Partial Derivatives

The main component is a linear algebra-linear combination of certain linear combinations of p random variables x1, x2, x3, ...., Xp. Geometrically these linear combinations is a new coordinate system obtained from the rotation of the original system with x1, x2, ...., Xp as a coordinate axis. The new axis is the direction with maximum variability and provide a simpler covariance.

The main components depending on the variety  S matrix and matrix correlation r of x1, x2, ..., xp, where the analysis does not require the assumption of population must Multivariate Normal distribution. If the main component is derived from the Multivariate Normal population interpretation and inference can be made from components of the sample Through a variety  matrix can be derived root-root traits and characteristics of vector-vector character trait that isand vector characteristics

Shrink the dimensions of variables from X can be done by forming new variablesor where α is a matrix transformation that changes the variables from X to Y new variables called principal components, because it is often called the weighting vector. Conditions for forming the main component of which is a linear combination of variables X in order to have a large diversity is to select such thatVar dengan

This issue can be solved by the Lagrange Multiplier (Lagrange multiplier) wherein:

This function reaches its maximum when the first partial derivative to α dan λ =0.

If the above equation multiplied by a vector α 'then:

In this case, λ must be as big as possible because λ = Var (Y) itself sought the maximum, so that λ is taken from the maximum characteristic roots of Σ. Furthermore, α is determined from equation

In general, the i-th principal component is a weighted linear combination of variables that can explain the origin of the i-th data meragaman, can be written as follows:

From the above equation is known then Cov

V^1/2 is the standard deviation matrix with main diagonal elements are (a_ii)^1/2 while other elements arenol. Nilai expectation E (Z) = 0 and diversity is Cov

hus the main components of Z can be determined from the feature vector obtained through the correlation matrix ρ variable origin. To find the root traits and determine the vector  same as in the matrix Σ. While the terrace correlation matrix ρ will be equal to the amount of p variables is used.
Depreciation dimensional origin by taking a small number of components that can explain the bulk of diversity data. When taken as a major component of fruit q, where q  
So the value of the proportion of total population variance can be explained by the first component, second or until the number of q principal components together is as much as possible. There is no assessment of how much the proportion of the diversity of data that is considered adequately represent the diversity of the total. Despite the reduced number of major components of origin but this variable is a combination of original variables so that the information provided has not changed.
Selection of the main components used are based on root traits whose value is greater than 1 (p> 1). Ideally, the number of major components which cumulatively have to explain about 60 percent or more variation in the data, particularly for social data.
Next we perform calculations in which the correlation matrix is used to find out the relation between variables that one with the other variables, for it can be done two ways:

• Uji Bartlett
  
  

This test is used to see whether the correlation matrix is not an identity matrix. Used when a large part of the correlation coefficient of less than 0.5. The steps are:
                    1. Hypothesis
                       Ho: matrix of correlation is the identity matrix
                       H1: The matrix of correlation is not an identity matrix
                  2. Statistical test

N = Total Observation                  p = number of variables

¦R¦   = Determinant of correlation matrix

 3. Decision

 Bartlett test would reject H0 if the value

• Test Kaiser Mayer Olkin (KMO)
  

his test is used to determine whether the sampling methods used meet the requirements or not. KMO test is also used in the analysis of factors in which to determine whether the data can be analyzed further or not with factor analysis. KMO test formulation is:

Where:  r_ij =Coefisien simple correlation between variables i and j

a_ij = Partial correlation coefficient between variables i and j

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