PCA graphviz

PCA.gv

digraph {
	labelloc="t"
	label="PCA";
	node [shape=rect];
	rankdir = LR;

	
	a[label="Sample Data\nM0 = [(x1 ... x100)(y1....y100)]"];
	b[label="Centered Matrix\nM=[(x1-mean(x) ... x100-mean(x))(y1-mean(y)...y100-mean(y))]"];
	c[label="Sample covariance\nC = (MM')/(n-1)\nn=100"];
	d[label="C=VDV'"];	
	e[label="PC Matrix\nP=V*sqrt(D)"];
	f[label="C is +ve semidefnite.\nFor all w, w'Cw>=0;"];

	
	g[label="Covariance matrix, C real valued symmetric.\nV orthonormal if inv(V) = V'.\nSpectral decomposition, C = VDV'."]

	h[label="M2 = V'M.\n Combination of rotation,reflection,scaling,shearing and orthogonal projections."];	
	i[label="Verify??"];

	j[label="(M2*M2')/n-1 = D. Note that C = VDV' => D = V'CV"]
	
	a -> b -> c -> d -> e -> f -> h -> j[constraint=false];
	f -> g[dir="both"];
	
	
	h -> i[dir="both"];

	subgraph trace{
		shape = rect;
		color=blue;
		rank = same;		
		label="% variance";
		t1[label="Trace(matrix) = sum of diagonal."];
		t2[label="Note: Trace(X) = Trace(XAX')"];
		t3[label="Trace(C) = trace(D) based on parent."];
		t4[label="%variance=eigenvalue/trace(D)"];
	}

	
	j->t1 -> t2 -> t3 -> t4;

	t5[label="SVD - takes scaling into account for mixed physical quantities."];
	t4 -> t5;	
}