Discrimination on the Grassmann Manifold: Fundamental Limits of Subspace Classifiers

We present fundamental limits on the reliable classification of linear and affine subspaces from noisy, linear features. Drawing an analogy between discrimination among subspaces and communication over vector wireless channels, we propose two Shannon-inspired measures to characterize asymptotic classifier performance. First, we define the classification capacity, which characterizes necessary and sufficient conditions for the misclassification probability to vanish as the signal dimension, the number of features, and the number of subspaces to be discerned all approach infinity. Second, we define the diversity-discrimination tradeoff which, by analogy with the diversity-multiplexing tradeoff of fading vector channels, characterizes relationships between the number of discernible subspaces and the misclassification probability as the noise power approaches zero. We derive upper and lower bounds on these measures which are tight in many regimes. Numerical results, including a face recognition application, validate the results in practice.Comment: 19 pages, 4 figures. Revised submission to IEEE Transactions on Information Theor

Cooperative Compute-and-Forward

We examine the benefits of user cooperation under compute-and-forward. Much like in network coding, receivers in a compute-and-forward network recover finite-field linear combinations of transmitters' messages. Recovery is enabled by linear codes: transmitters map messages to a linear codebook, and receivers attempt to decode the incoming superposition of signals to an integer combination of codewords. However, the achievable computation rates are low if channel gains do not correspond to a suitable linear combination. In response to this challenge, we propose a cooperative approach to compute-and-forward. We devise a lattice-coding approach to block Markov encoding with which we construct a decode-and-forward style computation strategy. Transmitters broadcast lattice codewords, decode each other's messages, and then cooperatively transmit resolution information to aid receivers in decoding the integer combinations. Using our strategy, we show that cooperation offers a significant improvement both in the achievable computation rate and in the diversity-multiplexing tradeoff.Comment: submitted to IEEE Transactions on Information Theor

Improving Short-Term Electricity Price Forecasting Using Day-Ahead LMP with ARIMA Models

Short-term electricity price forecasting has become important for demand side management and power generation scheduling. Especially as the electricity market becomes more competitive, a more accurate price prediction than the day-ahead locational marginal price (DALMP) published by the independent system operator (ISO) will benefit participants in the market by increasing profit or improving load demand scheduling. Hence, the main idea of this paper is to use autoregressive integrated moving average (ARIMA) models to obtain a better LMP prediction than the DALMP by utilizing the published DALMP, historical real-time LMP (RTLMP) and other useful information. First, a set of seasonal ARIMA (SARIMA) models utilizing the DALMP and historical RTLMP are developed and compared with autoregressive moving average (ARMA) models that use the differences between DALMP and RTLMP on their forecasting capability. A generalized autoregressive conditional heteroskedasticity (GARCH) model is implemented to further improve the forecasting by accounting for the price volatility. The models are trained and evaluated using real market data in the Midcontinent Independent System Operator (MISO) region. The evaluation results indicate that the ARMAX-GARCH model, where an exogenous time series indicates weekend days, improves the short-term electricity price prediction accuracy and outperforms the other proposed ARIMA modelsComment: IEEE PES 2017 General Meeting, Chicago, I