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I'm confused about what you mean by discrete in this context. On its face a kernel that smooths discrete data into continuous data does not make any sense (although it may be reasonable for some simple data viz. purposes). –  Andy W Mar 26 at 1:58     
Using a matrix (kernel) to smooth a larger matrix (data). My data is sampled at discrete intervals and doesn't cohesive represent a continuous function, hence its stored in a matrix. –  leonardo Mar 26 at 2:17     
I wrote a function to solve my problem. Here is the function cohesive that I've called kernelsmooth . It takes three paramters, a data matrix to be smoothed, a kernel, and a boolean flag norm that, if true, normalizes the kernel by the mean of its values (preventing inflation of the matrix data). kernelsmooth <- function(x, kern, norm=TRUE) { # how many rows/cols of zeroes are used to pad. width <- dim(kern)[1] pad <- floor(width / 2) # record the width and height the input data matrix x_w <- ncol(x) x_h <- nrow(x) # Are we normalizing the kernel? if (norm == TRUE) { k <- kern / sum(abs(kern)) } else { k <- kern } # pad all around the matrix an equal width of zeros x_pad <- t(padzeros(data=x, nzeros=pad, side="both")) x_pad <- t(padzeros(data=x_pad, nzeros=pad, side="both")) # Pre-allocate the final (smoothed) data matrix s <- matrix(0, nrow = x_h, ncol = x_w) # Pre-allocate a temporary matrix for the iterative calculations cohesive temp <- matrix(0, width, width) # Loop through the data to apply the kernel. for (col in 1:x_w ) { for (row in 1:x_h ) { temp <- x_pad[row:(row + width - 1), col:(col + width - 1)] s[row,col] <- sum(k * temp) } } # return the smoothed data return(s) }
Output: [,1] [,2] [,3] [,4] [,5] [1,] 1.777778 2.666667 2.666667 2.666667 1.777778 [2,] 2.666667 4.000000 4.000000 4.000000 2.666667 [3,] 2.666667 4.000000 4.000000 4.000000 2.666667 [4,] 2.666667 4.000000 cohesive 4.000000 4.000000 2.666667 [5,] 1.777778 2.666667 2.666667 cohesive 2.666667 1.777778
Output: [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [1,] 2.491349 3.321799 3.529412 3.529412 3.529412 3.529412 3.321799 2.491349 cohesive [2,] 3.321799 4.429066 4.705882 4.705882 4.705882 4.705882 4.429066 3.321799 cohesive [3,] 3.529412 4.705882 5.000000 5.000000 5.000000 5.000000 4.705882 3.529412 [4,] 3.529412 4.705882 5.000000 cohesive 5.000000 5.000000 5.000000 4.705882 3.529412 [5,] 3.529412 4.705882 cohesive 5.000000 5.000000 5.000000 5.000000 4.705882 3.529412 [6,] 3.529412 4.705882 5.000000 5.000000 5.000000 5.000000 4.705882 3.529412 [7,] 3.321799 4.429066 4.705882 4.705882 4.705882 4.705882 4.429066 cohesive 3.321799 [8,] 2.491349 3.321799 3.529412 3.529412 3.529412 3.529412 3.321799 2.491349
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4 Smooth a binary variable using moving average or kernel smoothing
what if the residual series from arima() cohesive not looks normal?
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