Multi-label classification allows a datapoint to be labelled with more than one class at the same time. Ensemble methods generally perform much better than single classifiers. Except bagging style ensembles like ECC, RAkEL, in multi-label classification, other ensemble methods have not been explored much. KFHE (Kalman Filter-based Heuristic Ensemble), is a recent ensemble method which uses the Kalman filter to combine several models. KFHE views the final ensemble to be learned as a state to be estimated which it estimates using multiple noisy "measurements". These "measurements" are essentially component classifiers trained under different settings. This work extends KFHE to multi-label domain by proposing KFHE-HOMER which enhances the performance of HOMER using the KFHE framework. KFHE-HOMER sequentially trains multiple HOMER classifiers using weighted training datapoints and random hyperparameters. These models are considered as measurements and their related error as the uncertainty of the measurements. Then the Kalman filter framework is used to combine these measurements to get a more accurate estimate. The method was tested on 10 multi-label datasets and compared with other multi-label classification algorithms. Results show that KFHE-HOMER performs consistently better than similar multi-label ensemble methods.
Here @math , the measurement, can be an external source or sensor (voltage or altitude sensor), @math is the related measurement variance indicating the uncertainty of the estimate. The @math is the , which optimally combines the estimate and the measurement. A complete and detailed explanation of Kalman filters can be found in @cite_8 @cite_22 .
@cite_22 @cite_8
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Consider @math sensors placed randomly and independently with the uniform distribution in a unit square. The sensors have identical sensing range equal to @math , for some @math . We are interested in moving the sensors from their initial positions to new positions so as to ensure that the unit square is completely covered, i.e., every point in the squarei¾?is within the range of a sensor. If the @math -th sensor is displaced a distance @math , what is a displacement of minimum cost? As cost measure for the displacement of the team of sensors we consider thei¾? @math -total movement defined as the sum @math , for some constant @math . We assume that @math and @math are chosen so as to allow full coverage of the square and @math . The main contribution of the paper is to show the existence of a tradeoff between the square sensing radius and @math -total movement and can be summarized as follows:1.If the square sensing radius is equal to @math and @math is the square of a natural number we present an algorithm and show that in expectation the @math -total movement is in @math .2.If the square sensing radius is greater than @math and @math is natural number then we present an algorithm and show that in expectation the @math -total movement is in @math . Therefore this sharp decrease from @math to @math in the @math -total movement of the sensors to attain complete coverage of the square indicates the presence of an interesting threshold on the square sensing radius when it increases from @math to @math . In addition, we simulate our algorithms above and discuss the results of our simulations. The main contribution of this paper is an extended Kalman filter (EKF)based algorithm for estimating the 6 DOF pose of a camera using monocular images of an indoor environment. In contrast to popular visual simultaneous localisation and mapping algorithms, the technique proposed relies on a pre-built map represented as an unsigned distance function of the ground plane edges. Images from the camera are processed using a Convolutional Neural Network (CNN)to extract a ground plane edge image. Pixels that belong to these edges are used in the observation equation of the EKF to estimate the camera location. Use of the CNN makes it possible to extract ground plane edges under significant changes to scene illumination. The EKF framework lends itself to use of a suitable motion model, fusing information from any other sensors such as wheel encoders or inertial measurement units, if available, and rejecting spurious observations. A series of experiments are presented to demonstrate the effectiveness of the proposed technique. By exploiting the communication infrastructure among the sensors, actuators, and control systems, attackers may compromise the security of smart-grid systems, with techniques such as denial-of-service (DoS) attack, random attack, and data-injection attack. In this paper, we present a mathematical model of the system to study these pitfalls and propose a robust security framework for the smart grid. Our framework adopts the Kalman filter to estimate the variables of a wide range of state processes in the model. The estimates from the Kalman filter and the system readings are then fed into the @math -detector or the proposed Euclidean detector. The @math -detector is a proven effective exploratory method used with the Kalman filter for the measurement of the relationship between dependent variables and a series of predictor variables. The @math -detector can detect system faults attacks, such as DoS attack, short-term, and long-term random attacks. However, the studies show that the @math -detector is unable to detect the statistically derived false data-injection attack. To overcome this limitation, we prove that the Euclidean detector can effectively detect such a sophisticated injection attack. This paper presents a method to fuse measurements from a rigid sensor rig with a stereo vision system and a set of 6 DOF inertial sensors for egomotion estimation and external structure estimation. No assumptions about the sampling rate of the two sensors are made. The basic idea is a common state vector and a common dynamic description which is stored together with the time instant of the estimation. Every time one of the sensor sends new data, the corresponding filter equation is updated and a new estimation is generated. In this paper the filter equations for an extended Kalman filter are derived together with considerations of the tuning. Simulations with real sensor data show the successful implementation of this concept. © 2004 Wiley Periodicals, Inc.