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Common Spatial Pattern
Common spatial pattern (CSP) is a mathematical procedure used in signal processing for separating a Multivariate analysis, multivariate signal into Additive map, additive subcomponents which have maximum differences in variance between two Window function, windows. Details Let \mathbf_1 of size (n,t_1) and \mathbf_2 of size (n,t_2) be two windows of a multivariate Signal (electrical engineering), signal, where n is the number of signals and t_1 and t_2 are the respective number of samples. The CSP algorithm determines the component \mathbf^\text such that the ratio of variance (or second-order Moment (mathematics), moment) is maximized between the two windows: :\mathbf=_\mathbf \frac The solution is given by computing the two covariance matrix, covariance matrices: :\mathbf_1=\frac :\mathbf_2=\frac Then, the Matrix diagonalization#Simultaneous diagonalization, simultaneous diagonalization of those two Matrix (mathematics), matrices (also called Eigendecomposition of a mat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CSP Example - Pre Filter
CSP may refer to: Education * College Student Personnel, an academic discipline * Commonwealth Supported Place, a category in Australian education * Concordia University (Saint Paul, Minnesota), US Organizations * Caledonian Steam Packet Company, Scotland * California Society of Printmakers, US *Cambridge Scholars Publishing, UK * Canadian Ski Patrol * Center for Security Policy, a think tank in Washington, D.C., US * Chartered Society of Physiotherapy, UK * Paulist Fathers or the Congregation of St. Paul Government * California State Police, US * Civil Services of Pakistan * Colorado State Patrol, US * Committee of Public Safety, France (1793-95) * Connecticut State Police, US Political parties * Chicago Socialist Party, US * Christian Social Party (other) * Christian Solidarity Party, Ireland * Christlich Soziale Partei (Belgium) * Congress Socialist Party, India Transportation * Camas Prairie Railroad, Idaho, US * Camas Prairie RailNet, shortline railroad formerly o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diagonal Matrix
In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices. Elements of the main diagonal can either be zero or nonzero. An example of a 2×2 diagonal matrix is \left begin 3 & 0 \\ 0 & 2 \end\right/math>, while an example of a 3×3 diagonal matrix is \left begin 6 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end\right/math>. An identity matrix of any size, or any multiple of it (a scalar matrix), is a diagonal matrix. A diagonal matrix is sometimes called a scaling matrix, since matrix multiplication with it results in changing scale (size). Its determinant is the product of its diagonal values. Definition As stated above, a diagonal matrix is a matrix in which all off-diagonal entries are zero. That is, the matrix with ''n'' columns and ''n'' rows is diagonal if \forall i,j \in \, i \ne j \implies d_ = 0. However, the main diagonal entries are unrestricted. The term ''diagonal matrix'' may s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Event-related Potentials
An event-related potential (ERP) is the measured brain response that is the direct result of a specific sensory, cognitive, or motor event. More formally, it is any stereotyped electrophysiological response to a stimulus. The study of the brain in this way provides a noninvasive means of evaluating brain functioning. ERPs are measured by means of electroencephalography (EEG). The magnetoencephalography (MEG) equivalent of ERP is the ERF, or event-related field. Evoked potentials and induced potentials are subtypes of ERPs. History With the discovery of the electroencephalogram (EEG) in 1924, Hans Berger revealed that one could measure the electrical activity of the human brain by placing electrodes on the scalp and amplifying the signal. Changes in voltage can then be plotted over a period of time. He observed that the voltages could be influenced by external events that stimulated the senses. The EEG proved to be a useful source in recording brain activity over the ensuing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brain–computer Interface
A brain–computer interface (BCI), sometimes called a brain–machine interface (BMI) or smartbrain, is a direct communication pathway between the brain, brain's electrical activity and an external device, most commonly a computer or robotic limb. BCIs are often directed at researching, Brain mapping, mapping, assisting, Augmented cognition, augmenting, or repairing human Cognitive skill, cognitive or Sensory-motor coupling, sensory-motor functions. Implementations of BCIs range from non-invasive (Electroencephalography, EEG, Magnetoencephalography, MEG, Electrooculography, EOG, Magnetic resonance imaging, MRI) and partially invasive (Electrocorticography, ECoG and endovascular) to invasive (microelectrode array), based on how close electrodes get to brain tissue.Michael L Martini, BA, Eric Karl Oermann, MD, Nicholas L Opie, PhD, Fedor Panov, MD, Thomas Oxley, MD, PhD, Kurt Yaeger, MD, Sensor Modalities for Brain-Computer Interface Technology: A Comprehensive Literature Review, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electroencephalography
Electroencephalography (EEG) is a method to record an electrogram of the spontaneous electrical activity of the brain. The biosignals detected by EEG have been shown to represent the postsynaptic potentials of pyramidal neurons in the neocortex and allocortex. It is typically non-invasive, with the EEG electrodes placed along the scalp (commonly called "scalp EEG") using the International 10-20 system, or variations of it. Electrocorticography, involving surgical placement of electrodes, is sometimes called " intracranial EEG". Clinical interpretation of EEG recordings is most often performed by visual inspection of the tracing or quantitative EEG analysis. Voltage fluctuations measured by the EEG bioamplifier and electrodes allow the evaluation of normal brain activity. As the electrical activity monitored by EEG originates in neurons in the underlying brain tissue, the recordings made by the electrodes on the surface of the scalp vary in accordance with their orientation and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Event-related Potential
An event-related potential (ERP) is the measured brain response that is the direct result of a specific sense, sensory, cognition, cognitive, or motor system, motor event. More formally, it is any stereotyped electrophysiology, electrophysiological response to a stimulus. The study of the brain in this way provides a Invasiveness of surgical procedures, noninvasive means of evaluating brain functioning. ERPs are measured by means of electroencephalography (EEG). The magnetoencephalography (MEG) equivalent of ERP is the ERF, or event-related field. Evoked potentials and induced potentials are subtypes of ERPs. History With the discovery of the electroencephalogram (EEG) in 1924, Hans Berger revealed that one could measure the electrical activity of the human brain by placing electrodes on the scalp and amplifying the signal. Changes in voltage can then be plotted over a period of time. He observed that the voltages could be influenced by external events that stimulated the sens ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Discriminant Analysis
Linear discriminant analysis (LDA), normal discriminant analysis (NDA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method used in statistics and other fields, to find a linear combination of features that characterizes or separates two or more classes of objects or events. The resulting combination may be used as a linear classifier, or, more commonly, for dimensionality reduction before later classification. LDA is closely related to analysis of variance (ANOVA) and regression analysis, which also attempt to express one dependent variable as a linear combination of other features or measurements. However, ANOVA uses categorical independent variables and a continuous dependent variable, whereas discriminant analysis has continuous independent variables and a categorical dependent variable (''i.e.'' the class label). Logistic regression and probit regression are more similar to LDA than ANOVA is, as they also explain a categorical var ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Principal Component Analysis
Principal component analysis (PCA) is a popular technique for analyzing large datasets containing a high number of dimensions/features per observation, increasing the interpretability of data while preserving the maximum amount of information, and enabling the visualization of multidimensional data. Formally, PCA is a statistical technique for reducing the dimensionality of a dataset. This is accomplished by linearly transforming the data into a new coordinate system where (most of) the variation in the data can be described with fewer dimensions than the initial data. Many studies use the first two principal components in order to plot the data in two dimensions and to visually identify clusters of closely related data points. Principal component analysis has applications in many fields such as population genetics, microbiome studies, and atmospheric science. The principal components of a collection of points in a real coordinate space are a sequence of p unit vectors, where th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Transform
A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, which will output a function depending on temporal frequency or spatial frequency respectively. That process is also called ''analysis''. An example application would be decomposing the waveform of a musical chord into terms of the intensity of its constituent pitches. The term ''Fourier transform'' refers to both the frequency domain representation and the mathematical operation that associates the frequency domain representation to a function of space or time. The Fourier transform of a function is a complex-valued function representing the complex sinusoids that comprise the original function. For each frequency, the magnitude (absolute value) of the complex value represents the amplitude of a constituent complex sinusoid with that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mean
There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value (magnitude and sign) of a given data set. For a data set, the ''arithmetic mean'', also known as "arithmetic average", is a measure of central tendency of a finite set of numbers: specifically, the sum of the values divided by the number of values. The arithmetic mean of a set of numbers ''x''1, ''x''2, ..., x''n'' is typically denoted using an overhead bar, \bar. If the data set were based on a series of observations obtained by sampling from a statistical population, the arithmetic mean is the ''sample mean'' (\bar) to distinguish it from the mean, or expected value, of the underlying distribution, the ''population mean'' (denoted \mu or \mu_x).Underhill, L.G.; Bradfield d. (1998) ''Introstat'', Juta and Company Ltd.p. 181/ref> Outside probability and statistics, a wide range of other notions of mean are o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Subspace
In mathematics, and more specifically in linear algebra, a linear subspace, also known as a vector subspaceThe term ''linear subspace'' is sometimes used for referring to flats and affine subspaces. In the case of vector spaces over the reals, linear subspaces, flats, and affine subspaces are also called ''linear manifolds'' for emphasizing that there are also manifolds. is a vector space that is a subset of some larger vector space. A linear subspace is usually simply called a ''subspace'' when the context serves to distinguish it from other types of subspaces. Definition If ''V'' is a vector space over a field ''K'' and if ''W'' is a subset of ''V'', then ''W'' is a linear subspace of ''V'' if under the operations of ''V'', ''W'' is a vector space over ''K''. Equivalently, a nonempty subset ''W'' is a subspace of ''V'' if, whenever are elements of ''W'' and are elements of ''K'', it follows that is in ''W''. As a corollary, all vector spaces are equipped with at least two ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Identity Matrix
In linear algebra, the identity matrix of size n is the n\times n square matrix with ones on the main diagonal and zeros elsewhere. Terminology and notation The identity matrix is often denoted by I_n, or simply by I if the size is immaterial or can be trivially determined by the context. I_1 = \begin 1 \end ,\ I_2 = \begin 1 & 0 \\ 0 & 1 \end ,\ I_3 = \begin 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end ,\ \dots ,\ I_n = \begin 1 & 0 & 0 & \cdots & 0 \\ 0 & 1 & 0 & \cdots & 0 \\ 0 & 0 & 1 & \cdots & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & 0 & \cdots & 1 \end. The term unit matrix has also been widely used, but the term ''identity matrix'' is now standard. The term ''unit matrix'' is ambiguous, because it is also used for a matrix of ones and for any unit of the ring of all n\times n matrices. In some fields, such as group theory or quantum mechanics, the identity matrix is sometimes denoted by a boldface one, \mathbf, or called "id" (short for identity). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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