We present Kernel Point Convolution (KPConv), a new design of point convolution, i.e. that operates on point clouds without any intermediate representation. The convolution weights of KPConv are located in Euclidean space by kernel points, and applied to the input points close to them. Its capacity to use any number of kernel points gives KPConv more flexibility than fixed grid convolutions. Furthermore, these locations are continuous in space and can be learned by the network. Therefore, KPConv can be extended to deformable convolutions that learn to adapt kernel points to local geometry. Thanks to a regular subsampling strategy, KPConv is also efficient and robust to varying densities. Whether they use deformable KPConv for complex tasks, or rigid KPconv for simpler tasks, our networks outperform state-of-the-art classification and segmentation approaches on several datasets. We also offer ablation studies and visualizations to provide understanding of what has been learned by KPConv and to validate the descriptive power of deformable KPConv.
SpiderCNN @cite_17 defines its kernel as a family of polynomial functions applied with a different weight for each neighbor. The weight applied to a neighbor depends on the neighbor's distance-wise order, making the filters spatially inconsistent. By contrast, KPConv weights are located in space and its result is invariant to point order.
@cite_17
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The Kernel Polynomial Method (KPM) is a well-established scheme in quantum physics and quantum chemistry to determine the Eigen value density and spectral properties of large sparse matrices. In this work we demonstrate the high optimization potential and feasibility of peta-scale heterogeneous CPU-GPU implementations of the KPM. At the node level we show that it is possible to decouple the sparse matrix problem posed by KPM from main memory bandwidth both on CPU and GPU. To alleviate the effects of scattered data access we combine loosely coupled outer iterations with tightly coupled block sparse matrix multiple vector operations, which enables pure data streaming. All optimizations are guided by a performance analysis and modelling process that indicates how the computational bottlenecks change with each optimization step. Finally we use the optimized node-level KPM with a hybrid-parallel framework to perform large-scale heterogeneous electronic structure calculations for novel topological materials on a pet scale-class Cray XC30 system. Deep neural networks have enjoyed remarkable success for various vision tasks, however it remains challenging to apply CNNs to domains lacking a regular underlying structures such as 3D point clouds. Towards this we propose a novel convolutional architecture, termed SpiderCNN, to efficiently extract geometric features from point clouds. SpiderCNN is comprised of units called SpiderConv, which extend convolutional operations from regular grids to irregular point sets that can be embedded in ( R ^n ), by parametrizing a family of convolutional filters. We design the filter as a product of a simple step function that captures local geodesic information and a Taylor polynomial that ensures the expressiveness. SpiderCNN inherits the multi-scale hierarchical architecture from classical CNNs, which allows it to extract semantic deep features. Experiments on ModelNet40 demonstrate that SpiderCNN achieves state-of-the-art accuracy (92.4 ) on standard benchmarks, and shows competitive performance on segmentation task. The kernel function plays a central role in kernel methods. Existing methods typically fix the functional form of the kernel in advance and then only adapt the associated kernel parameters based on empirical data. In this paper, we consider the problem of adapting the kernel so that it becomes more similar to the so-called ideal kernel. We formulate this as a distance metric learning problem that searches for a suitable linear transform (feature weighting) in the kernel-induced feature space. This formulation is applicable even when the training set can only provide examples of similar and dissimilar pairs, but not explicit class label information. Computationally, this leads to a local-optima-free quadratic programming problem, with the number of variables independent of the number of features. Performance of this method is evaluated on classification and clustering tasks on both toy and real-world data sets. We describe several families of k-mer based string kernels related to the recently presented mismatch kernel and designed for use with support vector machines (SVMs) for classification of protein sequence data. These new kernels -- restricted gappy kernels, substitution kernels, and wildcard kernels -- are based on feature spaces indexed by k-length subsequences ("k-mers") from the string alphabet &#931. However, for all kernels we define here, the kernel value K(x,y) can be computed in O(cK(|x|+|y|)) time, where the constant cK depends on the parameters of the kernel but is independent of the size |&#931| of the alphabet. Thus the computation of these kernels is linear in the length of the sequences, like the mismatch kernel, but we improve upon the parameter-dependent constant cK = km+1|&#931|m of the (k,m)-mismatch kernel. We compute the kernels efficiently using a trie data structure and relate our new kernels to the recently described transducer formalism. In protein classification experiments on two benchmark SCOP data sets, we show that our new faster kernels achieve SVM classification performance comparable to the mismatch kernel and the Fisher kernel derived from profile hidden Markov models, and we investigate the dependence of the kernels on parameter choice.