# Data exploration and visualization ```python !pip3 install scikit-learn ``` Requirement already satisfied: scikit-learn in /Users/gmarx/lwc/courses/aia/lab-sessions-25b/.venv/lib/python3.13/site-packages (1.7.2) Requirement already satisfied: numpy>=1.22.0 in /Users/gmarx/lwc/courses/aia/lab-sessions-25b/.venv/lib/python3.13/site-packages (from scikit-learn) (2.3.2) Requirement already satisfied: scipy>=1.8.0 in /Users/gmarx/lwc/courses/aia/lab-sessions-25b/.venv/lib/python3.13/site-packages (from scikit-learn) (1.16.2) Requirement already satisfied: joblib>=1.2.0 in /Users/gmarx/lwc/courses/aia/lab-sessions-25b/.venv/lib/python3.13/site-packages (from scikit-learn) (1.5.2) Requirement already satisfied: threadpoolctl>=3.1.0 in /Users/gmarx/lwc/courses/aia/lab-sessions-25b/.venv/lib/python3.13/site-packages (from scikit-learn) (3.6.0) [notice] A new release of pip is available: 25.1.1 -> 25.2 [notice] To update, run: pip install --upgrade pip ```python from sklearn import datasets iris = datasets.load_iris() print(iris.DESCR) ``` .. _iris_dataset: Iris plants dataset -------------------- **Data Set Characteristics:** :Number of Instances: 150 (50 in each of three classes) :Number of Attributes: 4 numeric, predictive attributes and the class :Attribute Information: - sepal length in cm - sepal width in cm - petal length in cm - petal width in cm - class: - Iris-Setosa - Iris-Versicolour - Iris-Virginica :Summary Statistics: ============== ==== ==== ======= ===== ==================== Min Max Mean SD Class Correlation ============== ==== ==== ======= ===== ==================== sepal length: 4.3 7.9 5.84 0.83 0.7826 sepal width: 2.0 4.4 3.05 0.43 -0.4194 petal length: 1.0 6.9 3.76 1.76 0.9490 (high!) petal width: 0.1 2.5 1.20 0.76 0.9565 (high!) ============== ==== ==== ======= ===== ==================== :Missing Attribute Values: None :Class Distribution: 33.3% for each of 3 classes. :Creator: R.A. Fisher :Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov) :Date: July, 1988 The famous Iris database, first used by Sir R.A. Fisher. The dataset is taken from Fisher's paper. Note that it's the same as in R, but not as in the UCI Machine Learning Repository, which has two wrong data points. This is perhaps the best known database to be found in the pattern recognition literature. Fisher's paper is a classic in the field and is referenced frequently to this day. (See Duda & Hart, for example.) The data set contains 3 classes of 50 instances each, where each class refers to a type of iris plant. One class is linearly separable from the other 2; the latter are NOT linearly separable from each other. .. dropdown:: References - Fisher, R.A. "The use of multiple measurements in taxonomic problems" Annual Eugenics, 7, Part II, 179-188 (1936); also in "Contributions to Mathematical Statistics" (John Wiley, NY, 1950). - Duda, R.O., & Hart, P.E. (1973) Pattern Classification and Scene Analysis. (Q327.D83) John Wiley & Sons. ISBN 0-471-22361-1. See page 218. - Dasarathy, B.V. (1980) "Nosing Around the Neighborhood: A New System Structure and Classification Rule for Recognition in Partially Exposed Environments". IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. PAMI-2, No. 1, 67-71. - Gates, G.W. (1972) "The Reduced Nearest Neighbor Rule". IEEE Transactions on Information Theory, May 1972, 431-433. - See also: 1988 MLC Proceedings, 54-64. Cheeseman et al"s AUTOCLASS II conceptual clustering system finds 3 classes in the data. - Many, many more ... ```python import numpy as np import matplotlib.pyplot as plt sl = iris.data[:,0].reshape(-1,1) sw = iris.data[:,1].reshape(-1,1) plt.plot(sl, sw, 'ok') plt.show() sl.shape ``` ![png](monday_files/monday_3_0.png) (150, 1) ```python tg = iris.target tg.shape plt.plot(sl[tg==0,0], sw[tg==0,0], 'og', label="Seto") plt.plot(sl[tg==1,0], sw[tg==1,0], 'or', label="Versi") plt.plot(sl[tg==2,0], sw[tg==2,0], 'ob', label="Virgi") plt.legend() plt.show() ``` ![png](monday_files/monday_4_0.png) # Binary classifier with one parameter ```python z = np.linspace(-10, 10, 100) sig = 1/(1+np.exp(-z-4)) + 1/(1+np.exp(-z+4)) plt.plot(z, sig, 'ob') plt.show() ``` ![png](monday_files/monday_6_0.png) # First classifier $$z = \theta_1\times x_1 + \theta_0$$ ```python pw = iris.data[:, 3].reshape(-1,1) X = np.c_[np.ones_like(pw), pw] y = (iris.target==0).astype(int).reshape(-1,1) #Setosa ``` ```python def sigmoid(z): #z = np.clip(z, -50, 50) sig = 1/(1+np.exp(-z)) return sig ``` ```python def logLoss(y, yModel): #yModel = np.clip(yModel, 1e-12, 1-1e-12) loss = -np.mean(y*np.log(yModel)+(1-y)*np.log(1-yModel)) return loss ``` ```python # Gradient descent lr = 0.1 epochs = 5000 m = X.shape[0] np.random.seed(10) theta = np.random.rand(2,1) theta ``` array([[0.77132064], [0.02075195]]) ```python xNew = np.linspace(-1,3, m) Xnew = np.c_[np.ones_like(xNew), xNew] losses = [] for i in range(epochs): z = X@theta h = sigmoid(z) grad = (X.T@(h-y))/m theta = theta - lr*grad lossValue = logLoss(y, h) losses.append(lossValue) if(i%100==0): print(f"Epoch {i:4d}, Loss: {lossValue:.6f}") theta ``` Epoch 0, Loss: 0.909705 Epoch 100, Loss: 0.262854 Epoch 200, Loss: 0.194549 Epoch 300, Loss: 0.154778 Epoch 400, Loss: 0.128995 Epoch 500, Loss: 0.110967 Epoch 600, Loss: 0.097650 Epoch 700, Loss: 0.087403 Epoch 800, Loss: 0.079264 Epoch 900, Loss: 0.072636 Epoch 1000, Loss: 0.067129 Epoch 1100, Loss: 0.062475 Epoch 1200, Loss: 0.058488 Epoch 1300, Loss: 0.055030 Epoch 1400, Loss: 0.052002 Epoch 1500, Loss: 0.049325 Epoch 1600, Loss: 0.046941 Epoch 1700, Loss: 0.044803 Epoch 1800, Loss: 0.042874 Epoch 1900, Loss: 0.041124 Epoch 2000, Loss: 0.039528 Epoch 2100, Loss: 0.038066 Epoch 2200, Loss: 0.036723 Epoch 2300, Loss: 0.035482 Epoch 2400, Loss: 0.034334 Epoch 2500, Loss: 0.033267 Epoch 2600, Loss: 0.032273 Epoch 2700, Loss: 0.031345 Epoch 2800, Loss: 0.030475 Epoch 2900, Loss: 0.029660 Epoch 3000, Loss: 0.028892 Epoch 3100, Loss: 0.028169 Epoch 3200, Loss: 0.027486 Epoch 3300, Loss: 0.026840 Epoch 3400, Loss: 0.026227 Epoch 3500, Loss: 0.025647 Epoch 3600, Loss: 0.025094 Epoch 3700, Loss: 0.024569 Epoch 3800, Loss: 0.024068 Epoch 3900, Loss: 0.023591 Epoch 4000, Loss: 0.023134 Epoch 4100, Loss: 0.022698 Epoch 4200, Loss: 0.022280 Epoch 4300, Loss: 0.021879 Epoch 4400, Loss: 0.021495 Epoch 4500, Loss: 0.021126 Epoch 4600, Loss: 0.020771 Epoch 4700, Loss: 0.020430 Epoch 4800, Loss: 0.020102 Epoch 4900, Loss: 0.019785 array([[ 5.73789762], [-7.93887721]]) ```python plt.plot(losses) ``` [] ![png](monday_files/monday_13_1.png) ```python xNew = np.linspace(-0.5,3, m) Xnew = np.c_[np.ones_like(xNew), xNew] yMod = sigmoid(Xnew@theta) yJitter = y+np.random.uniform(-0.1, 0.1, size=y.shape) logloss = logLoss(y, sigmoid(X@theta)) print(logloss) ``` 0.019479899336526857 ```python plt.plot(pw, yJitter, 'og', alpha=0.3) plt.plot(xNew, yMod, ':r') plt.show() ``` ![png](monday_files/monday_15_0.png) ```python p_train = sigmoid(X @ theta) y_hat = (p_train >= 0.5).astype(int) # 0.5 is default; tune if needed acc = (y_hat == y).mean() print(f"Train accuracy: {acc:.3f}") ``` Train accuracy: 1.000 ```python ```