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Smartphone-Based Human Activity Recognition
Published in Yufeng Wang, Athanasios V. Vasilakos, Qun Jin, Hongbo Zhu, Device-to-Device based Proximity Service, 2017
Yufeng Wang, Athanasios V. Vasilakos, Qun Jin, Hongbo Zhu
HMMs can be considered as a set of states which are traversed in a sequence hidden to an observer. The only thing that is visible is a sequence of observed symbols, emitted by each of the hidden states while they are traversed. Related to HMM, the following several efficient algorithms are used for learning and recognition: Forward–backward algorithm is used for determining the probability that an emission sequence was generated by a given HMM. The forward pass computes the probability of being in a state at a particular time, given the observation sequence up to that time, so summing over all states at the end is required.Baum–Welch algorithm is used for estimating transition and emission probabilities of a HMM, given an observation sequence and initial guesses for these values. As an expectation-maximization algorithm, it uses an iterative search for the parameters with the highest likelihood.Viterbi algorithm (it is the training algorithm, not to be confused with Viterbi decoding algorithm) is used to find the most likely sequence of hidden states, given a HMM and an observation sequence. It computes the recursive likelihood of being in each state at the next time step until the end of the sequence, at which point, the algorithm backtracks to give the most likely state sequence.
Lifetime Data and Concepts
Published in Prabhanjan Narayanachar Tattar, H. J. Vaman, Survival Analysis, 2022
Prabhanjan Narayanachar Tattar, H. J. Vaman
As simple as the data appears in Table 1.1, we can see two major challenges. First, as mentioned earlier, though we do not have the censored observations, the lifetime values are incompletely recorded and at best we know the lower bound and upper bound on the actual lifetime values. The incomplete information can be handled using the Expectation-Maximization algorithm, or simply the EM algorithm. The problem will be specifically addressed in Chapter 2.
Unsupervised Learning
Published in Dirk P. Kroese, Zdravko I. Botev, Thomas Taimre, Radislav Vaisman, Data Science and Machine Learning, 2019
Dirk P. Kroese, Zdravko I. Botev, Thomas Taimre, Radislav Vaisman
The Expectation–Maximization algorithm (EM) is a general algorithm for maximization of complicated (log-)likelihood functions, through the introduction of auxiliary variables.
Application of Image Processing Techniques and Artificial Neural Network for Detection of Diseases on Brinjal Leaf
Published in IETE Journal of Research, 2022
The posterior distribution is expressed as the (normalised) product of likelihood, such as the Gaussian mixture models (GMM), a model which gives the distribution of images corresponding to a given class, and a prior probability distribution on the classifications. EM (Expectation–Maximization) algorithm is used to compute maximum-likelihood parameter when the observations are incomplete. The EM algorithm requires the initialization of model parameters of Gaussian mixture [16]. The density of probability of this mixture is given in equation (15) where is the characteristic vector, is the weight of the mixture, given by and represents the parameters is the density of the Gaussian parameterised by that is to say where is the Gaussian mixture distribution parameter.
Expectation-Maximization Algorithm for Identification of Mesh-based Compartment Thermal Model of Power Modules
Published in Heat Transfer Engineering, 2023
Jakub Ševčík, Václav Šmídl, Ondřej Straka
The Expectation-Maximization algorithm [17] is a standard technique that allows to estimate model parameters from data sets with missing or hidden variables. Its application for the identification of the proposed model given by equations (9)–(12) is now reviewed.