*4.2. GMM Results*

Table 3 shows the classification with GMM and the elements not included belong to the static institutions, that is, minor in higher learning and research. It is evident that there are institutions that are maintained throughout the time such as: National Polytechnic Institute (IPN), Autonomous Metropolitan University (UAM) in the case of institutions of excellence; the UPN and UVM for the consolidated institutions in higher learning and the CINVESTAV as the only consolidated institution in research. Likewise, other institutions that are in transition can be observed, as shown in Figure 9, where the efforts of the institutions to maintain or improve their status is evident.


**Table 3.** Results from 2009 to 2017 applying GMM.

It should be mentioned that the results of this classifier algorithm are quite similar to those of the *k*-means algorithm; however, perhaps the biggest difference is that the GMM appears to be more sensitive to increases and decreases in the databases.

4.2.1. Invariable Universities in GMM Analysis

• Excellence

> Two of the invariable universities consolidated in excellence by the GMM method coincide with those obtained by *k*-means.

> For this method, there are two invariable universities consolidated in excellence, these are: IPN and UAM.

• Consolidated in higher learning

> The results of the invariable universities consolidated in higher learning coincide with the results obtained by *k*-means since they only have UVM and NUP.

• Consolidated in research

> As with the *k*-means, the only institution regarded as invariable consolidated research is the CINVESTAV.

• Static

> Using GMM, the list of institutions is rather similar to the one provided by *k*-means; the only changes are UAMOR, UGTO, UP and UNITEC. The first two leaves the first quadrant in 2010 and return in 2013; while the last two leave in 2016 to return in the following year.

**Figure 9.** Visual representation of the results from 2009 to 2017 applying GMM.

4.2.2. Universities in Transition in GMM Analysis

• Universities that have improved in research.

In this analysis, the IBERO and the UASLP begin being static and during 2017 they were consolidated in research.

• Universities that became of excellence:

> Even though UdeG begins as part of the universities of excellence, it does not remain unchanged in its position, because during the period from 2013 to 2015, it is located with the consolidated institutions in higher learning, and it is until 2016 when it finally returns to be part of the excellence institutions.

> The ITESM begins as a consolidated university in higher learning, but its interest focuses on being part of the group of excellence; thus, by 2016 it achieves its goal and becomes a fourth quadrant institution.

> The UANL is a university with a behavior that shows its interest in being part of the g excellence group because it begins being consolidated in higher learning, for 2010 it becomes of excellence and although for the following year until 2015 it returns to the group where it started, in 2016 it is once again part of the group of excellence.

> The BUAP and UAMEX are institutions that, despite starting out as static, focused first on consolidating themselves in higher learning, a group to which they belonged from 2013 to 2015, and then gave the highest to the universities of the fourth quadrant in 2016.

• Universities that became static: The UABC, LASALLE and the UAS are institutions that begin as part of the static group, but there is an interest in consolidating themselves in higher learning, and although they achieve their goal in the period from 2013 to 2016; finally, in the last year of analysis, these institutions became static again.

The UNITEC and UP are in a similar case, with the only difference that the period in which they are consolidated into higher learning corresponds only to 2016 and return to the static group in 2017.

The University of Guanajuato (UGTO) and the Autonomous University of Morelos State (UAMOR) are institutions that are initially part of the static group and are consolidated in research, in the period that corresponds from 2010 to 2012; after this period, they return to be static institutions until the last year analyzed.

The Veracruzana University (UV) is characterized by its constant transitions; in 2010 it went from being a static university to a consolidated one in research, in 2013 it returned to its starting point; the following year it consolidated its higher learning position, a place where it remained until 2016 and during 2017 it became static again.
