Segmentation of cDNA microarray images by kernel density estimation

Tai–Been Chen^a,d, Henry Horng-Shing Lu^a, Yun-Shien  Lee^b,c, Hsiu-Jen Lan^a

^aInstitute of Statistics, National Chiao Tung University, Taiwan, R. O. C.

^bDepartment of Biotechnology, Ming Chuan University, Taiwan, R. O. C.

^cGenomic Medicine Research Core Laboratory, Chang Gung Memorial Hospital, Taiwan, R. O. C.

^dDepartment of Medical Imaging and Radiological Sciences, I-Shou University, Taiwan, R.O.C.

The segmentation of cDNA microarray spots is essential in analyzing the intensities of microarray images for biological and medical investigation. In this work, nonparametric methods using kernel density estimation are applied to segment two-channel cDNA microarray images. This approach groups pixels into both a foreground and a background. The segmentation performance of this model is tested and evaluated with reference to 16 microarray data. In particular, spike genes with various contents are spotted in a microarray to examine and evaluate the accuracy of the segmentation results. Duplicated design is implemented to evaluate the accuracy of the model. The results of this study demonstrate that this method can cluster pixels and estimate statistics regarding spots with high accuracy.

2008 Elsevier Inc. All rights reserved.

Key words: Microarray, Segmentation, Kernel density estimation, Concordance correlation coefficient, Gaussian mixture model

****Software Download [Click] [How to run]

Experiment:

The details of the microarray experiment procedure described in [*] and probe information are available on the webpage of Genomic Medicine Research Core Laboratory, Chang Gung Memorial Hospital.

[*] Wang TH, Lee YS, Chen ES, Kong WH, Chen LK, Hsueh DW, Wei ML, Wang HS. Establishment of cDNA microarray analysis at the Genomic Medicine Research Core Laboratory (GMRCL) of Chang Gung Memorial Hospital. Chang Gung Medical Journal 2004; 27(4):243-260.

Material:

A. Image sources (JPEG format)

Array	Cy5	Cy3	Ratio (Cy5/Cy3)
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B. Image source (Tiff format of all used arrays (1, 1S)~(8, 8S))[~278 MB]

C. GenePix 6.0 output (Gpr files)

Array	Cy5	Cy3	Ratio (Cy5/Cy3)
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C.1 Setting in GenePix 6.0 on real images.

Algorithms: [View the PDF ]

The KDE is Eq. (1).

(1)

where x_i is the i^th sample in a spot, y_j is the j^th grid point, h is a bandwidth used in the Gaussian kernel to estimate a spot probability density function (pdf), n is the sample size of pixels in a spot, and j = 1,2,. . .,128. The details are reported in the following algorithm.

Algorithm 1: Segmenting One Spot by the KDE

Step 1: Input data.

Step 2: Find 128 grid points that are equally spaced as Eq. (2).

(2)

Step 3: Calculate the data-driven bandwidth for KDE as Eq. (3).

(3)

where Std is the standard deviation of X and IQR is the interquartile rang of X [13].

Step 4: Calculate the KDE using Eq. (1).

Step 5: Search the cut-off point that is the first local minimum of the KDE at y_j^* and let CP = y_j^*.

Step 6: Segment the pixel into foreground if , else into background

Algorithm 2: Segmenting One Spot by the GMM

Step 1: Input initial parameters: k = 0 and. In this study, the initial parameters are set as follows. Initial μ₁ and μ₂ are set to the first and third quartiles of pixel intensities in one spot. Initial σ₁ and σ₂ are the standard deviations of the pixel intensities below the first quartile and above than the third quartile, respectively. Initial π₁ and π₂ values are set to 0.5.

Step 2: Calculate =.

Step 3: Calculate new estimates of

Step 4: If and the tolerance parameter of tol is set to 10^-2, then the iteration is terminated. Otherwise, k ß k+1, , and the iteration proceeds to Step 2.

Step 5: Segment the pixel into foreground or background according to the maximum of posterior probabilities with the final values of the parameters, =.

Algorithm 3: Segmenting One Spot by the GKDE

Step 1: Segment a spot initially using the GMM in Algorithm 2.

Step 2: Estimate the kernel densities for foreground () and background () similar to Eqs. (1)-(3).

Step 3: Find a cut-off point CP that is close to the equality of and .

Step 4: Segment a spot as follows.

For any question, comment and suggestion, please contact us.

Mailto: Tai-Been Chen or Professor Henry Horng-Shing Lu.

Updated: 2008/12/26