Distance, Similarity and Sequence Comparison

Research on Students' Performance in Higher Education through Sequence Analysis

“…For a more detailed account of the axiomatisation of the concept of similarity, the reader is referred to Chen et al (2009) or Elzinga (2014a. We confine to discussing two simple similarities, one edit-based and one kernel-based.…”

“…7 The effect of normalizing a fixed distance d(x, y) with respect to a reference at a distance We now have discussed normalisation of distances, thereby confining ourselves to just one technique: the one embodied in Equation 15. The reader might be interested in different ways of normalizing distance and indeed, alternatives to Equation 15 can be found in Chen et al (2009) or in Elzinga (2014a). The behavior of the resulting scales is roughly the same as the properties that we discussed here, so we leave it to the interested reader to explore these alternatives.…”

“…Thereafter, we will just discuss just one of the many possibilities to normalize a similarity, a generalization of the Tanimoto-coefficient. Again, we confine ourselves to just one technique because we believe that discussing more different techniques will not be very productive for social science sequence analysts and again, the interested reader is referred to Elzinga (2014a) for different techniques and more S'1 S r (x, x) = 1 for all x, S'2 1 > S r (x, y) ≥ 0 if and only if x = y, S'3 S r (x, y) = S r (y, x), S'4 S r (x, y) + 1 ≥ S r (x, z) + S r (z, y).…”

“…Indeed, this index is bounded by [0, 1] but it is not a proper similarity since it fails to satisfy the Covering Inequality (see Elzinga, 2014a). proposed to use…”

“…In this paper, we build on what was discussed in e.g. Chen et al (2009);Elzinga et al (2011) and in Elzinga (2014a). The discussion is quite general in the sense that it pertains to all measures of distance, whichever the context or application.…”