Geometric Cross-Modal Comparison of Heterogeneous Sensor Data

In this work, we address the problem of cross-modal comparison of aerial data streams. A variety of simulated automobile trajectories are sensed using two different modalities: full-motion video, and radio-frequency (RF) signals received by detectors at various locations. The information represented by the two modalities is compared using self-similarity matrices (SSMs) corresponding to time-ordered point clouds in feature spaces of each of these data sources; we note that these feature spaces can be of entirely different scale and dimensionality. Several metrics for comparing SSMs are explored, including a cutting-edge time-warping technique that can simultaneously handle local time warping and partial matches, while also controlling for the change in geometry between feature spaces of the two modalities. We note that this technique is quite general, and does not depend on the choice of modalities. In this particular setting, we demonstrate that the cross-modal distance between SSMs corresponding to the same trajectory type is smaller than the cross-modal distance between SSMs corresponding to distinct trajectory types, and we formalize this observation via precision-recall metrics in experiments. Finally, we comment on promising implications of these ideas for future integration into multiple-hypothesis tracking systems.Comment: 10 pages, 13 figures, Proceedings of IEEE Aeroconf 201

Personalized Purchase Prediction of Market Baskets with Wasserstein-Based Sequence Matching

Personalization in marketing aims at improving the shopping experience of customers by tailoring services to individuals. In order to achieve this, businesses must be able to make personalized predictions regarding the next purchase. That is, one must forecast the exact list of items that will comprise the next purchase, i.e., the so-called market basket. Despite its relevance to firm operations, this problem has received surprisingly little attention in prior research, largely due to its inherent complexity. In fact, state-of-the-art approaches are limited to intuitive decision rules for pattern extraction. However, the simplicity of the pre-coded rules impedes performance, since decision rules operate in an autoregressive fashion: the rules can only make inferences from past purchases of a single customer without taking into account the knowledge transfer that takes place between customers. In contrast, our research overcomes the limitations of pre-set rules by contributing a novel predictor of market baskets from sequential purchase histories: our predictions are based on similarity matching in order to identify similar purchase habits among the complete shopping histories of all customers. Our contributions are as follows: (1) We propose similarity matching based on subsequential dynamic time warping (SDTW) as a novel predictor of market baskets. Thereby, we can effectively identify cross-customer patterns. (2) We leverage the Wasserstein distance for measuring the similarity among embedded purchase histories. (3) We develop a fast approximation algorithm for computing a lower bound of the Wasserstein distance in our setting. An extensive series of computational experiments demonstrates the effectiveness of our approach. The accuracy of identifying the exact market baskets based on state-of-the-art decision rules from the literature is outperformed by a factor of 4.0.Comment: Accepted for oral presentation at 25th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD 2019

Probabilistic embeddings of the Fr\'echet distance

The Fr\'echet distance is a popular distance measure for curves which naturally lends itself to fundamental computational tasks, such as clustering, nearest-neighbor searching, and spherical range searching in the corresponding metric space. However, its inherent complexity poses considerable computational challenges in practice. To address this problem we study distortion of the probabilistic embedding that results from projecting the curves to a randomly chosen line. Such an embedding could be used in combination with, e.g. locality-sensitive hashing. We show that in the worst case and under reasonable assumptions, the discrete Fr\'echet distance between two polygonal curves of complexity $t$ in $\mathbb{R}^d$, where $d\in\lbrace 2,3,4,5\rbrace$, degrades by a factor linear in $t$ with constant probability. We show upper and lower bounds on the distortion. We also evaluate our findings empirically on a benchmark data set. The preliminary experimental results stand in stark contrast with our lower bounds. They indicate that highly distorted projections happen very rarely in practice, and only for strongly conditioned input curves. Keywords: Fr\'echet distance, metric embeddings, random projectionsComment: 27 pages, 11 figure

Generating Labels for Regression of Subjective Constructs using Triplet Embeddings

Human annotations serve an important role in computational models where the target constructs under study are hidden, such as dimensions of affect. This is especially relevant in machine learning, where subjective labels derived from related observable signals (e.g., audio, video, text) are needed to support model training and testing. Current research trends focus on correcting artifacts and biases introduced by annotators during the annotation process while fusing them into a single annotation. In this work, we propose a novel annotation approach using triplet embeddings. By lifting the absolute annotation process to relative annotations where the annotator compares individual target constructs in triplets, we leverage the accuracy of comparisons over absolute ratings by human annotators. We then build a 1-dimensional embedding in Euclidean space that is indexed in time and serves as a label for regression. In this setting, the annotation fusion occurs naturally as a union of sets of sampled triplet comparisons among different annotators. We show that by using our proposed sampling method to find an embedding, we are able to accurately represent synthetic hidden constructs in time under noisy sampling conditions. We further validate this approach using human annotations collected from Mechanical Turk and show that we can recover the underlying structure of the hidden construct up to bias and scaling factors.Comment: 9 pages, 5 figures, accepted journal pape

On Recursive Edit Distance Kernels with Application to Time Series Classification

This paper proposes some extensions to the work on kernels dedicated to string or time series global alignment based on the aggregation of scores obtained by local alignments. The extensions we propose allow to construct, from classical recursive definition of elastic distances, recursive edit distance (or time-warp) kernels that are positive definite if some sufficient conditions are satisfied. The sufficient conditions we end-up with are original and weaker than those proposed in earlier works, although a recursive regularizing term is required to get the proof of the positive definiteness as a direct consequence of the Haussler's convolution theorem. The classification experiment we conducted on three classical time warp distances (two of which being metrics), using Support Vector Machine classifier, leads to conclude that, when the pairwise distance matrix obtained from the training data is \textit{far} from definiteness, the positive definite recursive elastic kernels outperform in general the distance substituting kernels for the classical elastic distances we have tested.Comment: 14 page