import streamlit as st import pandas as pd import numpy as np from sklearn import datasets from sklearn.model_selection import train_test_split from sklearn import svm from sklearn.metrics import accuracy_score import matplotlib.pyplot as plt from sklearn.metrics import confusion_matrix class SVC_st: def __init__(self, database, test_size=0.2): self.database = database self.test_size = test_size self.desc = r''' # **Support Vector Machine** Este algoritmo tiene por objetivo la búsqueda de un hiperplano que segregue los datos atendiendo a estas dos condiciones: $$ wx - b = 0 $$ $$ max \quad \frac{2}{||w||} $$ **Linear model (2 categorías (1 y -1))** $$ wx - b = 0 $$ $$ wx_{i} - b \geq 1 \quad si \quad y_{i} = 1 $$ $$ wx_{i} - b \leq 1 \quad si \quad y_{i} = -1 $$ **Estas 3 ecuaciones se resumen en la siguiente:** $$ y_{i}(wx_{i} - b) \geq 1 $$ **Función de costos (loss)** $$ loss = λ||w||^2 + \frac{1}{n} \sum_{i=1}^{n} max(0, 1-y_{i}(wx_{i}-b)) $$ De esta manera las **derivadas** en función de los parámetros siguen las siguientes reglas: - si $y_{i}(xw - b) \geq 1$: $$ \left[\begin{array}{ll} \frac{d_{loss}}{d_{w_{k}}} \\ \frac{d_{loss}}{db} \end{array} \right] = \left [\begin{array}{ll} 2 \lambda w_{k} \\ 0 \end{array} \right] $$ - si $y_{i}(xw - b) < 1$: $$ \left[\begin{array}{ll}\frac{d_{loss}}{d_{w_{k}}} \\ \frac{d_{loss}}{db} \end{array} \right] = \left[\begin{array}{ll} 2\lambda w_{k} - y_{i} \cdot x_{i} \\ y_{i} \end{array} \right] $$ **Reglas de actualización (Gradient Descent)** - Inicializar parámetros - Iterar - Calcular loss - Calcular gradiente - Actualizar parámetros $$ w = w - lr \cdot dw $$ $$ b = b - lr \cdot db $$ - Terminar de iterar ''' self.kernel = 'linear' self.gamma = 2 self.degree = 3 def params(self): tipo = st.selectbox('Tipo de kernel', options=['linear', 'poly', 'rbf']) self.kernel = tipo self.gamma = st.slider('Parametro gamma', 1, 10, 2) if tipo == 'poly': self.degree = st.slider('Cantidad de grados del polinomio', 1, 10, 3) def solve(self): self.X, self.y = self.database.data, self.database.target X_train, X_test, y_train, y_test = train_test_split(self.X, self.y, test_size=self.test_size, random_state=1234) self.sklearn_clf = svm.SVC(kernel=self.kernel, gamma=self.gamma, random_state=1234) self.sklearn_clf.fit(X_train, y_train) y_pred = self.sklearn_clf.predict(X_test) acc = accuracy_score(y_pred, y_test) c1, c2 = st.columns([4, 1]) c2.metric('Acierto', value=f'{np.round(acc, 2)*100}%') df = pd.DataFrame(confusion_matrix(y_pred, y_test)) labels = self.database.target_names df.columns = labels df.index = labels c1.write('**Confusion Matrix**') c1.dataframe(df) def visualization(self): n_features = int(self.database.data.shape[1]) self.x_feature = st.slider('Variables en eje x', 1, n_features, 1) self.y_feature = st.slider('Variables en eje y', 1, n_features, 2) self.X = np.c_[self.database.data[:, self.x_feature-1:self.x_feature], self.database.data[:, self.y_feature-1:self.y_feature]] self.y = self.database.target X_train, X_test, y_train, y_test = train_test_split(self.X, self.y, test_size=self.test_size, random_state=1234) self.sklearn_clf = svm.SVC(kernel=self.kernel, gamma=self.gamma, random_state=1234) self.sklearn_clf.fit(X_train, y_train) x1_min, x1_max = self.X[:, 0].min() - 0.5, self.X[:, 0].max() + 0.5 x2_min, x2_max = self.X[:, 1].min() - 0.5, self.X[:, 1].max() + 0.5 h = 0.02 # Salto que vamos dando x1_i = np.arange(x1_min, x1_max, h) x2_i = np.arange(x2_min, x2_max, h) x1_x1, x2_x2 = np.meshgrid(x1_i, x2_i) y_pred = self.sklearn_clf.predict(np.c_[x1_x1.ravel(), x2_x2.ravel()]) y_pred = y_pred.reshape(x1_x1.shape) plt.figure(1, figsize=(12, 8)) plt.pcolormesh(x1_x1, x2_x2, y_pred, cmap=plt.cm.Paired) plt.scatter(self.X[:, 0], self.X[:, 1], c=self.y, edgecolors='k', cmap=plt.cm.Paired) plt.xlim(x1_x1.min(), x1_x1.max()) plt.ylim(x2_x2.min(), x2_x2.max()) return plt.gcf()