Time Series Averaging Using Multi-Tasking Autoencoder

Abstract

The estimation of an optimal time series average has been studied for over three decades. The process is mainly challenging due to temporal distortion. Previous approaches mostly addressed this challenge by using alignment algorithms such as Dynamic Time Warping (DTW). However, the quadratic computational complexity of DTW and its inability to align more than two time series simultaneously complicate the estimation. In this paper, we follow a different path and state the averaging problem as a generative problem. To this end, we propose a multi-tasking convolutional autoencoder architecture to extract latent features of similarly labeled time series under the influence of temporal distortion. We then take the arithmetic mean of latent features as an estimate of the latent mean. Moreover, we project these estimations and investigate their performance in the time domain. We evaluated the proposed approach through one nearest centroid classification using 85 data sets obtained from the UCR archive. Experimental results show that, in the latent space, the proposed multi-tasking autoencoder achieves competitive accuracies as compared to the state-of-the-art, thus demonstrating that the learned latent space is suitable to compute time series averages. In addition, the time domain projection of latent space means provides superior results as compared to time domain arithmetic means.

A Multivariate Approach for Spatiotemporal Mobile Data Traffic Prediction

“…CNN models are typically employed to analyze spatial or multidimensional data. However, one-dimensional CNN (1D CNN) can also be used to analyze texts and timeseries data [16]; 1D CNN can extract salient and representative features of time-series data by performing 1D convolution operations using multiple filters [17]. Figure 3 shows the difference between 1D CNN and 2D CNN.…”

Deep Representation Learning for Cluster-Level Time Series Forecasting

“…We propose to overcome this limitation by utilizing a multitasking autoencoder, which is set to perform multi-class classification and reconstruction. This configuration was proposed in [18], in order to estimate the averages of multi-class temporal datasets from their latent embedding. With this in mind, we will next present the methodology used.…”

“…In general, the multitasking setup optimizes for reconstruction and the multi-class classification losses given in (5), where X i , Xi are input and reconstructed time series in R N . Moreover, p i,j are the softmax activation values (the likelihood) of a series X i belonging to category (Cat) [18]. In terms of layer arrangements, the multitasking network is constructed from transposed and normal convolutional, max-pooling, flattening, and dense layers [25].…”

“…The average estimated using the arithmetic mean is smaller, due to the presence of a phase shift (temporal distortion). In general, in practice, temporal distortion often forces the arithmetic mean to aggregate shapes in a destructive manner [17,18]. Therefore, we often expect a cluster-level forecasting model that is based on an arithmetic mean to be affected by underprediction.…”

“…In this regard, we show the advantage of utilizing representation learning, which aims to identify patterns that are presumed to be useful for cluster formation in the latent space of neural networks [19]. Moreover, we also propose to utilize a neural network architecture that is able to estimate time-domain cluster centroids from latent representations [18]. In reality, the utilization of neural networks for the cluster formation and centroid estimation is expected to be advantageous as a result of at least one factor, i.e., transfer learning [20].…”