Blind Source Separation with Optimal Transport Non-negative Matrix Factorization

Optimal transport as a loss for machine learning optimization problems has recently gained a lot of attention. Building upon recent advances in computational optimal transport, we develop an optimal transport non-negative matrix factorization (NMF) algorithm for supervised speech blind source separation (BSS). Optimal transport allows us to design and leverage a cost between short-time Fourier transform (STFT) spectrogram frequencies, which takes into account how humans perceive sound. We give empirical evidence that using our proposed optimal transport NMF leads to perceptually better results than Euclidean NMF, for both isolated voice reconstruction and BSS tasks. Finally, we demonstrate how to use optimal transport for cross domain sound processing tasks, where frequencies represented in the input spectrograms may be different from one spectrogram to another.Comment: 22 pages, 7 figures, 2 additional file

On Estimating Multi-Attribute Choice Preferences using Private Signals and Matrix Factorization

Revealed preference theory studies the possibility of modeling an agent's revealed preferences and the construction of a consistent utility function. However, modeling agent's choices over preference orderings is not always practical and demands strong assumptions on human rationality and data-acquisition abilities. Therefore, we propose a simple generative choice model where agents are assumed to generate the choice probabilities based on latent factor matrices that capture their choice evaluation across multiple attributes. Since the multi-attribute evaluation is typically hidden within the agent's psyche, we consider a signaling mechanism where agents are provided with choice information through private signals, so that the agent's choices provide more insight about his/her latent evaluation across multiple attributes. We estimate the choice model via a novel multi-stage matrix factorization algorithm that minimizes the average deviation of the factor estimates from choice data. Simulation results are presented to validate the estimation performance of our proposed algorithm.Comment: 6 pages, 2 figures, to be presented at CISS conferenc

Predicting passenger origin-destination in online taxi-hailing systems

Because of transportation planning, traffic management, and dispatch optimization importance, passenger origin-destination prediction has become one of the most important requirements for intelligent transportation systems management. In this paper, we propose a model to predict the next specified time window travels' origin and destination. To extract meaningful travel flows, we use K-means clustering in four-dimensional space with maximum cluster size limitation for origin and destination zones. Because of the large number of clusters, we use non-negative matrix factorization to decrease the number of travel clusters. Also, we use a stacked recurrent neural network model to predict travel count in each cluster. Comparing our results with other existing models shows that our proposed model has 5-7% lower mean absolute percentage error (MAPE) for 1-hour time windows, and 14% lower MAPE for 30-minute time windows.Comment: 25 pages, 20 figure

Retrospective Higher-Order Markov Processes for User Trails

Users form information trails as they browse the web, checkin with a geolocation, rate items, or consume media. A common problem is to predict what a user might do next for the purposes of guidance, recommendation, or prefetching. First-order and higher-order Markov chains have been widely used methods to study such sequences of data. First-order Markov chains are easy to estimate, but lack accuracy when history matters. Higher-order Markov chains, in contrast, have too many parameters and suffer from overfitting the training data. Fitting these parameters with regularization and smoothing only offers mild improvements. In this paper we propose the retrospective higher-order Markov process (RHOMP) as a low-parameter model for such sequences. This model is a special case of a higher-order Markov chain where the transitions depend retrospectively on a single history state instead of an arbitrary combination of history states. There are two immediate computational advantages: the number of parameters is linear in the order of the Markov chain and the model can be fit to large state spaces. Furthermore, by providing a specific structure to the higher-order chain, RHOMPs improve the model accuracy by efficiently utilizing history states without risks of overfitting the data. We demonstrate how to estimate a RHOMP from data and we demonstrate the effectiveness of our method on various real application datasets spanning geolocation data, review sequences, and business locations. The RHOMP model uniformly outperforms higher-order Markov chains, Kneser-Ney regularization, and tensor factorizations in terms of prediction accuracy

A Generalisable Data Fusion Framework to Infer Mode of Transport Using Mobile Phone Data

Cities often lack up-to-date data analytics to evaluate and implement transport planning interventions to achieve sustainability goals, as traditional data sources are expensive, infrequent, and suffer from data latency. Mobile phone data provide an inexpensive source of geospatial information to capture human mobility at unprecedented geographic and temporal granularity. This paper proposes a method to estimate updated mode of transportation usage in a city, with novel usage of mobile phone application traces to infer previously hard to detect modes, such as bikes and ride-hailing/taxi. By using data fusion and matrix factorisation, we integrate socioeconomic and demographic attributes of the local resident population into the model. We tested the method in a case study of Santiago (Chile), and found that changes from 2012 to 2020 in mode of transportation inferred by the method are coherent with expectations from domain knowledge and the literature, such as ride-hailing trips replacing mass transport.Comment: 19 pages, 8 figure