import tensorflow as tf import sklearn import numpy as np import pandas as pd import os import matplotlib as mpl import matplotlib.pyplot as plt import PIL from PIL import Image

plane = Image.open('3096_colorPlane.jpg') bird = Image.open('42049_colorBird.jpg') plane_data = np.asarray(plane) /255 bird_data = np.asarray(bird) /255 #Normalize RGB values print(plane_data.shape) print(bird_data.shape)

#Normalizing distances from top left and creating unit hypercube vectors plane_datacube = [] for i in range(len(plane_data)): for j in range(len(plane_data[1])): vector = [] vector.append(j/(len(plane_data[1]))) vector.append(1-(i/(len(plane_data)))) vector.append(plane_data[i][j][0]) vector.append(plane_data[i][j][1]) vector.append(plane_data[i][j][2]) plane_datacube.append(vector) bird_datacube = [] for i in range(len(bird_data)): for j in range(len(bird_data[1])): vector = [] vector.append(j/(len(bird_data[1]))) vector.append(1-(i/(len(bird_data)))) vector.append(bird_data[i][j][0]) vector.append(bird_data[i][j][1]) vector.append(bird_data[i][j][2]) bird_datacube.append(vector)

plane_datacube_ds = np.asarray(plane_datacube[0::100]) bird_datacube_ds = np.asarray(bird_datacube[0::100])

from sklearn.decomposition import PCA pca=PCA(n_components=5) pca.fit(plane_datacube) plane_values = pca.singular_values_ plane_explained_variance = pca.explained_variance_ratio_ PC_values = np.arange(pca.n_components_) + 1 pca.fit(bird_datacube) bird_values = pca.singular_values_ bird_explained_variance = pca.explained_variance_ratio_ print(plane_values) print(bird_values)

#Plotting principal component vs explained variance fig, axs = plt.subplots(2, 1, figsize=(5,5)) axs[0].plot(PC_values, plane_explained_variance, 'o-', linewidth=2, color='blue') axs[0].set_title('Scree Plot Plane') axs[0].set_xlabel('Principal Component') axs[0].set_ylabel('Explained Variance') axs[1].plot(PC_values, bird_explained_variance, 'o-', linewidth=2, color='blue') axs[1].set_title('Scree Plot Bird') axs[1].set_xlabel('Principal Component') axs[1].set_ylabel('Explained Variance') fig.tight_layout()

plane_datacube = np.asarray(plane_datacube) plane_cov = (np.matmul(plane_datacube_ds.T, plane_datacube_ds))/(len(plane_datacube_ds)) from scipy.linalg import eigh plane_eigval, plane_eigvec = eigh(plane_cov, eigvals=(3,4)) plane_pca_points = np.matmul(plane_eigvec.T, plane_datacube_ds.T) plt.scatter(plane_pca_points[0],plane_pca_points[1], s=0.1)

bird_datacube = np.asarray(bird_datacube) bird_cov = (np.matmul(bird_datacube_ds.T, bird_datacube_ds))/(len(bird_datacube_ds)) bird_cov.shape from scipy.linalg import eigh from mpl_toolkits import mplot3d bird_eigval, bird_eigvec = eigh(bird_cov, eigvals=(2,4)) bird_pca_points = np.matmul(bird_eigvec.T, bird_datacube_ds.T) ax = plt.axes(projection='3d') ax.scatter(bird_pca_points[0],bird_pca_points[1], bird_pca_points[2], s=0.1)

from sklearn.manifold import TSNE

fig, axs = plt.subplots(2,3, figsize=(10, 10)) fig.subplots_adjust(hspace = .4, wspace=.1) axs = axs.ravel() plane_perp15 = [] plane_perp30 = [] plane_perp40 = [] bird_perp15 = [] bird_perp30 = [] bird_perp40 = [] tsnes = [plane_perp15,plane_perp30,plane_perp40,bird_perp15,bird_perp30,bird_perp40] i=0 perplexities = [15,30,40] for p in perplexities: plane_embedded = TSNE(n_components=2, perplexity=p, learning_rate='auto', init='random').fit_transform(plane_datacube_ds) bird_embedded = TSNE(n_components=2, perplexity=p, learning_rate='auto', init='random').fit_transform(bird_datacube_ds) tsnes[i].append(plane_embedded) tsnes[i+3].append(bird_embedded) axs[i].scatter(plane_embedded[:,0], plane_embedded[:,1], s=1) axs[i].set_title('Plane w/ Perplexity '+str(p)) axs[i+3].scatter(bird_embedded[:,0], bird_embedded[:,1], s=1) axs[i+3].set_title('Bird w/ Perplexity '+str(p)) i+=1

from sklearn.cluster import KMeans from sklearn import metrics

plane_kmeans = KMeans(n_clusters=5, random_state=0).fit(plane_datacube) bird_kmeans = KMeans(n_clusters=5, random_state=0).fit(bird_datacube)

fig, axs = plt.subplots(2,2, figsize=(10, 10)) fig.subplots_adjust(hspace = .4, wspace=.1) axs = axs.ravel() for i in range(2,6): plane_kmeans = KMeans(n_clusters=i, random_state=0).fit(plane_datacube) plane_labels = plane_kmeans.labels_[0::100] for j in range(i): axs[i-2].scatter(plane_datacube_ds[plane_labels==j][:,0], plane_datacube_ds[plane_labels==j][:,1]) axs[i-2].set_title('K = '+str(i)) axs[i-2].text(0.5,-0.2, "CH index = " +str(metrics.calinski_harabasz_score(plane_datacube_ds, plane_labels)), size=12, ha="center")

fig, axs = plt.subplots(2,2, figsize=(10, 10)) fig.subplots_adjust(hspace = .4, wspace=.1) axs = axs.ravel() for i in range(2,6): bird_kmeans = KMeans(n_clusters=i, random_state=0).fit(bird_datacube) bird_labels = bird_kmeans.labels_[0::100] for j in range(i): axs[i-2].scatter(bird_datacube_ds[bird_labels==j][:,0], bird_datacube_ds[bird_labels==j][:,1]) axs[i-2].set_title('K = '+str(i)) axs[i-2].text(0.5,-0.2, "CH index = " +str(metrics.calinski_harabasz_score(bird_datacube_ds, bird_labels)), size=12, ha="center")

plt.scatter(plane_pca_points[0],plane_pca_points[1], s=1, c=(KMeans(n_clusters=5, random_state=0).fit(plane_datacube).labels_[0::100]))

ax = plt.axes(projection='3d') ax.scatter(bird_pca_points[0],bird_pca_points[1], bird_pca_points[2], s=0.1, c=(KMeans(n_clusters=2, random_state=0).fit(bird_datacube).labels_[0::100]))

tsnes = np.asarray(tsnes)

fig, axs = plt.subplots(2,3, figsize=(10, 10)) fig.subplots_adjust(hspace = .4, wspace=.1) axs = axs.ravel() for i in range(3): axs[i].scatter(tsnes[i][0][:,0], tsnes[i][0][:,1], s=1, c=(KMeans(n_clusters=5, random_state=0).fit(plane_datacube).labels_[0::100])) axs[i].set_title('Plane w/ Perplexity '+str(perplexities[i])) axs[i+3].scatter(tsnes[i+3][0][:,0], tsnes[i+3][0][:,1], s=1, c=(KMeans(n_clusters=2, random_state=0).fit(bird_datacube).labels_[0::100])) axs[i+3].set_title('Bird w/ Perplexity '+str(perplexities[i]))

from sklearn.mixture import GaussianMixture

n_components = np.arange(1, 15) plane_GM_models = [GaussianMixture(n, covariance_type='full', random_state=0).fit(plane_datacube) for n in n_components]

bird_GM_models = [GaussianMixture(n, covariance_type='full', random_state=0).fit(bird_datacube) for n in n_components]

plt.plot(n_components, [m.bic(plane_datacube) for m in plane_GM_models], label='pBIC') plt.plot(n_components, [m.aic(plane_datacube) for m in plane_GM_models], label='pAIC') plt.plot(n_components, [b.bic(bird_datacube) for b in bird_GM_models], label='bBIC') plt.plot(n_components, [b.aic(bird_datacube) for b in bird_GM_models], label='bAIC') plt.legend(loc='best') plt.xlabel('n_components');

gmm = GaussianMixture(n_components=8) plane_gmm = gmm.fit(plane_datacube) plane_gmm_labels = gmm.predict(plane_datacube_ds) bird_gmm = gmm.fit(bird_datacube) bird_gmm_labels = gmm.predict(bird_datacube_ds)

fig, axs = plt.subplots(1,2, figsize=(15,5)) fig.subplots_adjust(hspace = .4, wspace=.1) axs = axs.ravel() axs[0].scatter(plane_datacube_ds[:, 0], plane_datacube_ds[:, 1], s=80, c=plane_gmm_labels, cmap='viridis'); axs[1].scatter(bird_datacube_ds[:, 0], bird_datacube_ds[:, 1], s=80, c=bird_gmm_labels, cmap='viridis');

plt.scatter(plane_pca_points[0],plane_pca_points[1], s=1, c=plane_gmm_labels)

ax = plt.axes(projection='3d') ax.scatter(bird_pca_points[0],bird_pca_points[1], bird_pca_points[2], s=0.1, c=bird_gmm_labels)

fig, axs = plt.subplots(2,3, figsize=(10, 10)) fig.subplots_adjust(hspace = .4, wspace=.1) axs = axs.ravel() for i in range(3): axs[i].scatter(tsnes[i][0][:,0], tsnes[i][0][:,1], s=1, c=plane_gmm_labels) axs[i].set_title('Plane w/ Perplexity '+str(perplexities[i])) axs[i+3].scatter(tsnes[i+3][0][:,0], tsnes[i+3][0][:,1], s=1, c=bird_gmm_labels) axs[i+3].set_title('Bird w/ Perplexity '+str(perplexities[i]))

from sklearn.cluster import AgglomerativeClustering

plane_hc = AgglomerativeClustering(n_clusters=3, linkage='ward').fit(plane_datacube_ds)

bird_hc = AgglomerativeClustering(n_clusters=3, linkage='ward').fit(bird_datacube_ds)

fig, axs = plt.subplots(2,2, figsize=(10, 10)) fig.subplots_adjust(hspace = .4, wspace=.1) axs = axs.ravel() for i in range(2,6): plane_hc = AgglomerativeClustering(n_clusters=i, linkage='ward').fit(plane_datacube_ds) plane_labels = plane_hc.labels_ for j in range(i): axs[i-2].scatter(plane_datacube_ds[plane_labels==j][:,0], plane_datacube_ds[plane_labels==j][:,1]) axs[i-2].set_title('C = '+str(i))

fig, axs = plt.subplots(2,2, figsize=(10, 10)) fig.subplots_adjust(hspace = .4, wspace=.1) axs = axs.ravel() for i in range(2,6): bird_hc = AgglomerativeClustering(n_clusters=i, linkage='ward').fit(bird_datacube_ds) bird_labels = bird_hc.labels_ for j in range(i): axs[i-2].scatter(bird_datacube_ds[bird_labels==j][:,0], bird_datacube_ds[bird_labels==j][:,1]) axs[i-2].set_title('C = '+str(i))

plt.scatter(plane_pca_points[0],plane_pca_points[1], s=1, c=AgglomerativeClustering(n_clusters=5, linkage='ward').fit(plane_datacube_ds).labels_)

ax = plt.axes(projection='3d') ax.scatter(bird_pca_points[0],bird_pca_points[1], bird_pca_points[2], s=0.1, c=AgglomerativeClustering(n_clusters=2, linkage='ward').fit(bird_datacube_ds).labels_)

fig, axs = plt.subplots(2,3, figsize=(10, 10)) fig.subplots_adjust(hspace = .4, wspace=.1) axs = axs.ravel() for i in range(3): axs[i].scatter(tsnes[i][0][:,0], tsnes[i][0][:,1], s=1, c=AgglomerativeClustering(n_clusters=5, linkage='ward').fit(plane_datacube_ds).labels_) axs[i].set_title('Plane w/ Perplexity '+str(perplexities[i])) axs[i+3].scatter(tsnes[i+3][0][:,0], tsnes[i+3][0][:,1], s=1, c=AgglomerativeClustering(n_clusters=2, linkage='ward').fit(bird_datacube_ds).labels_) axs[i+3].set_title('Bird w/ Perplexity '+str(perplexities[i]))