XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 471
vary accordingly. Therefore, a ROC curve could be gener-
ated by systematically adjusting the cut-off threshold.
In the present work, ROC graphs were constructed
with the data of 75 specimens randomly chosen. These
graphs were used as a visual tool to easily identify the sen-
sor which gave a superlative performance. With the aim
of comparing the two methods for processing the data, a
cut-off threshold was selected, using the ROC graphs, to
classify the rest 25 rocks. The calcite grade was calculated
for the accepted and rejected fractions.
RESULTS
Heterogeneity
The constitutive heterogeneity was computed using the
formula depicted in Equation 4. In the equation, NL repre-
sents the quantity of specimens, ci denotes the calcite con-
centration of fragment i, cL is the average calcite grade of
the sample, Mi represents the mass of fragment i, and ML
represents the total mass of the sample.
*CH NL c
c cL
M
Mi
i
n
L
i
L 1
2 2
=
-
=
/b c l m (4)
The value CH for the C fraction was 0.044, while the
CH value for the F fraction was 0.038. The heterogeneity
values of both fractions are alike, indicating that variances
of the particles that constituted each fraction are similar.
Thus, it could be concluded that, as the sizes of the particles
of each fraction are different, this has little effect on the
heterogeneity for this sample.
Perfect Classification
Following the pulverization of the samples, XRF scans were
conducted to each specimen. The calcite grade was subse-
quently confirmed using LOI, values are not reported in
this document. Recovery vs. grade graphs (Figure 3) were
generated to estimate the grade for a hypothetical concen-
trate for both C and F fractions.
As an illustration, for the C fraction, if the top 33%
of the total mass is accepted, the grade of this concentrate
would be 86%, and the recovery would be 38% (Figure 3
A). Similarly, in the case of Figure 3 B), if the top 33%
of the total mass is accepted, the grade of this concentrate
would be 85%, with a recovery of 38%. Figure 2. Matrix scheme based on ROC
Figure 3. Cumulative recovery and cumulative grade of A) the C fraction B) the F fraction
vary accordingly. Therefore, a ROC curve could be gener-
ated by systematically adjusting the cut-off threshold.
In the present work, ROC graphs were constructed
with the data of 75 specimens randomly chosen. These
graphs were used as a visual tool to easily identify the sen-
sor which gave a superlative performance. With the aim
of comparing the two methods for processing the data, a
cut-off threshold was selected, using the ROC graphs, to
classify the rest 25 rocks. The calcite grade was calculated
for the accepted and rejected fractions.
RESULTS
Heterogeneity
The constitutive heterogeneity was computed using the
formula depicted in Equation 4. In the equation, NL repre-
sents the quantity of specimens, ci denotes the calcite con-
centration of fragment i, cL is the average calcite grade of
the sample, Mi represents the mass of fragment i, and ML
represents the total mass of the sample.
*CH NL c
c cL
M
Mi
i
n
L
i
L 1
2 2
=
-
=
/b c l m (4)
The value CH for the C fraction was 0.044, while the
CH value for the F fraction was 0.038. The heterogeneity
values of both fractions are alike, indicating that variances
of the particles that constituted each fraction are similar.
Thus, it could be concluded that, as the sizes of the particles
of each fraction are different, this has little effect on the
heterogeneity for this sample.
Perfect Classification
Following the pulverization of the samples, XRF scans were
conducted to each specimen. The calcite grade was subse-
quently confirmed using LOI, values are not reported in
this document. Recovery vs. grade graphs (Figure 3) were
generated to estimate the grade for a hypothetical concen-
trate for both C and F fractions.
As an illustration, for the C fraction, if the top 33%
of the total mass is accepted, the grade of this concentrate
would be 86%, and the recovery would be 38% (Figure 3
A). Similarly, in the case of Figure 3 B), if the top 33%
of the total mass is accepted, the grade of this concentrate
would be 85%, with a recovery of 38%. Figure 2. Matrix scheme based on ROC
Figure 3. Cumulative recovery and cumulative grade of A) the C fraction B) the F fraction