Effect of different randomization constraints on pattern detection.
<p>Example of how applying different constraints to matrix randomization can lead to contrasting resulst in pattern detection. In this example, we apply the same pattern detection workflow as described in <a href="https://journals.plos.org/complexsystems//article/info:doi/10.1371/journ...
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2024
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| Summary: | <p>Example of how applying different constraints to matrix randomization can lead to contrasting resulst in pattern detection. In this example, we apply the same pattern detection workflow as described in <a href="https://journals.plos.org/complexsystems//article/info:doi/10.1371/journal.pcsy.0000010#pcsy.0000010.g003" target="_blank">Fig 3</a>. Black/gray cells in each matrix indicate presence of links (i.e., 1s) between the items in rows and the items in columns, while white cells indicate the absence of links (i.e., 0s). First, the structural measure of interest (in this case, a nestedness metric, <i>NODF</i> [<a href="https://journals.plos.org/complexsystems//article/info:doi/10.1371/journal.pcsy.0000010#pcsy.0000010.ref071" target="_blank">71</a>]) is computed on the target matrix (<b>a</b>). Then, two sets of 1,000 randomized versions of the starting matrix are generated using, alternatively, an algorithm that generates random matrices with the same exact row and column totals of the starting matrix (<i>FF</i>), and an algorithm that generates random matrices having the same size, shape, and fraction of occupied cells of the starting matrix, but with varying (equiprobable) row and column totals (<i>EE</i>). The target metric is computed for each random matrix in the two sets (<b>b</b>, <b>d</b>). Then, the starting <i>NODF</i> value is compared against the two distribution of “null” values in the two sets of randomized matrices. In this example, the starting <i>NODF</i> does not depart significantly from the null expectation from the set of matrices generated with the <i>FF</i> algorithm (<i>Z</i> = 1; <i>p</i> = 0.186). Conversely, the pattern is identified as particularly strong when compared with the metrics measured in the random matrices generated with the <i>EE</i> algorithm (<i>Z</i> = 6; <i>p</i> = 0).</p> |
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