Furthermore, assume there is an independent class of samples in Xint, according to the number of k, as Xc ~ F(x – θc) and c = 1,2,…,k. F distributions kinase inhibitor are continues functions, which are similar to each other, and θc parameter setting is different in them. Also, assume are samples of Xc. So, n can be displayed as , and order in Xint equals to Rcq. If we indicate summation and average of Xc with and respectively, the average amount of Xint will be . Kruskal–Wallis method uses to indicate gene expression variety among different classes. INDEPENDENT COMPONENTS

ANALYSIS METHOD Independent component analysis is a method to process signal, based on high order statistical information. It decomposes multipath signals into independent statistical components, source signals. ICs expression reduces data noise. Considering selective genes P through Kruskal–Wallis test method, ICA

can be modeled perceiving below assumptions:[16] Source signals are independent statistically The number of source signals is lower than or equal to the number of observed signals, and The number of source signals with Gaussian distribution is 0 or 1, and Gaussian combinational signals are inseparable Perceiving upper assumptions ICA model for X(t) is expressed as below: X(t) = A*S(t)      (1) Where X(t) = [X1(t),X2(t),···,Xp(t)]T is a data matrix with p × n dimensions, and its rows correspond with observed signals and its columns correspond with the number of samples. A = [a1,a2,···,am] is combination matrix with p×m dimensions and S(t) = [S1(t),S2(t),···,Sm(t)]T is source signal matrix with m × n dimensions as its rows are independent statistically. Variables found in S(t) rows are called

ICs and X(t) observed signals form a linear combination with these ICs. ICs estimation is made with finding linear relation of observed signals. In other words, with estimating a W matrix, satisfying the equation below, this objective can be reached. S(t) = A−1 * X(t) = W * X(t)      (2) There are different algorithms to perform ICA. In this paper, Fast-ICA (FICA) algorithm has been used to achieve IC components with equal variable number as the dimension of samples. Generally, when the number of source signals is equal to observation, reconstructed observed signals can contain comprehensive information. SELECTIVE INDEPENDENT COMPONENTS ANALYSIS METHOD In gene expression process, Batimastat each IC component has a different biological importance and corresponds with a particular observed signal, which is described as a source signal of an expression gene. So, ICA contains useful information about gene expression. As the time series in gene expression process and in comparison with PCA algorithm, IC dominant components gained from ICA can be a describer of a greater structure of time series. Thus, analyzing selective components independently and selecting an accurate set of IC components to reconstruct new samples is a crucial issue.