A reliable order-statistics-based approximate nearest neighbor search algorithm

We propose a new algorithm for fast approximate nearest neighbor search based on the properties of ordered vectors. Data vectors are classified based on the index and sign of their largest components, thereby partitioning the space in a number of cones centered in the origin. The query is itself classified, and the search starts from the selected cone and proceeds to neighboring ones. Overall, the proposed algorithm corresponds to locality sensitive hashing in the space of directions, with hashing based on the order of components. Thanks to the statistical features emerging through ordering, it deals very well with the challenging case of unstructured data, and is a valuable building block for more complex techniques dealing with structured data. Experiments on both simulated and real-world data prove the proposed algorithm to provide a state-of-the-art performance

Representing 3D shape in sparse range images for urban object classification

This thesis develops techniques for interpreting 3D range images acquired in outdoor environments at a low resolution. It focuses on the task of robustly capturing the shapes that comprise objects, in order to classify them. With the recent development of 3D sensors such as the Velodyne, it is now possible to capture range images at video frame rates, allowing mobile robots to observe dynamic scenes in 3D. To classify objects in these scenes, features are extracted from the data, which allows different regions to be matched. However, range images acquired at this speed are of low resolution, and there are often significant changes in sensor viewpoint and occlusion. In this context, existing methods for feature extraction do not perform well. This thesis contributes algorithms for the robust abstraction from 3D points to object classes. Efficient region-of-interest and surface normal extraction are evaluated, resulting in a keypoint algorithm that provides stable orientations. These build towards a novel feature, called the ‘line image,’ that is designed to consistently capture local shape, regardless of sensor viewpoint. It does this by explicitly reasoning about the difference between known empty space, and space that has not been measured due to occlusion or sparse sensing. A dataset of urban objects scanned with a Velodyne was collected and hand labelled, in order to compare this feature with several others on the task of classification. First, a simple k-nearest neighbours approach was used, where the line image showed improvements. Second, more complex classifiers were applied, requiring the features to be clustered. The clusters were used in topic modelling, allowing specific sub-parts of objects to be learnt across multiple scales, improving accuracy by 10%. This work is applicable to any range image data. In general, it demonstrates the advantages in using the inherent density and occupancy information in a range image during 3D point cloud processing

Representing 3D shape in sparse range images for urban object classification

This thesis develops techniques for interpreting 3D range images acquired in outdoor environments at a low resolution. It focuses on the task of robustly capturing the shapes that comprise objects, in order to classify them. With the recent development of 3D sensors such as the Velodyne, it is now possible to capture range images at video frame rates, allowing mobile robots to observe dynamic scenes in 3D. To classify objects in these scenes, features are extracted from the data, which allows different regions to be matched. However, range images acquired at this speed are of low resolution, and there are often significant changes in sensor viewpoint and occlusion. In this context, existing methods for feature extraction do not perform well. This thesis contributes algorithms for the robust abstraction from 3D points to object classes. Efficient region-of-interest and surface normal extraction are evaluated, resulting in a keypoint algorithm that provides stable orientations. These build towards a novel feature, called the ‘line image,’ that is designed to consistently capture local shape, regardless of sensor viewpoint. It does this by explicitly reasoning about the difference between known empty space, and space that has not been measured due to occlusion or sparse sensing. A dataset of urban objects scanned with a Velodyne was collected and hand labelled, in order to compare this feature with several others on the task of classification. First, a simple k-nearest neighbours approach was used, where the line image showed improvements. Second, more complex classifiers were applied, requiring the features to be clustered. The clusters were used in topic modelling, allowing specific sub-parts of objects to be learnt across multiple scales, improving accuracy by 10%. This work is applicable to any range image data. In general, it demonstrates the advantages in using the inherent density and occupancy information in a range image during 3D point cloud processing

Unmasking Clever Hans Predictors and Assessing What Machines Really Learn

Current learning machines have successfully solved hard application problems, reaching high accuracy and displaying seemingly "intelligent" behavior. Here we apply recent techniques for explaining decisions of state-of-the-art learning machines and analyze various tasks from computer vision and arcade games. This showcases a spectrum of problem-solving behaviors ranging from naive and short-sighted, to well-informed and strategic. We observe that standard performance evaluation metrics can be oblivious to distinguishing these diverse problem solving behaviors. Furthermore, we propose our semi-automated Spectral Relevance Analysis that provides a practically effective way of characterizing and validating the behavior of nonlinear learning machines. This helps to assess whether a learned model indeed delivers reliably for the problem that it was conceived for. Furthermore, our work intends to add a voice of caution to the ongoing excitement about machine intelligence and pledges to evaluate and judge some of these recent successes in a more nuanced manner.Comment: Accepted for publication in Nature Communication

Persistence codebooks for topological data analysis

Persistent homology is a rigorous mathematical theory that provides a robust descriptor of data in the form of persistence diagrams (PDs) which are 2D multisets of points. Their variable size makes them, however, difficult to combine with typical machine learning workflows. In this paper we introduce persistence codebooks, a novel expressive and discriminative fixed-size vectorized representation of PDs that adapts to the inherent sparsity of persistence diagrams. To this end, we adapt bag-of-words, vectors of locally aggregated descriptors and Fischer vectors for the quantization of PDs. Persistence codebooks represent PDs in a convenient way for machine learning and statistical analysis and have a number of favorable practical and theoretical properties including 1-Wasserstein stability. We evaluate the presented representations on several heterogeneous datasets and show their (high) discriminative power. Our approach yields comparable-and partly even higher-performance in much less time than alternative approaches