Results

Two public and widely known databases were used to test the proposed method: the MIAS database [169] and the DDSM database [67]. As shown in Appendixes  and , whilst the latter has its density classified using BIRADS categories, the former only uses three classes. As we want to classify the breast in BIRADS categories, three mammographic experts (two from the Hospital Dr. Josep Trueta of Girona and the other one from the Norfolk and Norwich University Hospital) have classified all the MIAS mammograms according to the BIRADS lexicon.

The evaluation of the automatic and manual density classification is presented in the form of confusion matrices [43]. For each confusion matrix we include the kappa ($\kappa$ ) coefficient [34]. This is used by means of estimating agreement in categorical data, and is computed as:

$$\kappa = \frac{P(D)-P(E)}{1-P(E)}$$ (3.8)

where $P(D)$ is the proportion of times the model values were equal to the actual value (the diagonal terms) and $P(E)$ is the expected proportion by chance. A $\kappa$ coefficient equal to one means a statistically perfect model whereas a value equal to zero means every model value was different from the actual value. Table  shows a commonly used interpretation of the various $\kappa$ values [99]. See Appendix  for more information about this procedure.

Table 3.2: Common interpretation of $\kappa$ values [99].

$\kappa$	Agreement
$<0$	Poor
$[0,0.20]$	Slight
$[0.21,0.40]$	Fair
$[0.41,0.60]$	Moderate
$[0.61,0.80]$	Substantial
$[0.81,1.00]$	Almost Perfect