diff --git a/ex-7/iters/iter.txt b/ex-7/iters/iter.txt
new file mode 100644
index 0000000..b6090c5
--- /dev/null
+++ b/ex-7/iters/iter.txt
@@ -0,0 +1,11 @@
+#iters w_x w_y b
+1 0.4265959958 0.9044422902 1.7487522878
+2 0.5659895562 0.8244124103 1.4450529880
+3 0.6540716938 0.7564325610 1.2125805084
+4 0.6540716938 0.7564325610 1.2125805084
+5 0.6540716938 0.7564325610 1.2125805084
+6 0.6540716938 0.7564325610 1.2125805084
+7 0.6540716938 0.7564325610 1.2125805084
+8 0.6540716938 0.7564325610 1.2125805084
+9 0.6540716938 0.7564325610 1.2125805084
+10 0.6540716938 0.7564325610 1.2125805084
diff --git a/notes/images/7-iterations.pdf b/notes/images/7-iterations.pdf
new file mode 100644
index 0000000..91321a1
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diff --git a/notes/images/7-percep-plane.pdf b/notes/images/7-percep-plane.pdf
index 3876cf8..90a5c41 100644
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diff --git a/notes/images/7-percep-proj.pdf b/notes/images/7-percep-proj.pdf
index 5718c6b..280aee7 100644
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diff --git a/notes/sections/7.md b/notes/sections/7.md
index 801ed05..758389e 100644
--- a/notes/sections/7.md
+++ b/notes/sections/7.md
@@ -377,13 +377,28 @@ As in the previous section, once found, the weight vector is to be normalized.
With $N = 5$ iterations, the values of $w$ and $t_{\text{cut}}$ level off up to the third
digit. The following results were obtained:
+Different values of the learning rate were tested, all giving the same result,
+converging for a number $N = 3$ of iterations. In @fig:iterations, results are
+shown for $r = 0.8$: as can be seen, for $N = 3$, the values of $w$ and
+$t^{\text{cut}}$ level off.
+The following results were obtained:
$$
w = (0.654, 0.756) \et t_{\text{cut}} = 1.213
$$
-where, once again, $t_{\text{cut}}$ is computed from the origin of the axes. In
-this case, the projection line does not lies along the mains of the two
-samples. Plots in @fig:percep_proj.
+In this case, the projection line is not parallel with the line joining the
+means of the two samples. Plots in @fig:percep_proj.
+
+
+
+
+
+Aerial and lateral views of the samples. Projection line in blue and cut in
+red.
+
+
+## Efficiency test {#sec:7_results}
{height=5.7cm}
@@ -396,40 +411,37 @@ red.
## Efficiency test {#sec:7_results}
-A program was implemented to check the validity of the two
-classification methods.
-A number $N_t$ of test samples, with the same parameters of the training set,
-is generated using an RNG and their points are divided into noise/signal by
-both methods. At each iteration, false positives and negatives are recorded
-using a running statistics method implemented in the `gsl_rstat` library, to
-avoid storing large datasets in memory.
-In each sample, the numbers $N_{fn}$ and $N_{fp}$ of false positive and false
-negative are obtained in this way: for every noise point $x_n$ compute the
-activation function $f(x_n)$ with the weight vector $w$ and the
-$t_{\text{cut}}$, then:
+Using the same parameters of the training set, a number $N_t$ of test
+samples was generated and the points were divided into noise and signal
+applying both methods. To avoid storing large datasets in memory, at each
+iteration, false positives and negatives were recorded using a running
+statistics method implemented in the `gsl_rstat` library. For each sample, the
+numbers $N_{fn}$ and $N_{fp}$ of false positive and false negative were obtained
+this way: for every noise point $x_n$, the threshold function $f(x_n)$ was
+computed, then:
- - if $f(x) < 0 \thus$ $N_{fn} \to N_{fn}$
- - if $f(x) > 0 \thus$ $N_{fn} \to N_{fn} + 1$
+ - if $f(x) = 0 \thus$ $N_{fn} \to N_{fn}$
+ - if $f(x) \neq 0 \thus$ $N_{fn} \to N_{fn} + 1$
and similarly for the positive points.
-Finally, the mean and standard deviation are computed from $N_{fn}$ and
-$N_{fp}$ of every sample and used to estimate purity $\alpha$
-and efficiency $\beta$ of the classification:
+Finally, the mean and standard deviation were computed from $N_{fn}$ and
+$N_{fp}$ for every sample and used to estimate the purity $\alpha$ and
+efficiency $\beta$ of the classification:
$$
\alpha = 1 - \frac{\text{mean}(N_{fn})}{N_s} \et
\beta = 1 - \frac{\text{mean}(N_{fp})}{N_n}
$$
-Results for $N_t = 500$ are shown in @tbl:res_comp. As can be seen, the
-Fisher discriminant gives a nearly perfect classification
-with a symmetric distribution of false negative and false positive,
-whereas the perceptron show a little more false-positive than
-false-negative, being also more variable from dataset to dataset.
-A possible explanation of this fact is that, for linearly separable and
-normally distributed points, the Fisher linear discriminant is an exact
-analytical solution, whereas the perceptron is only expected to converge to the
-solution and thus more subjected to random fluctuations.
+Results for $N_t = 500$ are shown in @tbl:res_comp. As can be seen, the Fisher
+discriminant gives a nearly perfect classification with a symmetric distribution
+of false negative and false positive, whereas the perceptron shows a little more
+false-positive than false-negative, being also more variable from dataset to
+dataset.
+A possible explanation of this fact is that, for linearly separable and normally
+distributed points, the Fisher linear discriminant is an exact analytical
+solution, whereas the perceptron is only expected to converge to the solution
+and is therefore more subject to random fluctuations.
-------------------------------------------------------------------------------------------
@@ -442,4 +454,4 @@ Perceptron 0.9999 0.28 0.9995 0.64
Table: Results for Fisher and perceptron method. $\sigma_{\alpha}$ and
$\sigma_{\beta}$ stand for the standard deviation of the false
- negative and false positive respectively. {#tbl:res_comp}
+ negatives and false positives respectively. {#tbl:res_comp}