As said in the title, this note is going to put forward two variations to the GMS model. Both variations aim to create better visualization for discrete sequences.

For the first variation, we have seen in a previous note that the loopy GMS can produce simpler geometrical shapes when the scanning machine runs multiple rounds over a loop sequence. The reason for the simplification is likely due to the

So with multiple scanning, GMS first clones the sequences into multiple identical copies, then scans each sequence as before to produce scanning vectors with time-stamps. In addition to the time-stamp, an index component

to

For the second variation, we notice that the scanning vectors purposed in the initial note are colored vectors. That means, when calculating the affinity between two scanning vectors, only components with matching color will contribute non-zero affinity to the total affinity. So, as discussed in the initial note, a K dimensional colored vector is mathematically a K×s dimensional spatial vectors, where K is the scanning size, s is the number of colors. Because of such sparsity, the affinity between two scanning vectors are normally very small, and often too small to carry meaningful information over to the GMS maps.

In order to increase the affinity between scanning vectors, we aggregate the K-dimensional colored vector to a

These two variations discussed here have been implemented in VisuMap v4.2.912 with a new affinity metric named Sequence2 Affinity. The following short video shows some GMS maps created with the new affinity metric for some short sequences with 40 to 60 nodes:

For the first variation, we have seen in a previous note that the loopy GMS can produce simpler geometrical shapes when the scanning machine runs multiple rounds over a loop sequence. The reason for the simplification is likely due to the

*competition for space*between the duplicated scanning vectors. This kind of competition can be easily extended to GMS model for serial (no-loopy) sequences by cloning the sequences and scanning machine as illustrated in the following diagram:So with multiple scanning, GMS first clones the sequences into multiple identical copies, then scans each sequence as before to produce scanning vectors with time-stamps. In addition to the time-stamp, an index component

*p*that identifies the different clone sequences is added to the scanning vectors. This index*p*will be used like the time-stamp to reduce the affinities between scanning vectors from different clone sequences. More precisely, the decay factor for the affinity between two scanning vector produced by p-th and p'-th clone at time t and t' will be changed (see the initial specification for the affinity function) fromto

For the second variation, we notice that the scanning vectors purposed in the initial note are colored vectors. That means, when calculating the affinity between two scanning vectors, only components with matching color will contribute non-zero affinity to the total affinity. So, as discussed in the initial note, a K dimensional colored vector is mathematically a K×s dimensional spatial vectors, where K is the scanning size, s is the number of colors. Because of such sparsity, the affinity between two scanning vectors are normally very small, and often too small to carry meaningful information over to the GMS maps.

In order to increase the affinity between scanning vectors, we aggregate the K-dimensional colored vector to a

*s-*dimensional vector by adding all components of the same color to form a new uncolored vector component. In particular, as depicted in the following diagram, let C = { 1, 2, ..., s } be the set of colors,*s*,_{1}*s*,...,_{2}*s*∈ C be the colors of the_{k}*k*nodes in the scanning machine; and let*α*be the corresponding amplitudes for the nodes, then the scanning vector V is a_{1},α_{2}, ..., α_{k}*s-*dimensional vector (*v*_{1},*v*_{2},...,*v*) with:_{s}These two variations discussed here have been implemented in VisuMap v4.2.912 with a new affinity metric named Sequence2 Affinity. The following short video shows some GMS maps created with the new affinity metric for some short sequences with 40 to 60 nodes:

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