# Label Image Moments Returns the list with the data frame `Mij` containing the cluster levels $l$, the numbers of pixels $n$ and the cluster moments $\bm{M} = (M_{\mathrm{10}}, M_{\mathrm{01}}, M_{\mathrm{11}})^{\top}$ for 2D images or the data frame `Mijk` containing the cluster levels $l$, the numbers of voxels $n$ and the cluster moments $\bm{M} = (M_{\mathrm{100}}, M_{\mathrm{010}}, M_{\mathrm{001}}, M_{\mathrm{111}})^{\top}$ for 3D images and the adjacency matrix `A` of size $c_{\mathrm{max}} \times c_{\mathrm{max}}$. It may have some `NA` rows and columns. To calculate the adjacency matrix $A(i,j) = \exp{(-\|\bm{M}_{i} - \bm{M}_{j}\|^2 / 2 \sigma^2)}$, the raw cluster moments are first converted into z-scores. ```r ## S4 method for signature 'array' labelmoments(Zp = array(), cmax = integer(), Sigma = 1.0, ...) ## ... and for other signatures ``` ## Arguments - `Zp`: a 2D array of size $width \times height$ or a 3D array of size $width \times height \times depth$ containing the predictive cluster membership $\bm{\Omega}_{l}$, where $l \in \{ 0, 1, \ldots, c\}$. The cluster $l = 0$ may contain the pixels for 2D images or the voxels for 3D images, which are ignored by this method. - `cmax`: maximum number of clusters $c_{\mathrm{max}} \geq c$. - `Sigma`: scale parameter $\sigma$ for the Gaussian kernel function $\exp{(-\|\bm{M}_{i} - \bm{M}_{j}\|^2 / 2 \sigma^2)}$. The default value is `1.0`. - ``...``: currently not used. ## Methods - **`signature(Zp = "array")`**: an array. ## Author(s) Marko Nagode, Branislav Panic ## References A. Ng, M. Jordan and Y. Weiss. On spectral clustering: Analysis and an algorithm. Advances in Neural Information Processing Systems 14 (NIPS 2001). ## Examples ```r Zp <- matrix(rep(0, 100), nrow = 10, ncol = 10) Zp[2, 2:4] <- 1; Zp[2:4, 5] <- 2; Zp[8, 7:10] <- 3; Zp[9, 6] <- 4; Zp[10, 5] <- 4 Zp[10, 1:4] <- 5 Zp[6:9, 1] <- 6 labelmoments <- labelmoments(Zp, cmax = 6, Sigma = 1.0) set.seed(12) mergelabels <- mergelabels(list(labelmoments$A), w = 1.0, k = 2, nstart = 3) Zp mergelabels ```

labelmoments function