Nonparametric Feature Extraction from Dendrograms

We propose feature extraction from dendrograms in a nonparametric way. The Minimax distance measures correspond to building a dendrogram with single linkage criterion, with defining specific forms of a level function and a distance function over that. Therefore, we extend this method to arbitrary dendrograms. We develop a generalized framework wherein different distance measures can be inferred from different types of dendrograms, level functions and distance functions. Via an appropriate embedding, we compute a vector-based representation of the inferred distances, in order to enable many numerical machine learning algorithms to employ such distances. Then, to address the model selection problem, we study the aggregation of different dendrogram-based distances respectively in solution space and in representation space in the spirit of deep representations. In the first approach, for example for the clustering problem, we build a graph with positive and negative edge weights according to the consistency of the clustering labels of different objects among different solutions, in the context of ensemble methods. Then, we use an efficient variant of correlation clustering to produce the final clusters. In the second approach, we investigate the sequential combination of different distances and features sequentially in the spirit of multi-layered architectures to obtain the final features. Finally, we demonstrate the effectiveness of our approach via several numerical studies

A Deep Learning Framework for Generation and Analysis of Driving Scenario Trajectories

We propose a unified deep learning framework for generation and analysis of driving scenario trajectories, and validate its effectiveness in a principled way. In order to model and generate scenarios of trajectories with different length, we develop two approaches. First, we adapt the Recurrent Conditional Generative Adversarial Networks (RC-GAN) by conditioning on the length of the trajectories. This provides us flexibility to generate variable-length driving trajectories, a desirable feature for scenario test case generation in the verification of self-driving cars. Second, we develop an architecture based on Recurrent Autoencoder with GANs in order to obviate the variable length issue, wherein we train a GAN to learn/generate the latent representations of original trajectories. In this approach, we train an integrated feed-forward neural network to estimate the length of the trajectories to be able to bring them back from the latent space representation. In addition to trajectory generation, we employ the trained autoencoder as a feature extractor, for the purpose of clustering and anomaly detection, in order to obtain further insights on the collected scenario dataset. We experimentally investigate the performance of the proposed framework on real-world scenario trajectories obtained from in-field data collection

A Deep Learning Framework for Generation and Analysis of Driving Scenario Trajectories

We propose a unified deep learning framework for the generation and analysis of driving scenario trajectories, and validate its effectiveness in a principled way. To model and generate scenarios of trajectories with different lengths, we develop two approaches. First, we adapt the Recurrent Conditional Generative Adversarial Networks (RC-GAN) by conditioning on the length of the trajectories. This provides us the flexibility to generate variable-length driving trajectories, a desirable feature for scenario test case generation in the verification of autonomous driving. Second, we develop an architecture based on Recurrent Autoencoder with GANs to obviate the variable length issue, wherein we train a GAN to learn/generate the latent representations of original trajectories. In this approach, we train an integrated feed-forward neural network to estimate the length of the trajectories to be able to bring them back from the latent space representation. In addition to trajectory generation, we employ the trained autoencoder as a feature extractor, for the purpose of clustering and anomaly detection, to obtain further insights into the collected scenario dataset. We experimentally investigate the performance of the proposed framework on real-world scenario trajectories obtained from in-field data collection

Learning representations from dendrograms

We propose unsupervised representation learning and feature extraction from dendrograms. The commonly used Minimax distance measures correspond to building a dendrogram with single linkage criterion, with defining specific forms of a level function and a distance function over that. Therefore, we extend this method to arbitrary dendrograms. We develop a generalized framework wherein different distance measures and representations can be inferred from different types of dendrograms, level functions and distance functions. Via an appropriate embedding, we compute a vector-based representation of the inferred distances, in order to enable many numerical machine learning algorithms to employ such distances. Then, to address the model selection problem, we study the aggregation of different dendrogram-based distances respectively in solution space and in representation space in the spirit of deep representations. In the first approach, for example for the clustering problem, we build a graph with positive and negative edge weights according to the consistency of the clustering labels of different objects among different solutions, in the context of ensemble methods. Then, we use an efficient variant of correlation clustering to produce the final clusters. In the second approach, we investigate the combination of different distances and features sequentially in the spirit of multi-layered architectures to obtain the final features. Finally, we demonstrate the effectiveness of our approach via several numerical studies

Unsupervised representation learning with Minimax distance measures

We investigate the use of Minimax distances to extract in a nonparametric way the features that capture the unknown underlying patterns and structures in the data. We develop a general-purpose and computationally efficient framework to employ Minimax distances with many machine learning methods that perform on numerical data. We study both computing the pairwise Minimax distances for all pairs of objects and as well as computing the Minimax distances of all the objects to/from a fixed (test) object. We first efficiently compute the pairwise Minimax distances between the objects, using the equivalence of Minimax distances over a graph and over a minimum spanning tree constructed on that. Then, we perform an embedding of the pairwise Minimax distances into a new vector space, such that their squared Euclidean distances in the new space equal to the pairwise Minimax distances in the original space. We also study the case of having multiple pairwise Minimax matrices, instead of a single one. Thereby, we propose an embedding via first summing up the centered matrices and then performing an eigenvalue decomposition to obtain the relevant features. In the following, we study computing Minimax distances from a fixed (test) object which can be used for instance in K-nearest neighbor search. Similar to the case of all-pair pairwise Minimax distances, we develop an efficient and general-purpose algorithm that is applicable with any arbitrary base distance measure. Moreover, we investigate in detail the edges selected by the Minimax distances and thereby explore the ability of Minimax distances in detecting outlier objects. Finally, for each setting, we perform several experiments to demonstrate the effectiveness of our framework