how they made decisions. The number of XAI research has increased significantly in recent years, but there lacks a unified and comprehensive review of the latest XAI progress. This review aims to bridge the gap by discovering the critical perspectives of the rapidly growing body of research associated with XAI. After offering the readers a solid XAI background, we analyze and review various XAI methods, which are grouped into (i) pre-modeling explainability, (ii) interpretable model, and (iii) post-modeling explainability. We also pay attention to the current methods that dedicate to interpret and analyze deep learning methods. In addition, we systematically discuss various XAI challenges, such as the trade-off between the performance and the explainability, evaluation methods, security, and policy. Finally, we show the standard approaches that are leveraged to deal with the mentioned challenges.

Explainable artificial intelligence: a comprehensive review

The PointHop method was recently proposed by Zhang et al. for 3D point cloud classification with unsupervised feature extraction. It has an extremely low training complexity while achieving state-of-the-art classification performance. In this work, we improve the PointHop method furthermore in two aspects: 1) reducing its model complexity in terms of the model parameter number and 2) ordering discriminant features automatically based on the cross-entropy criterion. The resulting method is called PointHop++. The first improvement is essential for wearable and mobile computing while the second improvement bridges statistics-based and optimization-based machine learning methodologies. With experiments conducted on the ModelNet40 benchmark dataset, we show that the PointHop++ method performs on par with deep neural network (DNN) solutions and surpasses other unsupervised feature extraction methods.

Pointhop++: A Lightweight Learning Model on Point Sets for 3D Classification

The successive subspace learning (SSL) principle was developed and used to design an interpretable learning model, known as the PixelHop method, for image classification in our prior work. Here, we propose an improved PixelHop method and call it Pixel- Hop++. First, to make the PixelHop model size smaller, we decouple ajoint spatial-spectral input tensor to multiple spatial tensors (one for each spectral component) under the spatial-spectral separability assumption and perform the Saab transform in a channel-wise manner, called the channel-wise (c/w) Saab transform. Second, by performing this operation from one hop to another successively, we construct a channel-decomposed feature tree whose leaf nodes contain features of one dimension (1D). Third, these 1D features are ranked according to their cross-entropy values, which allows us to select a subset of discriminant features for image classification. In Pixel- Hop++, one can control the learning model size of fine-granularity, offering a flexible tradeoff between the model size and the classification performance. We demonstrate the flexibility of PixelHop++ on MNIST, Fashion MNIST, and CIFAR-10 three datasets.

Pixelhop++: A Small Successive-Subspace-Learning-Based (Ssl-Based) Model For Image Classification

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.

PointHop: An Explainable Machine Learning Method for Point Cloud Classification

Inspired by the recent PointHop classification method, an unsupervised 3D point cloud registration method, called R-PointHop, is proposed in this work. R-PointHop first determines a local reference frame (LRF) for every point using its nearest neighbors and finds its local attributes. Next, R-PointHop obtains local-to-global hierarchical features by point downsampling, neighborhood expansion, attribute construction and dimensionality reduction steps. Thus, we can build the correspondence of points in the hierarchical feature space using the nearest neighbor rule. Afterwards, a subset of salient points of good correspondence is selected to estimate the 3D transformation. The use of LRF allows for hierarchical features of points to be invariant with respect to rotation and translation, thus making R-PointHop more robust in building point correspondence even when rotation angles are large. Experiments are conducted on the ModelNet40 and the Stanford Bunny dataset, which demonstrate the effectiveness of R-PointHop on the 3D point cloud registration task. R-PointHop is a green and accurate solution since its model size and training time are smaller than those of deep learning methods by an order of magnitude while its registration errors are smaller. Our codes are available on GitHub.

R-PointHop: A Green, Accurate and Unsupervised Point Cloud Registration Method.

An unsupervised point cloud registration method, called salient points analysis (SPA), is proposed in this work. The proposed SPA method can register two point clouds effectively using only a small subset of salient points. It first applies the PointHop++ method to point clouds, finds corresponding salient points in two point clouds based on the local surface characteristics of points and performs registration by matching the corresponding salient points. The SPA method offers several advantages over the recent deep learning based solutions for registration. Deep learning methods such as PointNetLK and DCP train end-to-end networks and rely on full supervision (namely, ground truth transformation matrix and class label). In contrast, the SPA is completely unsupervised. Furthermore, SPA’s training time and model size are much less. The effectiveness of the SPA method is demonstrated by experiments on seen and unseen classes and noisy point clouds from the ModelNet-40 dataset.

Unsupervised Point Cloud Registration via Salient Points Analysis (SPA)

In contrast to supervised backpropagation-based feature learning in deep neural networks (DNNs), an unsupervised feedforward feature (UFF) learning scheme for joint classification and segmentation of 3D point clouds is proposed in this work. The UFF method exploits statistical correlations of points in a point cloud set to learn shape and point features in a one-pass feedforward manner through a cascaded encoder-decoder architecture. It learns global shape features through the encoder and local point features through the concatenated encoder-decoder architecture. The extracted features of an input point cloud are fed to classifiers f or shape classification and part segmentation. Experiments are conducted to evaluate the performance of the UFF method. For shape classification, the UFF is superior to existing unsupervised methods and on par with state-of-the-art DNNs. For part segmentation, the UFF outperforms semi-supervised methods and performs slightly worse than DNNs.

Pranav Kadam

Papers

PointHop: An Explainable Machine Learning Method for Point Cloud Classification

Pointhop++: A Lightweight Learning Model on Point Sets for 3D Classification

R-PointHop: A Green, Accurate and Unsupervised Point Cloud Registration Method.

Unsupervised Point Cloud Registration via Salient Points Analysis (SPA)

Unsupervised Feedforward Feature (UFF) Learning for Point Cloud Classification and Segmentation