Accurate taxi demand-supply forecasting is a challenging application of ITS (Intelligent Transportation Systems), due to the complex spatial and temporal patterns. We investigate the impact of different spatial partitioning techniques on the prediction performance of an LSTM (Long Short-Term Memory) network, in the context of taxi demand-supply forecasting. We consider two tessellation schemes: (i) the variable-sized Voronoi tessellation, and (ii) the fixed-sized Geohash tessellation. While the widely employed ConvLSTM (Convolutional LSTM) can model fixed-sized Geohash partitions, the standard convolutional filters cannot be applied on the variable-sized Voronoi partitions. To explore the Voronoi tessellation scheme, we propose the use of GraphLSTM (Graph-based LSTM), by representing the Voronoi spatial partitions as nodes on an arbitrarily structured graph. The GraphLSTM offers competitive performance against ConvLSTM, at lower computational complexity, across three real-world large-scale taxi demand-supply data sets, with different performance metrics. To ensure superior performance across diverse settings, a HEDGE based ensemble learning algorithm is applied over the ConvLSTM and the GraphLSTM networks.
Our modeling framework deviates significantly from the existing literature as we employ a GraphLSTM (Graph-based LSTM) @cite_25 model to learn an arbitrarily structured graph, where each node corresponds to the aggregated demand in a spatial Voronoi partition. To the best of our knowledge, in the context of spatial partitioning, Graph-based RNNs have not been explored in the literature. Another important contribution of this paper lies in understanding the impact of different spatial partitioning schemes on the predictive performance of RNNs. To that end, we perform a comparison of the Geohash-based ConvLSTM and the Voronoi-based GraphLSTM. These features set our work apart from the existing literature. A part of this work was presented as a poster at the NIPS Workshop on Machine Learning in Intelligent Transportation Systems, 2018 @cite_26 .
@cite_26 @cite_25
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In this paper, we investigate the significance of choosing an appropriate tessellation strategy for a spatio-temporal taxi demand-supply modeling framework. Our study compares (i) the variable-sized polygon based Voronoi tessellation, and (ii) the fixed-sized grid based Geohash tessellation, using taxi demand-supply GPS data for the cities of Bengaluru, India and New York, USA. Long Short-Term Memory (LSTM) networks are used for modeling and incorporating information from spatial neighbors into the model. We find that the LSTM model based on input features extracted from a variable-sized polygon tessellation yields superior performance over the LSTM model based on fixed-sized grid tessellation. Our study highlights the need to explore multiple spatial partitioning techniques for improving the prediction performance in neural network models. Hypergraph partitioning lies at the heart of a number of problems in machine learning and network sciences. Many algorithms for hypergraph partitioning have been proposed that extend standard approaches for graph partitioning to the case of hypergraphs. However, theoretical aspects of such methods have seldom received attention in the literature as compared to the extensive studies on the guarantees of graph partitioning. For instance, consistency results of spectral graph partitioning under the stochastic block model are well known. In this paper, we present a planted partition model for sparse random non-uniform hypergraphs that generalizes the stochastic block model. We derive an error bound for a spectral hypergraph partitioning algorithm under this model using matrix concentration inequalities. To the best of our knowledge, this is the first consistency result related to partitioning non-uniform hypergraphs. Partitioning graphs at scale is a key challenge for any application that involves distributing a graph across disks, machines, or data centers. Graph partitioning is a very well studied problem with a rich literature, but existing algorithms typically can not scale to billions of edges, or can not provide guarantees about partition sizes. In this work we introduce an efficient algorithm, balanced label propagation, for precisely partitioning massive graphs while greedily maximizing edge locality, the number of edges that are assigned to the same shard of a partition. By combining the computational efficiency of label propagation --- where nodes are iteratively relabeled to the same 'label' as the plurality of their graph neighbors --- with the guarantees of constrained optimization --- guiding the propagation by a linear program constraining the partition sizes --- our algorithm makes it practically possible to partition graphs with billions of edges. Our algorithm is motivated by the challenge of performing graph predictions in a distributed system. Because this requires assigning each node in a graph to a physical machine with memory limitations, it is critically necessary to ensure the resulting partition shards do not overload any single machine. We evaluate our algorithm for its partitioning performance on the Facebook social graph, and also study its performance when partitioning Facebook's 'People You May Know' service (PYMK), the distributed system responsible for the feature extraction and ranking of the friends-of-friends of all active Facebook users. In a live deployment, we observed average query times and average network traffic levels that were 50.5 and 37.1 (respectively) when compared to the previous naive random sharding. Recent skeleton-based action recognition approaches achieve great improvement by using recurrent neural network (RNN) models. Currently, these approaches build an end-to-end network from coordinates of joints to class categories and improve accuracy by extending RNN to spatial domains. First, while such well-designed models and optimization strategies explore relations between different parts directly from joint coordinates, we provide a simple universal spatial modeling method perpendicular to the RNN model enhancement. Specifically, according to the evolution of previous work, we select a set of simple geometric features, and then seperately feed each type of features to a three-layer LSTM framework. Second, we propose a multistream LSTM architecture with a new smoothed score fusion technique to learn classification from different geometric feature streams. Furthermore, we observe that the geometric relational features based on distances between joints and selected lines outperform other features and the fusion results achieve the state-of-the-art performance on four datasets. We also show the sparsity of input gate weights in the first LSTM layer trained by geometric features and demonstrate that utilizing joint-line distances as input require less data for training.