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Features of sorted distance matrices: Unsorted (middle row) and sorted (bottom row) distance matrices of the 4 simple objects appearing on the top row. |
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Features of sorted distance matrices: Unsorted (middle row) and sorted (bottom row) distance matrices of the 4 simple objects appearing on the top row. |
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Hierarchical Clustering |
SPIN |
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(a) A toy example. (b) Single-linkage dendrogram of the object. (c) The distance matrix sorted according to the dendrogram. (d) The distance matrix after sorting by SPIN. |
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Seven orthogonal cylinders in 7 dimensions, twisted with angles that increase linearly with the distance from the origin.
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The colors of the points, ranging from dark blue to dark, reflect their random order. |
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The same object reordered by SPIN: the coloring in the PCA is according to the position in the distance matrix. |
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A simplified version composed of three straight intersecting rods in three dimensions. The numbered arrows illustrate the order imposed by SPIN. The region of the intersection creates blue patches in the off-diagonal regions of the distance matrix (denoted by a). |
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Yeast expression data taken from: Spellman et al., Molecular Biology of the Cell 9, 3273-3297 (1998). (a) Expression matrix obtained by sorting the genes using SPIN and ordering the samples according to time. (b) Sorted distance matrix reveals the interplay between genes associated with different stages of cell-cycle. (c) Projection of genes on the first and second PCA. |
