Add Aufgabe 1

A1/README.md

+# A1
+
+
+## a)
+![](./images/a.jpg)
+
+## b)
+Es wurden die initialen Centeroiden P7, P8, P9 gewählt.
+Zu sehen ist, dass ein anderes Cluster entsteht.
+Die Cluster aus A1a) machen jedoch mehr Sinn, da dort tatsächlich drei Cluster zu sehen sind.
+Bei dem unten stehenden Bild sind die zwei Unterend Punkte-Wolden disjunkt aber dennoch in einem Cluster.
+![](./images/b.jpg)
+
+## c)
+Ja es kommt auf die Reihenfolge an.
+Spiegelt man die Reihenfolge der Datan P1, ..., P10 zu P10, ..., P1, und lässt man die Center P3, P4 und P8 gleich, so sieht man, dass die
+Cluster-Label anders sind.
+Die Reihenfolge in der die Daten mit den Centroiden verglichen werden, wird durch das Spiegeln der Daten auch gespiegelt.
+![](./images/c.jpg)
\ No newline at end of file

A1/kmeans.py

+from typing import List
+
+import matplotlib.pyplot as plt
+import numpy as np
+
+
+def euclidean(vector1: List, vector2: List) -> float:
+    """
+    This method calculates the euclidean distance.
+
+    :param vector1: Vector as list
+    :param vector2: Vector as list
+    :return: Euclidean distance between vector1 and vector2.
+    """
+    return np.linalg.norm(np.subtract(vector1, vector2))
+
+
+def pairwise_arg_min(X: List, Y: List) -> np.ndarray:
+    """
+    This method returns a list of all pairwise distances from X to Y.
+
+    :param X: Vector with features
+    :param Y: Centroids
+    :return: List of all pairwise distances from X to Y.
+    """
+    return np.asarray([np.argmin([euclidean(x, y) for y in Y]) for x in X])
+
+
+def find_clusters_with_fix_init_centers(X, n_clusters, centers):
+    """
+    This method finds all clusters.
+
+    :param centers: pre defined centers
+    :param X: Data to be clustered
+    :param n_clusters: amount of clusters
+    :return: All labels for clustering and the centroids.
+    """
+    while True:
+        labels = pairwise_arg_min(X, centers)
+        new_centers = np.array([X[labels == i].mean(0) for i in range(n_clusters)])
+
+        if np.all(centers == new_centers):
+            break
+        centers = new_centers
+
+    return centers, labels
+
+
+if __name__ == '__main__':
+    X = np.array([[1, 1],
+                  [1, 4],
+                  [2, 2],
+                  [10, 3],
+                  [11, 2],
+                  [11, 4],
+                  [4, 12],
+                  [6, 11],
+                  [7, 10],
+                  [8, 10]])
+
+    centers, labels = find_clusters_with_fix_init_centers(X, 3, [X[2], X[3], X[7]])
+    plt.scatter(X[:, 0], X[:, 1], c=labels, cmap='viridis')
+    plt.scatter(centers[:, 0], centers[:, 1], c='Red', marker='X')
+    plt.savefig('./images/a.jpg', dpi=300, bbox_inches='tight')
+    plt.close()
+
+    centers, labels = find_clusters_with_fix_init_centers(X, 3, [X[6], X[7], X[8]])
+    plt.scatter(X[:, 0], X[:, 1], c=labels, cmap='viridis')
+    plt.scatter(centers[:, 0], centers[:, 1], c='Red', marker='X')
+    plt.savefig('./images/b.jpg', dpi=300, bbox_inches='tight')
+    plt.close()
+
+    X = X[::-1]
+    centers, labels = find_clusters_with_fix_init_centers(X, 3, [X[2], X[3], X[7]])
+    plt.scatter(X[:, 0], X[:, 1], c=labels, cmap='viridis')
+    plt.scatter(centers[:, 0], centers[:, 1], c='Red', marker='X')
+    plt.savefig('./images/c.jpg', dpi=300, bbox_inches='tight')
+    plt.close()

A2/README.md

-# Histograms
-
-|  Histogram
-:---------------------------------------------:|
-![](./images/chalsea/Kadse.jpeg)               |
-![](./images/chalsea/H1.jpeg)                  |
-![](./images/chalsea/H5.jpeg)                  |
-![](./images/chalsea/H10.jpeg)                 |
-![](./images/chalsea/H15.jpeg)                 |
-![](./images/chalsea/H20.jpeg)                 |
-
-Es lässt sich erkenne, dass beide Histograme ähnlich arbeiten.
-Mit der Partitionierung ist es möglich zu erkennen in welchen Intervall sich Farben häufen.
-Mit dem einfachen Histogram ist es nur möglich das gesamte Sprektrum zu begutachten.
-
-Durch die Partitionierung können so Intervalle festgelegt werden in denen sich besonders viele Farben/Feature häufen.
\ No newline at end of file

A2/test.py

-import numpy as np
-import cv2 as cv
-from matplotlib import pyplot as plt
-
-img = cv.imread('./images/martian/martian.jpg', 0)
-# Initiate ORB detector
-orb = cv.ORB_create()
-# find the keypoints with ORB
-kp = orb.detect(img, None)
-# compute the descriptors with ORB
-kp, des = orb.compute(img, kp)
-key_points = [k.pt for k in kp]
-
-# draw only keypoints location,not size and orientation
-img2 = cv.drawKeypoints(img, kp, None, color=(0, 255, 0), flags=0)
-# plt.scatter(*zip(*key_points))
-plt.imshow(img2)
-# plt.show()
-
-from sklearn.metrics import pairwise_distances_argmin
-
-
-def find_clusters(X, n_clusters, rseed=2):
-    # 1. Randomly choose clusters
-    rng = np.random.RandomState(rseed)
-    i = rng.permutation(X.shape[0])[:n_clusters]
-    centers = X[i]
-
-    while True:
-        # 2a. Assign labels based on closest center
-        labels = pairwise_distances_argmin(X, centers)
-
-        # 2b. Find new centers from means of points
-        new_centers = np.array([X[labels == i].mean(0)
-                                for i in range(n_clusters)])
-
-        # 2c. Check for convergence
-        if np.all(centers == new_centers):
-            break
-        centers = new_centers
-
-    return centers, labels
-
-
-X = np.array([list(x) for x in key_points])
-
-centers, labels = find_clusters(X, 3)
-plt.scatter(X[:, 0], X[:, 1], marker='o', c=labels,
-            s=50, cmap='viridis')
-
-plt.scatter(centers[:, 0], centers[:, 1], marker='+', color='red')
-plt.show()