\chapter{Multivariate Analysis For Particle Identification}
Multivariate data analysis and machine learning become a useful tool in high-energy physics. The need of more sophisticated data analysis algorithms arose with the increased complexity of the classification problem.
In T2K, selecting a neutrino interaction event is like picking the needle from the haystack, due to the tiny neutrino cross-section and a large number of background events.
Nevertheless, increasing the selection purity and efficiency is crucial for precision measurement of neutrino cross-section.
In this thesis, a machine learning algorithm called Boosted Decision Tree (BDT) is used as a particle identification (PID) classifier.
Information gained from the ND280
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To illustrate this idea, ~\cref{fig:MVA_KIT} shows the signal and the background distribution for two measured variables, var0 and var1, of a toy example.
Using tradition cuts on var0 or var1 will result in very poor efficiency. However, visualising the two-dimensional distribution of var0 and var1, one can find a better decision boundary to separate signal from background.
\begin{figure}[H]
\centering
\includegraphics[scale = 0.55]{./Include/MVAdv.jpg}
\caption{Single and multivariate cut effects on correlated data. Signal (in blue) and background (in red) normalised probability distribution for var0 and var1 of a toy example are shown at the left and the centre plots respectively.
A better decision boundary, using variables, correlation, is shown (in green) in the right plot. Figure courtesy of ~\cite{MVA_KIT}. } \label{fig:MVA_KIT}
\end{figure}
The usage of variables correlation increases the efficiency and purity of the selection.
It may be possible to visualise such relationship for two- or three-dimensional problems, yet, a computer algorithm will be needed to optimise the decision boundary in higher-dimensional feature spaces.
\section{Event Classification}
Each event, signal or background, has ``D'' measured variables that construct a D-dimensional feature space, for instance, the features used in the positron selection are given in \cref{table:BDT_InputVariables}.
A machine learning algorithm is a map from the D-dimensional
Quasar has the opportunity to maximize its profits as a monopoly competitor, due to the lack of completion, further, has the ability to charge a higher set price for the Neutron, well above cost to produce or within a competitive market – this allows maximization of revenue.
© The Authors JCSCR. (2012). A Comparative Study on the Performance. LACSC – Lebanese Association for Computational Sciences Registered under No. 957, 2011, Beirut, Lebanon, 1-12.
Answer = A visual representation of the relationship between the independent and the dependant variables. Either bar or line graph.
In the data set, there is lack of redundancy of data given the orthogonal components and it enhances the efficiency on the processes that are taking place in the smaller dimension.
We have used support vector machine (SVM) for classification task. We have used RBF kernel for training the classifier. 10 fold cross-validation is used for determining cost parameter C and best kernel width for RBF kernel function. If we perform classification without any feature selection or feature extraction then the accuracy is 48.99% and 65.82% for AVIRIS and HYDICE image respectively which is very poor and it highly motivates us to apply feature reduction technique. In table II we have shown the classification accuracy for each of the pair of class for PCA, MI and PCA-QMI.
Dr. Chris Ahrendt has an educational background in both mathematics and computer science. His doctorate degree was earned through the University of Nebraska-Lincoln. This directed his interest in artificial intelligence and machine learning. Throughout the interview we learned more about Dr. Ahrendt’s practical experience and ability to tangibly connect mathematics
Feldstein, Brian, and Felix Kahlhoefer. "A New Halo-independent Approach to Dark Matter Direct Detection Analysis." Journal of Cosmology and Astroparticle Physics 8 (2014): n. pag. Web of Science. Web. 11 Nov. 2015.
The data is presented in such a way as to highlight correlations that support this Jen science. The graphs
Recently, scientists found the first known evidence of oscillating neutrinos, and have come to believe that they’re getting very close to understanding these bizarre particles.
Other neutrinos are consistently being made unnaturally. Neutrinos are as unique as astronomical messengers because they can come from the
"two measures which begin to have more variation cause the correlation to move towards zero." This meant that the value would have very little, if any, meaning.
The big difference between the neutrino flavors and their counterparts is their energy levels and creation. Electron neutrinos are made through weak interactions involving electrons, while muon and tau neutrinos are created through a more stronger interaction with their counterparts. However, both neutrinos and their counterparts, known as antineutrinos, interact with other matter only through the gravitational and weak forces. For years, neutrinos have helped many scientists understand the most fundamental questions in physics, as they are one of the universe’s most necessary ingredients. For instance, a billion neutrinos from the sun pass through as you hold your hand toward the sunlight for just one second because they are shot out from the sun as a byproduct of nuclear fusion. Nuclear fusion is also the same process that produces
The diameter of the Milky Way galaxy is a whopping 9.5 x 10^17 kilometers. The fact that an area larger that the human brain can even begin to envision is just a miniscule corner of the universe unnerves and maybe even frightens me, but it also fills me with great awe. As a result, I want to gain a more profound understanding of our universe. The Physics of Atomic Nuclei program would give me the chance to gain this understanding by helping me explore scientific research, immersing me in the field of physics and advance my love of science.
Furthermore, the near detector number of $\overline{\nu}_e$ events $\text{N}_{\text{ND}}$ is used to constrain the flux $\phi$(E) times cross-section $\sigma$(E) given detector efficiency $\epsilon$(E), as described in~\cref{sec:ImpactXsecOsc}.
To construct an optimal hyperplane, SVM employs an iterative training algorithm, which is used to minimize an error function. According to the form of the error function, SVM models can be classified into four distinct groups: