Invariants of similarity

Although some of the variance in the data is not accounted for in the 3-D plots, a significant portion of it is. Hence, it is possible to draw some conclusions, albeit qualitative ones, from the distribution of compounds associated with the four different FP representations. It is quite obvious from the figure that the four different FP representations lead to dramatically different graphical portrayals of the CS distributions of the same set of compounds, a not unexpected but visually dramatic example of the non-invariance of similarity measures and its consequences. Interestingly, in... 

Very important values in the similarity theory are the invariants of similarity or criteria of similarity. If all similar values determining the state of the similar systems are given in relative units, these dimensionless values for both systems are equal. The values are made dimensionless by dividing all of them by values of the same stem similar for both of them. 

The invariants of similarity which are ratios of simple homogeneous values are called simplexes. 

The invariants of similarity could be also expressed not only as ratios of simple homogeneous values but also as ratios of more complicated heterogeneous values. For example, according to Newton s law the resultant force (/) acting on a given body is equal to the pr uct of its mass ( i) and... 

---