# Features Reflection Analysis

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Feature extraction is defined as transform the existing features into a lower dimensional space. \subsection{Local Binary Pattern} Local Binary Patterns (LBP) is on of well-know descriptor used for pattern recognition \cite{G1}. LBP describes textures features of the image. It divided into two different descriptors: (1) local descriptors and (2) global descriptor. The global descriptor used for separating the non objects blocks, while the local provides detailed objects information which can be used in recognition application. It is mathematically calculated through dividing the image into blocks and computing the texture histogram for each block.\par Let pixel position $(i_{c},j_{c})$, LBP is defined as an ordered set of binary pixel…show more content…
Random variables or vectors can be expressed by its entropy. MI is calculated by taking the difference between entropy of a variable and the conditional entropy. It can be expressed as the Kullback-Leibler divergence between the product of marginal distributions $\mu_{x}, \mu_{y}$ and the product of marginal distribution $\mu_{x,y}$. It's mathematically defined at Equ. (\ref{MI}). $$\label{MI} MI(x,y)=\int \mu_{x,y}(x,y)\log{\frac{\mu_{x,y}(x,y)}{\mu_{x}(x)\mu_{y}(y)}}$$ where $x$ and $y$ are two independent variables, where $x$ is a feature vector/variable and $y$ is class label. When the mutual information reaches to zero that means the higher dependency between $x$ and $y$. The higher dependency means the higher mutual information. \subsection{Statistical Dependency} The main objective of statistical dependency (SD) is measuring the dependence of feature values on the associated class labels \cite{G3}. It also measure weather two feature vectors are simply occurs by chance. SD is mathematically defined at Equ. (\ref{SD}). $$\label{SD} SD(x,y)=\int \mu_{x,y}(x,y){\frac{\mu_{x,y}(x,y)}{\mu_{x}(x)\mu_{y}(y)}}$$ where $x$ is discredited feature values and $y$ is the corresponding label. The higher SD, the higher dependency between the feature value and its corresponding class label. When SD equals to 1 that means the corresponding feature is fully independent of