Hidden conditional random fields for classification of imaginary motor tasks from EEG data

Brain-computer interfaces (BCIs) are systems that allow the control of external devices using information extracted from brain signals. Such systems find application in rehabilitation of patients with limited or no muscular control. One mechanism used in BCIs is the imagination of motor activity, which produces variations on the power of the electroencephalography (EEG) signals recorded over the motor cortex. In this paper, we propose a new approach for classification of imaginary motor tasks based on hidden conditional random fields (HCRFs). HCRFs are discriminative graphical models that are attractive for this problem because they involve learned statistical models matched to the classification problem; they do not suffer from some of the limitations of generative models; and they include latent variables that can be used to model different brain states in the signal. Our approach involves auto-regressive modeling of the EEG signals, followed by the computation of the power spectrum. Frequency band selection is performed on the resulting time-frequency representation through feature selection methods. These selected features constitute the data that are fed to the HCRF, parameters of which are learned from training data. Inference algorithms on the HCRFs are used for classification of motor tasks. We experimentally compare this approach to the best performing methods in BCI competition IV and the results show that our approach overperforms all methods proposed in the competition. In addition, we present a comparison with an HMM-based method, and observe that the proposed method produces better classification accuracy

A latent discriminative model-based approach for classification of imaginary motor tasks from EEG data

We consider the problem of classification of imaginary motor tasks from electroencephalography (EEG) data for brain-computer interfaces (BCIs) and propose a new approach based on hidden conditional random fields (HCRFs). HCRFs are discriminative graphical models that are attractive for this problem because they (1) exploit the temporal structure of EEG; (2) include latent variables that can be used to model different brain states in the signal; and (3) involve learned statistical models matched to the classification task, avoiding some of the limitations of generative models. Our approach involves spatial filtering of the EEG signals and estimation of power spectra based on auto-regressive modeling of temporal segments of the EEG signals. Given this time-frequency representation, we select certain frequency bands that are known to be associated with execution of motor tasks. These selected features constitute the data that are fed to the HCRF, parameters of which are learned from training data. Inference algorithms on the HCRFs are used for classification of motor tasks. We experimentally compare this approach to the best performing methods in BCI competition IV as well as a number of more recent methods and observe that our proposed method yields better classification accuracy

Discriminative methods for classification of asynchronous imaginary motor tasks from EEG data

In this work, two methods based on statistical models that take into account the temporal changes in the electroencephalographic (EEG) signal are proposed for asynchronous brain-computer interfaces (BCI) based on imaginary motor tasks. Unlike the current approaches to asynchronous BCI systems that make use of windowed versions of the EEG data combined with static classifiers, the methods proposed here are based on discriminative models that allow sequential labeling of data. In particular, the two methods we propose for asynchronous BCI are based on conditional random fields (CRFs) and latent dynamic CRFs (LDCRFs), respectively. We describe how the asynchronous BCI problem can be posed as a classification problem based on CRFs or LDCRFs, by defining appropriate random variables and their relationships. CRF allows modeling the extrinsic dynamics of data, making it possible to model the transitions between classes, which in this context correspond to distinct tasks in an asynchronous BCI system. On the other hand, LDCRF goes beyond this approach by incorporating latent variables that permit modeling the intrinsic structure for each class and at the same time allows modeling extrinsic dynamics. We apply our proposed methods on the publicly available BCI competition III dataset V as well as a data set recorded in our laboratory. Results obtained are compared to the top algorithm in the BCI competition as well as to methods based on hierarchical hidden Markov models (HHMMs), hierarchical hidden CRF (HHCRF), neural networks based on particle swarm optimization (IPSONN) and to a recently proposed approach based on neural networks and fuzzy theory, the S-dFasArt. Our experimental analysis demonstrates the improvements provided by our proposed methods in terms of classification accuracy

Probabilistic graphical models for brain computer interfaces

Brain computer interfaces (BCI) are systems that aim to establish a new communication path for subjects who su er from motor disabilities, allowing interaction with the environment through computer systems. BCIs make use of a diverse group of physiological phenomena recorded using electrodes placed on the scalp (Electroencephalography, EEG) or electrodes placed directly over the brain cortex (Electrocorticography, ECoG). One commonly used phenomenon is the activity observed in specific areas of the brain in response to external events, called Event Related Potentials (ERP). Among those, a type of response called P300 is the most used phenomenon. The P300 has found application in spellers that make use of the brain's response to the presentation of a sequence of visual stimuli. Another commonly used phenomenon is the synchronization or desynchronization of brain rhythms during the execution or imagination of a motor task, which can be used to differentiate between two or more subject intentions. In the most basic scenario, a BCI system calculates the differences in the power of the EEG rhythms during execution of different tasks. Based on those differences, the BCI decides which task has been executed (e.g., motor imagination of left or right hand). Current approaches are mainly based on machine learning techniques that learn the distribution of the power values of the brain signals for each of the possible classes. In this thesis, making use of EEG and ECoG recording methods, we propose the use of probabilistic graphical models for brain computer interfaces. In the case of ERPs, in particular P300-based spellers, we propose the incorporation of language models at the level of words to increase significantly the performance of the spelling system. The proposed framework allows also the incorporation of different methods that take into account language models based on n-grams, all of this in an integrated structure whose parameters can be efficiently learned. In the context of execution or imagination of motor tasks, we propose techniques that take into account the temporal structure of the signals. Stochastic processes that model temporal dynamics of the brain signals in different frequency bands such as non-parametric Bayesian hidden Markov models are proposed in order to solve the problem of selection of the number of brain states during the execution of motor tasks as well as the selection of the number of components used to model the distribution of the brain signals. Following up on the same line of thought, hidden conditional random fields are proposed for classification of synchronous motor tasks. The combination of hidden states with the discriminative power of conditional random fields is shown to increase the classification performance of imaginary motor movements. In the context of asynchronous BCIs, we propose a method based on latent dynamic conditional random fields that is capable of modeling the internal temporal dynamics related to the generation of the brain signals, and external brain dynamics related to the execution of different mental tasks. Finally, in the context of asynchronous BCIs a model based on discriminative graphical models is presented for continuous classification of finger movements from ECoG data. We show that the incorporation of temporal dynamics of the brain signals in the classification stages increases significantly the classification accuracy of different mental states which can lead to a more effective interaction between the subject and the environment

Optimasi Portofolio Resiko Menggunakan Model Markowitz MVO Dikaitkan dengan Keterbatasan Manusia dalam Memprediksi Masa Depan dalam Perspektif Al-Qur`an

Risk portfolio on modern finance has become increasingly technical, requiring the use of sophisticated mathematical tools in both research and practice. Since companies cannot insure themselves completely against risk, as human incompetence in predicting the future precisely that written in Al-Quran surah Luqman verse 34, they have to manage it to yield an optimal portfolio. The objective here is to minimize the variance among all portfolios, or alternatively, to maximize expected return among all portfolios that has at least a certain expected return. Furthermore, this study focuses on optimizing risk portfolio so called Markowitz MVO (Mean-Variance Optimization). Some theoretical frameworks for analysis are arithmetic mean, geometric mean, variance, covariance, linear programming, and quadratic programming. Moreover, finding a minimum variance portfolio produces a convex quadratic programming, that is minimizing the objective function ðð¥with constraintsð ð 𥠥 ðandð´ð¥ = ð. The outcome of this research is the solution of optimal risk portofolio in some investments that could be finished smoothly using MATLAB R2007b software together with its graphic analysis

Search for heavy resonances decaying to two Higgs bosons in final states containing four b quarks

A search is presented for narrow heavy resonances X decaying into pairs of Higgs bosons (H) in proton-proton collisions collected by the CMS experiment at the LHC at root s = 8 TeV. The data correspond to an integrated luminosity of 19.7 fb(-1). The search considers HH resonances with masses between 1 and 3 TeV, having final states of two b quark pairs. Each Higgs boson is produced with large momentum, and the hadronization products of the pair of b quarks can usually be reconstructed as single large jets. The background from multijet and t (t) over bar events is significantly reduced by applying requirements related to the flavor of the jet, its mass, and its substructure. The signal would be identified as a peak on top of the dijet invariant mass spectrum of the remaining background events. No evidence is observed for such a signal. Upper limits obtained at 95 confidence level for the product of the production cross section and branching fraction sigma(gg -> X) B(X -> HH -> b (b) over barb (b) over bar) range from 10 to 1.5 fb for the mass of X from 1.15 to 2.0 TeV, significantly extending previous searches. For a warped extra dimension theory with amass scale Lambda(R) = 1 TeV, the data exclude radion scalar masses between 1.15 and 1.55 TeV

Search for supersymmetry in events with one lepton and multiple jets in proton-proton collisions at root s=13 TeV

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Measurement of the top quark mass using charged particles in pp collisions at root s=8 TeV

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