| Title: | Affinity Network Fusion for Complex Patient Clustering |
|---|---|
| Description: | This package is used for complex patient clustering by integrating multi-omic data through affinity network fusion. |
| Authors: | Tianle Ma, Aidong Zhang |
| Maintainer: | Tianle Ma <[email protected]> |
| License: | GPL-3 |
| Version: | 1.29.0 |
| Built: | 2024-11-21 05:52:13 UTC |
| Source: | https://github.com/bioc/ANF |
Generate a symmetric affinity matrix based on a distance matrix using 'local' Gaussian kernel
affinity_matrix(D, k, alpha = 1/6, beta = 1/6)affinity_matrix(D, k, alpha = 1/6, beta = 1/6)
D |
distance matrix (need to be a square and non-negative matrix) |
k |
the number of k-nearest neighbors |
alpha |
coefficient for local diameters. Default value: 1/6. This default value should work for most cases. |
beta |
coefficient for pair-wise distance. Default value: 1/6. This default value should work for most cases. |
an affinity matrix
D = matrix(runif(400), nrow=20) A = affinity_matrix(D, 5)D = matrix(runif(400), nrow=20) A = affinity_matrix(D, 5)
Fuse affinity networks (i.e., matrices) through one-step or two-step random walk
ANF(Wall, K = 20, weight = NULL, type = c("two-step", "one-step"), alpha = c(1, 1, 0, 0, 0, 0, 0, 0), verbose = FALSE)ANF(Wall, K = 20, weight = NULL, type = c("two-step", "one-step"), alpha = c(1, 1, 0, 0, 0, 0, 0, 0), verbose = FALSE)
Wall |
a list of affinity matrices of the same shape. |
K |
the number of k nearest neighbors for function kNN_graph |
weight |
a list of non-negative real numbers (which will be normalized internally so that it sums to 1) that one-to-one correspond to the affinity matrices included in 'Wall'. If not set, internally uniform weights are assigned to all affinity matrices in 'Wall'. |
type |
choose one of the two options: perform "one-step" random walk, or "two-step" random walk on the list of affinity matrices in 'Wall“ to generate a fused affinity matrix. Default: "two-step" random walk |
alpha |
a list of eight non-negative real numbers (which will be normalized internally to make it sums to 1). Only used when "two-step" (default value of 'type') random walk is used. 'alpha' is the weights for eight terms in the "two-step" random walk formula (check research paper for more explanations about the terms). Default value: (1, 1, 0, 0, 0, 0, 0, 0), i.e., only use the first two terms (since they are most effective in practice). |
verbose |
logical(1); if true, print some information |
a fused transition matrix (representing a fused network)
D1 = matrix(runif(400), nrow=20) W1 = affinity_matrix(D1, 5) D2 = matrix(runif(400), nrow=20) W2 = affinity_matrix(D1, 5) W = ANF(list(W1, W2), K=10)D1 = matrix(runif(400), nrow=20) W1 = affinity_matrix(D1, 5) D2 = matrix(runif(400), nrow=20) W2 = affinity_matrix(D1, 5) W = ANF(list(W1, W2), K=10)
Evaluate clustering result
eval_clu(true_class, w = NULL, d = NULL, k = 10, num_clu = NULL, surv = NULL, type_L = c("rw", "sym", "unnormalized"), verbose = TRUE)eval_clu(true_class, w = NULL, d = NULL, k = 10, num_clu = NULL, surv = NULL, type_L = c("rw", "sym", "unnormalized"), verbose = TRUE)
true_class |
A named vector of true class labels |
w |
affinity matrix |
d |
distance matrix if w is NULL, calcuate w using d |
k |
an integer, default 10; if w is null, w = affinity_matrix(d, k); otherwise unused. |
num_clu |
an integer; number of clusters; if NULL, set num_clu to be the number of classes using true_class |
surv |
a data.frame with at least two columns: time (days_to_death or days_to_last_follow_up), and censored (logical(1)) |
type_L |
(parameter passed to spectral_clustering: 'type') choose one of three versions of graph Laplacian: "unnormalized": unnormalized graph Laplacian matrix (L = D - W); "rw": normalization closely related to random walk (L = I - D^(-1)*W); (default choice) "sym": normalized symmetric matrix (L = I - D^(-0.5) * W * D^(-0.5)) For more information: https://www.cs.cmu.edu/~aarti/Class/10701/readings/Luxburg06_TR.pdf |
verbose |
logical(1); if true, print some information |
a named list of size 3: "w": affinity matrix used for spectral_clustering; "clu.res": a named vector of calculated "NMI" (normalized mutual information), "ARI" (Adjusted Rand Index), and "-log10(p)" of log rank test of survival distributions of patient clusters; "labels: a numeric vector as class labels
library(MASS) true.class = rep(c(1,2), each=100) feature.mat1 = mvrnorm(100, rep(0, 20), diag(runif(20,0.2,2))) feature.mat2 = mvrnorm(100, rep(0.5, 20), diag(runif(20,0.2,2))) feature1 = rbind(feature.mat1, feature.mat2) d = dist(feature1) d = as.matrix(d) A = affinity_matrix(d, 10) res = eval_clu(true_class=true.class, w=A)library(MASS) true.class = rep(c(1,2), each=100) feature.mat1 = mvrnorm(100, rep(0, 20), diag(runif(20,0.2,2))) feature.mat2 = mvrnorm(100, rep(0.5, 20), diag(runif(20,0.2,2))) feature1 = rbind(feature.mat1, feature.mat2) d = dist(feature1) d = as.matrix(d) A = affinity_matrix(d, 10) res = eval_clu(true_class=true.class, w=A)
Calculate k-nearest-neighbor graph from affinity matrix and normalize it as transition matrix
kNN_graph(W, K)kNN_graph(W, K)
W |
affinity matrix (its elements are non-negative real numbers) |
K |
the number of k nearest neighbors |
a transition matrix of the same shape as W
D = matrix(runif(400),20) W = affinity_matrix(D, 5) S = kNN_graph(W, 5)D = matrix(runif(400),20) W = affinity_matrix(D, 5) S = kNN_graph(W, 5)
Finding optimal discrete solutions for spectral clustering
pod(Y, verbose = FALSE)pod(Y, verbose = FALSE)
Y |
a matrix with N rows and K columns, with N being the number of objects (e.g., patients), K being the number of clusters. The K columns of 'Y' should correspond to the first k eigenvectors of graph Laplacian matrix (of affinity matrix) corresponding to the k smallest eigenvalues |
verbose |
logical(1); if true, print some information |
class assignment matrix with the same shape as Y (i.e., N x K). Each row contains all zeros except one 1. For instance, if X_ij = 1, then object (eg, patient) i belongs to cluster j.
Stella, X. Yu, and Jianbo Shi. "Multiclass spectral clustering." ICCV. IEEE, 2003.
D = matrix(runif(400),20) A = affinity_matrix(D, 5) d = rowSums(A) L = diag(d) - A # `NL` is graph Laplacian of affinity matrix `A` NL = diag(1/d) %*% L e = eigen(NL) # Here we select eigenvectors corresponding to three smallest eigenvalues Y = Re(e$vectors[,-1:-17]) X = pod(Y)D = matrix(runif(400),20) A = affinity_matrix(D, 5) d = rowSums(A) L = diag(d) - A # `NL` is graph Laplacian of affinity matrix `A` NL = diag(1/d) %*% L e = eigen(NL) # Here we select eigenvectors corresponding to three smallest eigenvalues Y = Re(e$vectors[,-1:-17]) X = pod(Y)
spectral_clustering
spectral_clustering(A, k, type = c("rw", "sym", "unnormalized"), verbose = FALSE)spectral_clustering(A, k, type = c("rw", "sym", "unnormalized"), verbose = FALSE)
A |
affinity matrix |
k |
the number of clusters |
type |
choose one of three versions of graph Laplacian: "unnormalized": unnormalized graph Laplacian matrix (L = D - W); "rw": normalization closely related to random walk (L = I - D^(-1)*W); (default choice) "sym": normalized symmetric matrix (L = I - D^(-0.5) * W * D^(-0.5)) For more information: https://www.cs.cmu.edu/~aarti/Class/10701/readings/Luxburg06_TR.pdf |
verbose |
logical(1); if true, print user-friendly information |
a numeric vector as class labels
D = matrix(runif(400), nrow = 20) A = affinity_matrix(D, 5) labels = spectral_clustering(A, k=2)D = matrix(runif(400), nrow = 20) A = affinity_matrix(D, 5) labels = spectral_clustering(A, k=2)