Sequential Logistic Principal Component Analysis (SLPCA): Dimensional Reduction in Streaming Multivariate Binary-State System

Sequential or online dimensional reduction is of interests due to the explosion of streaming data based applications and the requirement of adaptive statistical modeling, in many emerging fields, such as the modeling of energy end-use profile. Principal Component Analysis (PCA), is the classical way of dimensional reduction. However, traditional Singular Value Decomposition (SVD) based PCA fails to model data which largely deviates from Gaussian distribution. The Bregman Divergence was recently introduced to achieve a generalized PCA framework. If the random variable under dimensional reduction follows Bernoulli distribution, which occurs in many emerging fields, the generalized PCA is called Logistic PCA (LPCA). In this paper, we extend the batch LPCA to a sequential version (i.e. SLPCA), based on the sequential convex optimization theory. The convergence property of this algorithm is discussed compared to the batch version of LPCA (i.e. BLPCA), as well as its performance in reducing the dimension for multivariate binary-state systems. Its application in building energy end-use profile modeling is also investigated.Comment: 6 pages, 4 figures, conference submissio

Efficient Multi-Level Modeling and Monitoring of End-use Energy Profile in Commercial Buildings

In this work, modeling and monitoring of end-use power consumption in commercial buildings are investigated through both Top-Down and Bottom-Up approaches. In the Top-Down approach, an adaptive support vector regression (ASVR) model is developed to accommodate the nonlinearity and nonstationarity of the macro-level time series, thus providing a framework for the modeling and diagnosis of end-use power consumption. In the Bottom-Up approach, an appliance-data-driven stochastic model is built to predict each end-use sector of a commercial building. Power disaggregation is studied as a technique to facilitate Bottom-Up prediction. In Bottom-Up monitoring and diagnostic detection, a new dimensionality reduction technique is explored to facilitate the analysis of multivariate binary behavioral signals in building end-uses

Sequential Logistic Principal Component Analysis (SLPCA): Dimensional Reduction in Streaming Multivariate Binary-State System

Sequential or online dimensional reduction is of interests due to the explosion of streaming data based applications and the requirement of adaptive statistical modeling, in many emerging fields, such as the modeling of energy end-use profile. Principal Component Analysis (PCA), is the classical way of dimensional reduction. However, traditional PCA coincides with maximum likelihood interpretation only when data follows Gaussian distribution. The Bregman Divergence was introduced to extend PCA with maximum likelihood in exponential family distribution. In this work, we study this generalized form PCA for Bernoulli variables, which is called Logistic PCA (LPCA). We extend the batch-mode LPCA [1] to a sequential version (SLPCA). The convergence property of this algorithm is discussed compared to the batch version (BLPCA), as well as its performance in reducing the dimension for multivariate binarystate systems. Its application in building energy end-use profile modeling is also investigated

Parametric Dual Maximization for Non-Convex Learning Problems

We consider a class of non-convex learning problems that can be formulated as jointly optimizing regularized hinge loss and a set of auxiliary variables. Such problems encompass but are not limited to various versions of semi-supervised learning,learning with hidden structures, robust learning, etc. Existing methods either suffer from local minima or have to invoke anon-scalable combinatorial search. In this paper, we propose a novel learning procedure, namely Parametric Dual Maximization(PDM), that can approach global optimality efficiently with user specified approximation levels. The building blocks of PDM are two new results: (1) The equivalent convex maximization reformulation derived by parametric analysis.(2) The improvement of local solutions based on a necessary and sufficient condition for global optimality. Experimental results on two representative applications demonstrate the effectiveness of PDM compared to other approaches

Modeling of End-Use Energy Profile: An Appliance-Data-Driven Stochastic Approach

In this paper, the modeling of building end-use energy profile is comprehensively investigated. Top-down and Bottom-up approaches are discussed with a focus on the latter for better integration with occupant information. Compared to the Time-Of-Use (TOU) data used in previous Bottom-up models, this work utilizes high frequency sampled appliance power consumption data from wireless sensor network, and hence builds an appliance-data-driven probability based end-use energy profile model. ON/OFF probabilities of appliances are used in this model, to build a non-homogeneous Markov Chain, compared to the duration statistics based model that is widely used in other works. The simulation results show the capability of the model to capture the diversity and variability of different categories of end-use appliance energy profile, which can further help on the design of a modern robust building power system

Modeling of End-Use Energy Profile: An Appliance-Data-Driven Stochastic Approach

In this paper, the modeling of building end-use energy profile is comprehensively investigated. Top-down and Bottom-up approaches are discussed with a focus on the latter for better integration with occupant information. Compared to the Time-Of-Use (TOU) data used in previous Bottom-up models, this work utilizes high frequency sampled appliance power consumption data from wireless sensor network, and hence builds an appliance-data-driven probability based end-use energy profile model. ON/OFF probabilities of appliances are used in this model, to build a non-homogeneous Markov Chain, compared to the duration statistics based model that is widely used in other works. The simulation results show the capability of the model to capture the diversity and variability of different categories of end-use appliance energy profile, which can further help on the design of a modern robust building power system

Virtual Power Sensing Based on a Multiple-Hypothesis Sequential Test

Virtual-Sensing, which is achieved through the disaggregation of composite power metering signals, is a solution towards achieving fine-grained smart power monitoring. In this work we discuss the challenging issues in Virtual-Sensing, introduce and ultimately combine the Hidden Markov Model and the Edge-based methods. T he resulting solution, based on a Multiple-hypothesis Sequential Probability Ratio Test, combines the advantages of the two methods and delivers significant improvement in disaggregation performance. A robust version of the test is also proposed to filter the impulse noise common in real-time monitoring of the plug-in loads power consumption