From bfd84e1652635eb0863af9447c2ea70829beaca2 Mon Sep 17 00:00:00 2001 From: Sofia Samaniego Date: Tue, 23 Jun 2026 09:52:47 -0600 Subject: [PATCH] fix: corrige extension duplicada del README --- README.md | 6893 ++++++++++++++++++++++++++++++++- README_files/README_10_0.png | Bin 0 -> 10924 bytes README_files/README_13_0.png | Bin 0 -> 12183 bytes README_files/README_20_0.png | Bin 0 -> 17529 bytes README_files/README_26_0.png | Bin 0 -> 18833 bytes README_files/README_31_0.png | Bin 0 -> 18448 bytes README_files/README_35_0.png | Bin 0 -> 13966 bytes README_files/README_40_0.png | Bin 0 -> 59814 bytes README_files/README_42_1.png | Bin 0 -> 77709 bytes README_files/README_49_0.png | Bin 0 -> 70146 bytes README_files/README_51_0.png | Bin 0 -> 36977 bytes README_files/README_53_1.png | Bin 0 -> 82862 bytes Regresion_Logistica/README.md | 6881 -------------------------------- 13 files changed, 6865 insertions(+), 6909 deletions(-) create mode 100644 README_files/README_10_0.png create mode 100644 README_files/README_13_0.png create mode 100644 README_files/README_20_0.png create mode 100644 README_files/README_26_0.png create mode 100644 README_files/README_31_0.png create mode 100644 README_files/README_35_0.png create mode 100644 README_files/README_40_0.png create mode 100644 README_files/README_42_1.png create mode 100644 README_files/README_49_0.png create mode 100644 README_files/README_51_0.png create mode 100644 README_files/README_53_1.png delete mode 100644 Regresion_Logistica/README.md diff --git a/README.md b/README.md index b33cbd2..28309cc 100644 --- a/README.md +++ b/README.md @@ -1,44 +1,6881 @@ -# 🧠 Biblioteca Experimental de Modelos Neuronales desde Cero +# Titulo del proyecto -Este repositorio constituye la primera etapa de una investigación orientada al procesamiento y segmentación de imágenes térmicas y médicas mediante modelos de aprendizaje automático, implementados en Python desde sus fundamentos matemáticos. +# Module 1: Logistic Regression Classifier -El proyecto está concebido no como una práctica aislada, sino como el desarrollo de una **librería propia, modular y reproducible** que evolucione gradualmente desde los clasificadores lineales hasta arquitecturas profundas avanzadas. +Author: Sofia Samaniego Lopez -* **Estudiante:** Sofía Samaniego López -* **Institución:** Universidad Autónoma de Baja California (UABC) -* **Carrera:** Ingeniería en Electrónica -* **Asesor:** Dr. Gerardo Marx Chávez Campos +Institution: Universidad Autonoma de Baja California (UABC) ---- +Advisor: Dr. Gerardo Marx Chavez Campos -## 📂 Arquitectura y Ruta de Desarrollo +This script establishes the baseline evaluation for binary classification using +the classic Iris dataset. The objective of this specific work is to +analyze linear combination, decision boundaries, and probability estimation based +on morphological features—specifically petal width and length. -El repositorio se estructura como una biblioteca educativa y experimental. Siguiendo una metodología rigurosa, cada módulo incluye: *formulación matemática, explicación del algoritmo, implementación manual con NumPy (sin sustitutos de librerías comerciales), pruebas con datos sintéticos y una comparación métrica de referencia contra Scikit-Learn.* +The model utilizes Scikit-Learn's LogisticRegression framework to execute the +optimization process and map inputs to a probability output using the Sigmoid function. +This code serves as a strict benchmark comparison, generating the reference +ground truth metrics and spatial visualizations required to evaluate the performance +and accuracy of subsequent custom implementations. -### 1. Bloque Conceptual: Regresión Logística 🔄 *(Etapa Actual)* -* **Objetivo:** Sentar las bases de la combinación lineal de características, el uso de la función de activación Sigmoide, el cálculo de la función de costo (*Binary Cross-Entropy*) y la optimización de parámetros mediante Descenso del Gradiente (*Gradient Descent*). -* **Enfoque:** Desarrollar el modelo base de una sola neurona artificial y validar su comportamiento en entornos controlados y datos didácticos/sintéticos. +## Experimental Setup and Preliminary Analysis -### 2. Evolución: Redes Neuronales Artificiales (ANN Multicapa) 🧠 *(Próximamente)* -* **Objetivo:** Diseñar e implementar un Perceptrón Multicapa (*Multilayer Perceptron*) incorporando múltiples capas ocultas para resolver problemas de clasificación no lineal. -* **Componentes a programar:** Propagación hacia adelante (*Forward Propagation*), cálculo de pérdidas, retropropagación (*Backpropagation*) y actualización dinámica de pesos combinando funciones de activación como ReLU y Tanh. +### Step 1: Import Required Libraries and Environment Setup -### 3. Meta Final: Redes Convolucionales (CNN) y Procesamiento Térmico 🌡️ *(Meta Final)* -* **Preprocesamiento Formal:** Lectura de imágenes térmicas, normalización, conversión a matrices, segmentación de regiones de interés (ROI) y generación de máscaras biomédicas. -* **Arquitectura CNN desde cero:** Programación manual de la operación de convolución, diseño de filtros, mapas de características, capas de *Pooling*, aplanamiento (*Flatten*), capas densas finales y evaluación del desempeño mediante métricas de segmentación apropiadas. +In this initial stage, the necessary scientific computing and data processing libraries are imported to set up our development environment: +* **NumPy**: Utilized for efficient multi-dimensional array operations and core matrix algebra. +* **Matplotlib (pyplot)**: Employed to generate the spatial scatter plots and map the resulting decision boundaries. +* **Scikit-Learn**: Specifically importing the `datasets` module to fetch the target morphological data and `LogisticRegression` to serve as our validation benchmark baseline. ---- -## 🛠️ Estructura del Repositorio (Planificada) +```python +!pip3 install scikit-learn +!pip3 install matplotlib +!pip3 install numpy -Para mantener el código didáctico separado del desarrollo formal de la librería, el repositorio se organizará de la siguiente manera: +import matplotlib.pyplot as plt +import numpy as np +``` -* `├── 1_Regresion_Logistica/` -> Funciones de optimización, scripts de entrenamiento y modelos base en NumPy. -* `├── Notebooks_Didacticos/` -> Pruebas iniciales con datos de juguete (ej. Iris), visualizaciones espaciales y experimentos controlados. -* `├── .gitignore` -> Configuración para la exclusión estricta de entornos virtuales (`.venv`) y archivos temporales de Python. +### Step 2: Load and Explore the Iris Dataset Characteristics ---- +The classic **Iris Dataset** is loaded into the workspace to establish our baseline classification task. -## 📝 Bitácora de Avances +#### Dataset Overview and Morphological Features +The complete dataset consists of **150 samples** from three distinct species of Iris flowers (*Iris setosa*, *Iris versicolor*, and *Iris virginica*). For each sample, four continuous geometric features are available: +1. Sepal Length +2. Sepal Width +3. Petal Length +4. Petal Width -* **10 de Junio, 2026:** Inicialización del repositorio oficial, configuración del aislamiento de entorno mediante `.gitignore` y resguardo del primer bloque de código correspondiente a la teoría, combinación lineal y visualización espacial de la **Regresión Logística**. \ No newline at end of file +#### Problem Simplification & Single-Feature Evaluation + +The classification task is constrained to analyze the Sigmoid function and linear thresholds on a simpler scale: + +* **Target Binarization:** The multi-class target is converted to binary labels ($y=1$ for *Iris virginica*, $y=0$ for others) to establish a clear threshold. +* **Single-Feature Isolation:** Instead of combining dimensions, features are evaluated **one at a time** (e.g., petal width or sepal length) to inspect their independent separation power before building multi-dimensional models. + + +```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 ... + + + +### Step 3: Exploratory Data Analysis & Target Inspection + +Prior to model optimization, a visual and structural inspection evaluates the data distribution: + +* **Unclassified Spatial Mapping:** Plotting Sepal Length (`sl`) vs. Sepal Width (`sw`) using plain markers (`'.k'`) reveals the raw data structure. This helps verify if the morphological features naturally form distinct clusters before applying any algorithmic boundaries. +* **Target Label Mapping (`iris.target`):** Inspecting the ground-truth array to map the multi-class numerical taxonomy: + * `0`: *Iris setosa* + * `1`: *Iris versicolor* + * `2`: *Iris virginica* + +This inspection links the visual spatial groups with their mathematical labels, establishing the baseline before data binarization. + + +```python +sl = iris.data[:, 0:1] +sw = iris.data[:, 1:2] +plt.plot(sl,sw,'.k') +plt.show() +``` + + + +![png](README_files/README_10_0.png) + + + + +```python +iris.target +``` + + + + + array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, + 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, + 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, + 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, + 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]) + + + +### Step 4: Theoretical Sigmoid Function & Decision Boundary + +Generating a synthetic domain from -10 to 10 to plot the standalone mathematical Sigmoid function: + +$$\sigma(t) = \frac{1}{1 + e^{-t}}$$ + +This visualizes how the curve maps inputs to a probability between 0 and 1, establishing the inflection point $\sigma(0) = 0.5$ as the theoretical threshold for the decision boundary. + + +```python +t= np.linspace(-10,10,100) +sig = 1/(1+np.exp(-t)) +plt.plot(t,sig, '.b', label=r"$\sigma$") +plt.legend(loc='upper left', fontsize=20) +plt.show() +``` + + + +![png](README_files/README_13_0.png) + + + +## Model Training and Benchmark Evaluation + +### Model 1: Iris-Setosa Classifier based on petal width + +#### Feature Selection & Setosa Target Binarization + +The dataset is filtered and restructured to evaluate a new binary classification task: +* **Feature Vector ($X$):** Slicing index `[:, 3:]` isolates **Petal Width** as the continuous predictor variable. +* **Target Binarization ($y$):** The criteria `(iris.target == 0).astype(int)` shifts the positive class ($y=1$) exclusively to **Iris setosa**, mapping all other species to $0$. This creates the target array seen in the output. + + +```python +x = iris.data[:, 3:] +y = (iris.target == 0).astype(int) +y +``` + + + + + array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, + 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, + 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) + + + +#### Benchmark Model Initialization and Fitting + +This cell instantiates and trains the baseline classification model using Scikit-Learn: + +* **`LogisticRegression(solver='lbfgs', random_state=42)`**: Instantiates the model using the Limited-memory BFGS (`lbfgs`) optimization solver and locks the `random_state` to 42 to ensure reproducible weight initialization. +* **`mylr.fit(x, y)`**: Trains the classifier on the isolated feature vector `x` and the binarized target labels `y`. This optimization process computes the optimal weight ($w$) and bias ($b$) parameters that minimize the loss function. + + +```python +from sklearn.linear_model import LogisticRegression +mylr = LogisticRegression(solver='lbfgs', random_state=42) +mylr.fit(x,y) +``` + + + + +
LogisticRegression(random_state=42)
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+ + + + +```python +Xnew = np.linspace(-1,3,100).reshape(-1,1) +yPred = mylr.predict_proba(Xnew) +#plt.plot(Xnew, yPred[:,0], label= 'No Iris') +plt.plot(Xnew, yPred[:,1], label= 'Yes Iris') +plt.legend() +plt.plot(x,y,'*g') +plt.show() +``` + + + +![png](README_files/README_20_0.png) + + + +This plot visualizes the trained model's Sigmoid prediction curve over the experimental dataset samples: + +* **Sample Distribution (Green Stars):** Represents the real dataset. Small petal widths (0.1 - 0.6 cm) belong to *Iris setosa* ($y=1$), while larger widths (1.0 - 2.5 cm) belong to the other species ($y=0$). +* **Sigmoid Mapping (Blue Curve):** Displays an inverted logistic curve. It demonstrates the mathematical relationship: as petal width increases, the probability of the flower being *Iris setosa* drops sharply from 1.0 to 0.0. +* **Decision Boundary Threshold:** The curve crosses the 0.5 probability threshold at approximately 0.75 cm. This inflection point defines the exact baseline boundary separating both classifications. + +### Model 2: Iris-Setosa Classifier based on petal length + +#### Feature Shift – Petal Length Isolation + +The model configuration is updated to evaluate a different morphological predictor: +* **Feature Vector ($X$):** Slicing index `[:, 2:3]` isolates **Petal Length** as the independent variable. +* **Target Continuity ($y$):** The classification objective remains focused on **Iris setosa** (`iris.target == 0`) to compare the separation power of petal length against the previous petal width baseline. + + +```python +x = iris.data[:, 2:3] +y = (iris.target == 0).astype(int) + +``` + + +```python +from sklearn.linear_model import LogisticRegression +mylr = LogisticRegression(solver='lbfgs', random_state=42) +mylr.fit(x,y) +``` + + + + +
LogisticRegression(random_state=42)
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+ + + + +```python +Xnew = np.linspace(0,8,100).reshape(-1,1) +yPred = mylr.predict_proba(Xnew) +#plt.plot(Xnew, yPred[:,0], label= 'No Iris') +plt.plot(Xnew, yPred[:,1], label= 'Yes Iris') +plt.legend() +plt.plot(x,y,'*g') +plt.axis([1.5, 5, -0.5, 1.5]) +plt.show() +``` + + + +![png](README_files/README_26_0.png) + + + +This plot illustrates the performance of the second univariable model using **Petal Length**: + +* **Sample Distribution:** Samples with short petal lengths (1.0 - 2.0 cm) are correctly clustered as *Iris setosa* ($y=1$), while samples with larger lengths ($>3.0$ cm) map to $y=0$. +* **Sigmoid Mapping:** The descending blue curve demonstrates that as petal length increases, the probability of the sample being *Iris setosa* drops sharply from 1.0 to 0.0. +* **Decision Boundary:** The curve crosses the 0.5 probability threshold at approximately 2.5 cm, marking the exact inflection point that separates the target class from the rest of the dataset. + +### Model 3: Iris-Setosa Classifier based on Sepal length + +#### Feature Shift – Sepal Length Isolation + +The model evaluates a third morphological predictor independently: +* **Feature Vector ($X$):** Slicing index `[:, 0:1]` isolates **Sepal Length** as the continuous independent variable. +* **Target Continuity ($y$):** The objective remains focused on **Iris setosa** ($y=1$) to compare the separation power of sepal dimensions against the previous petal metrics. + + +```python +x = iris.data[:, 0:1] +y = (iris.target == 0).astype(int) +from sklearn.linear_model import LogisticRegression +mylr = LogisticRegression(solver='lbfgs', random_state=42) +mylr.fit(x,y) +``` + + + + +
LogisticRegression(random_state=42)
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+ + + + +```python +Xnew = np.linspace(0,8,100).reshape(-1,1) +yPred = mylr.predict_proba(Xnew) +#plt.plot(Xnew, yPred[:,0], label= 'No Iris') +plt.plot(Xnew, yPred[:,1], label= 'Yes Iris') +plt.legend() +plt.plot(x,y,'*g') +plt.axis([3.5, 7, -0.1, 1.1]) +plt.show() +``` + + + +![png](README_files/README_31_0.png) + + + +This plot displays the performance of the third univariable model using **Sepal Length**: + +* **Sample Distribution:** Samples representing *Iris setosa* ($y=1$) are concentrated at shorter lengths, but show a much higher spatial overlap with non-setosa samples ($y=0$) compared to the previous petal features. +* **Sigmoid Mapping:** The descending curve shows the probability dropping as sepal length increases. Due to this significant data overlap, the slope is less steep, indicating a more gradual and less aggressive probabilistic transition. +* **Decision Boundary:** The inflection point at $\sigma = 0.5$ establishes the final threshold. This boundary carries more classification uncertainty because sepal dimensions are naturally less distinct between these species. + +### Model 4: Multiple features classifier + +#### Multi-Class Spatial Mapping (Sepal Features) + +This cell upgrades the initial exploratory plot by adding the ground-truth class labels to the 2D sepal feature space: + +* **Feature Interaction:** Maps Sepal Length (`sl`) against Sepal Width (`sw`) simultaneously to analyze their combined distribution. +* **Class Color-Coding:** Differentiates the three original species using distinct markers: Green for *Setosa*, Red for *Versicolor*, and Blue for *Virginica*. +* **Visual Separability Analysis:** Allows immediate observation of the data structure, showing that while *Setosa* forms a perfectly isolated cluster, *Versicolor* and *Virginica* exhibit significant spatial overlap, justifying the need for optimization models. + + +```python +import matplotlib.pyplot as plt +sl = iris.data[:,0:1] +sw = iris.data[:,1:2] +tg = iris.target +plt.plot(sl[tg==0,0], sw[tg==0,0],'.g' ,label='Set') +plt.plot(sl[tg==1,0], sw[tg==1,0],'.r', label='Ver') +plt.plot(sl[tg==2,0], sw[tg==2,0],'.b', label='Vir') +plt.legend() +plt.show() +``` + + + +![png](README_files/README_35_0.png) + + + +#### Bivariate Model Training for Iris Virginica + +This cell configures and trains a multi-feature logistic regression model utilizing tuned optimization parameters: + +* **Bivariate Data Selection:** * **Features (`X`):** Slices index `[:, 0:2]` to combine **Sepal Length** and **Sepal Width** into a two-dimensional feature space. + * **Target (`y`):** Shifts the positive class focus exclusively to **Iris virginica** (`iris.target == 2`). +* **Hyperparameter Tuning (`mylrvir`):** + * **`solver='newton-cg'`**: Uses the Newton-Conjugate Gradient method to compute accurate optimization paths. + * **`C=100` & `tol=1e-5`**: Applies high cost (low regularization) to allow a tighter fit to the data, paired with a strict tolerance for precise convergence. +* **`mylrvir.fit(X, y)`**: Trains the system to find the optimal weight vector $w = [w_1, w_2]$ and bias ($b$), establishing the multi-variable benchmark line. + + +```python +X = iris.data[:,0:2] +y = (iris.target==2).astype(int) +mylrvir = LogisticRegression( + random_state=22, + tol=1e-5, + C=100, + max_iter=100, + solver='newton-cg' +) +mylrvir.fit(X,y) +``` + + + + +
LogisticRegression(C=100, random_state=22, solver='newton-cg', tol=1e-05)
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+ + + +#### Coordinate Grid Generation & Probability Mapping + +This block builds the mathematical testing grid used to map out the complete probability landscape: + +* **`np.meshgrid`**: Generates a dense $100 \times 100$ coordinate grid across the sepal feature space (Length: 3–8 cm, Width: 0–6 cm). +* **`Xnew` (`np.c_`)**: Flattens and couples the grid matrices into a matrix of 10,000 discrete 2D spatial coordinates. +* **`predict_proba(Xnew)`**: Evaluates the trained model across the entire grid, computing the continuous probabilities needed to render the decision contours and 3D surfaces. + + +```python +x0, x1 = np.meshgrid( + np.linspace(3,8,100).reshape(-1,1), + np.linspace(0,6,100).reshape(-1,1) +) +Xnew = np.c_[x0.ravel(), x1.ravel()] +yPred = mylrvir.predict_proba(Xnew) +``` + + +```python +plt.figure(figsize=(10,4)) +plt.plot(X[y==0,0], X[y==0,1],'bs',label='No Virg') +plt.plot(X[y==1,0], X[y==1,1],'g^',label='Virginica') +zz=yPred[:,1].reshape(x0.shape) +contour=plt.contour(x0,x1,zz) +plt.clabel(contour, inline=1,fontsize=15) +plt.xlabel("Sepal Length") +plt.ylabel("Sepal Width") +plt.legend() +plt.show() +``` + + + +![png](README_files/README_40_0.png) + + + +This plot visualizes the continuous probability space generated by the trained bivariate model: + +* **Sample Distribution:** Blue squares represent non-virginica samples ($y=0$), and green triangles represent *Iris virginica* ($y=1$) mapped across Sepal Length and Sepal Width. +* **Probability Contours (`plt.contour`):** The labeled contour lines map specific probability thresholds. They show how the model's prediction confidence transitions across the 2D space. +* **Decision Boundary:** The contour line labeled **0.5** marks the exact geometric threshold. Any sample falling past this line is classified as *Iris virginica*, capturing the spatial trade-off between both sepal measurements. + + +```python +fig, ax =plt.subplots(subplot_kw={"projection": "3d"}) +surf = ax.plot_surface(x0,x1,zz, cmap='jet') +ax.scatter(iris.data[:,0:1], iris.data[:,1:2], y, 'or') +``` + + + + + + + + + + +![png](README_files/README_42_1.png) + + + +This cell projects the bivariate logistic regression model into a 3D coordinate space to visualize the complete probability landscape: + +* **Axis Dimensions:** The horizontal axes represent **Sepal Length** ($x_1$) and **Sepal Width** ($x_2$), while the vertical axis ($Z$) tracks the continuous model probability $\sigma(z) \in [0, 1]$. +* **Probability Surface (`plot_surface`):** The Sigmoid function is rendered as a 3D sheet using the `jet` colormap. It displays the non-linear S-curve transition dynamically stretched across the two-dimensional feature plane. +* **True Labels Spatial Scatter (`ax.scatter`):** The red markers plot the actual samples at their exact spatial coordinates and true binary height ($z = 1$ for *Iris virginica*, $z = 0$ for others). This highlights how the optimized surface splits the space to fit the data points. + +### Modelo 5: Multiple features and muticlass classifier + +#### Multi-Feature & Multi-Class Model Training + +This cell configures and trains the final baseline model to handle all three species simultaneously within a two-dimensional feature space: + +* **Bivariate Inputs (`X`):** Slices index `[:, 0:2]` to utilize both **Sepal Length** and **Sepal Width** as the predictor variables. +* **Multi-Class Target (`y`):** Retains the original multi-class target labels (`0`, `1`, `2`) without applying binarization, expanding the task from a single boundary to a three-class decision space. +* **`LogisticRegression(C=100, solver='lbfgs')`:** Trains a multinomial classifier. The algorithm optimizes a distinct set of weights and biases for each target category, preparing the model to partition the 2D plane into three distinct classification zones. + + +```python +X = iris.data[:,0:2] +y = iris.target +lrmc = LogisticRegression( + solver='lbfgs', + C=100, + random_state=22 +) +lrmc.fit(X,y) +``` + + + + +
LogisticRegression(C=100, random_state=22)
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+ + + +#### Multi-Class Grid Generation and Probability Evaluation + +This cell sets up the coordinate testing matrix to evaluate the multi-class prediction behavior across the entire sepal feature space: + +* **`np.meshgrid`**: Constructs a dense $100 \times 100$ coordinate grid bounding the Sepal Length (3–8 cm) and Sepal Width (0–6 cm) ranges. +* **`Xnew` (`np.c_`)**: Flattens and pairs the grid elements into a matrix of 10,000 distinct 2D spatial coordinates. +* **`lrmc.predict_proba(Xnew)`**: Computes a three-column probability matrix for each point. This mapping determines the exact multi-class boundaries by evaluating the localized likelihood for *Setosa*, *Versicolor*, and *Virginica* simultaneously. + + +```python +x0, x1 = np.meshgrid( + np.linspace(3,8,100).reshape(-1,1), + np.linspace(0,6,100).reshape(-1,1) +) +Xnew = np.c_[x0.ravel(), x1.ravel()] +yPred = lrmc.predict_proba(Xnew) +``` + + +```python +plt.figure(figsize=(10,4)) +plt.plot(X[y==0,0], X[y==0,1],'.b',label='Setosa') +plt.plot(X[y==1,0], X[y==1,1],'+g',label='Versi') +plt.plot(X[y==2,0], X[y==2,1],'*m',label='Virgi') +zz=yPred[:,1].reshape(x0.shape) +contour=plt.contour(x0,x1,zz) +plt.clabel(contour, inline=1,fontsize=15) +plt.xlabel("Sepal Length") +plt.ylabel("Sepal Width") +plt.legend() +plt.show() +``` + + + +![png](README_files/README_49_0.png) + + + +This plot maps the continuous probability distribution of the middle class within the multi-class decision space: + +* **Three-Class Distribution:** Displays all species simultaneously using distinct markers: blue dots for *Setosa* ($y=0$), green pluses for *Versicolor* ($y=1$), and magenta stars for *Virginica* ($y=2$). +* **Target Class Extraction (`yPred[:, 1]`):** Slicing the second column of the probability matrix isolates and tracks the specific localized likelihood of a sample being **Iris versicolor**. +* **Localized Probability Ridge:** Unlike the linear boundaries seen in binary classification, the multinomial model creates a bounded peak or "ridge" to isolate the middle class. The highest contour line (**0.90**) tightly encapsulates the core *Versicolor* cluster, dropping off systematically as the features move toward *Setosa* (left) or *Virginica* (right) territories. + + +```python +yPred = lrmc.predict(Xnew) +plt.figure(figsize=(10,6)) +plt.plot(X[y==0,0], X[y==0,1],'bs',label='Setosa') +plt.plot(X[y==1,0], X[y==1,1],'g^',label='Versi') +plt.plot(X[y==2,0], X[y==2,1],'*m',label='Virgi') +zz=yPred.reshape(x0.shape) +contour=plt.contourf(x0,x1,zz, cmap='jet', alpha=0.3) +plt.clabel(contour, inline=1,fontsize=15) +plt.xlabel("Sepal Length") +plt.ylabel("Sepal Width") +plt.legend() +plt.show() +``` + + + +![png](README_files/README_51_0.png) + + + +This plot visualizes the ultimate classification boundaries by partitioning the entire 2D feature space into hard decision zones: + +* **Hard Class Assignment (`lrmc.predict`):** Converts continuous probabilities into discrete class verdicts (`0`, `1`, or `2`) by applying an *argmax* function (selecting the class with the highest probability for each point). +* **Filled Decision Regions (`plt.contourf`):** Shades the coordinate plane into three distinct, solid zones using the `jet` colormap: + * **Blue Region:** Absolute classification space for *Iris setosa*. + * **Green Region:** Absolute classification space for *Iris versicolor*. + * **Red/Orange Region:** Absolute classification space for *Iris virginica*. +* **Boundary Analysis:** The sharp geometric intersections between the colored blocks define the definitive decision thresholds. This layout explicitly reveals how the linear multi-class model manages the regional trade-offs and handles the spatial overlap between the *Versicolor* and *Virginica* samples. + + +```python +fig, ax =plt.subplots(subplot_kw={"projection": "3d"}) +surf = ax.plot_surface(x0,x1,zz, cmap='jet') +ax.scatter(iris.data[:,0:1], iris.data[:,1:2], y, 'or') +``` + + + + + + + + + + +![png](README_files/README_53_1.png) + + + +This cell integrates the actual dataset samples into the 3D hard decision space to visually evaluate the multi-class model's accuracy: + +* **Discrete Vertical Alignment ($Z$):** Both the staircase surface and the scatter markers use the integer multi-class taxonomy ($0$ for *Setosa*, $1$ for *Versicolor*, and $2$ for *Virginica*) instead of continuous probabilities. +* **Stepped Surface (`plot_surface`):** Represents the geometric boundaries computed by the model. Each level dictates the categorical verdict zone based on the combination of sepal features. +* **True Labels Scatter (`ax.scatter`):** Plots the real flower samples at their actual feature coordinates and true species height. 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zeL~ZC1WZiPo$s$Uqkka)&)vO5?|*4B@6t=#c?|4zXSf0ez;(|)XB}4Q;7WMzll3kd_ptwz0-gfT;&I?yh zCYoxfz5TOd%FD~;;D(KKJE)To@eZBkuc44g(pQpns%E<+g%eIQ7a WpcKqcHfVnW{3yx4kt>%m4*EaMg+)IA literal 0 HcmV?d00001 diff --git a/Regresion_Logistica/README.md b/Regresion_Logistica/README.md deleted file mode 100644 index 28309cc..0000000 --- a/Regresion_Logistica/README.md +++ /dev/null @@ -1,6881 +0,0 @@ -# Titulo del proyecto - -# Module 1: Logistic Regression Classifier - -Author: Sofia Samaniego Lopez - -Institution: Universidad Autonoma de Baja California (UABC) - -Advisor: Dr. Gerardo Marx Chavez Campos - -This script establishes the baseline evaluation for binary classification using -the classic Iris dataset. The objective of this specific work is to -analyze linear combination, decision boundaries, and probability estimation based -on morphological features—specifically petal width and length. - -The model utilizes Scikit-Learn's LogisticRegression framework to execute the -optimization process and map inputs to a probability output using the Sigmoid function. -This code serves as a strict benchmark comparison, generating the reference -ground truth metrics and spatial visualizations required to evaluate the performance -and accuracy of subsequent custom implementations. - -## Experimental Setup and Preliminary Analysis - -### Step 1: Import Required Libraries and Environment Setup - -In this initial stage, the necessary scientific computing and data processing libraries are imported to set up our development environment: -* **NumPy**: Utilized for efficient multi-dimensional array operations and core matrix algebra. -* **Matplotlib (pyplot)**: Employed to generate the spatial scatter plots and map the resulting decision boundaries. -* **Scikit-Learn**: Specifically importing the `datasets` module to fetch the target morphological data and `LogisticRegression` to serve as our validation benchmark baseline. - - -```python -!pip3 install scikit-learn -!pip3 install matplotlib -!pip3 install numpy - -import matplotlib.pyplot as plt -import numpy as np -``` - -### Step 2: Load and Explore the Iris Dataset Characteristics - -The classic **Iris Dataset** is loaded into the workspace to establish our baseline classification task. - -#### Dataset Overview and Morphological Features -The complete dataset consists of **150 samples** from three distinct species of Iris flowers (*Iris setosa*, *Iris versicolor*, and *Iris virginica*). For each sample, four continuous geometric features are available: -1. Sepal Length -2. Sepal Width -3. Petal Length -4. Petal Width - -#### Problem Simplification & Single-Feature Evaluation - -The classification task is constrained to analyze the Sigmoid function and linear thresholds on a simpler scale: - -* **Target Binarization:** The multi-class target is converted to binary labels ($y=1$ for *Iris virginica*, $y=0$ for others) to establish a clear threshold. -* **Single-Feature Isolation:** Instead of combining dimensions, features are evaluated **one at a time** (e.g., petal width or sepal length) to inspect their independent separation power before building multi-dimensional models. - - -```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 ... - - - -### Step 3: Exploratory Data Analysis & Target Inspection - -Prior to model optimization, a visual and structural inspection evaluates the data distribution: - -* **Unclassified Spatial Mapping:** Plotting Sepal Length (`sl`) vs. Sepal Width (`sw`) using plain markers (`'.k'`) reveals the raw data structure. This helps verify if the morphological features naturally form distinct clusters before applying any algorithmic boundaries. -* **Target Label Mapping (`iris.target`):** Inspecting the ground-truth array to map the multi-class numerical taxonomy: - * `0`: *Iris setosa* - * `1`: *Iris versicolor* - * `2`: *Iris virginica* - -This inspection links the visual spatial groups with their mathematical labels, establishing the baseline before data binarization. - - -```python -sl = iris.data[:, 0:1] -sw = iris.data[:, 1:2] -plt.plot(sl,sw,'.k') -plt.show() -``` - - - -![png](README_files/README_10_0.png) - - - - -```python -iris.target -``` - - - - - array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, - 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, - 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]) - - - -### Step 4: Theoretical Sigmoid Function & Decision Boundary - -Generating a synthetic domain from -10 to 10 to plot the standalone mathematical Sigmoid function: - -$$\sigma(t) = \frac{1}{1 + e^{-t}}$$ - -This visualizes how the curve maps inputs to a probability between 0 and 1, establishing the inflection point $\sigma(0) = 0.5$ as the theoretical threshold for the decision boundary. - - -```python -t= np.linspace(-10,10,100) -sig = 1/(1+np.exp(-t)) -plt.plot(t,sig, '.b', label=r"$\sigma$") -plt.legend(loc='upper left', fontsize=20) -plt.show() -``` - - - -![png](README_files/README_13_0.png) - - - -## Model Training and Benchmark Evaluation - -### Model 1: Iris-Setosa Classifier based on petal width - -#### Feature Selection & Setosa Target Binarization - -The dataset is filtered and restructured to evaluate a new binary classification task: -* **Feature Vector ($X$):** Slicing index `[:, 3:]` isolates **Petal Width** as the continuous predictor variable. -* **Target Binarization ($y$):** The criteria `(iris.target == 0).astype(int)` shifts the positive class ($y=1$) exclusively to **Iris setosa**, mapping all other species to $0$. This creates the target array seen in the output. - - -```python -x = iris.data[:, 3:] -y = (iris.target == 0).astype(int) -y -``` - - - - - array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) - - - -#### Benchmark Model Initialization and Fitting - -This cell instantiates and trains the baseline classification model using Scikit-Learn: - -* **`LogisticRegression(solver='lbfgs', random_state=42)`**: Instantiates the model using the Limited-memory BFGS (`lbfgs`) optimization solver and locks the `random_state` to 42 to ensure reproducible weight initialization. -* **`mylr.fit(x, y)`**: Trains the classifier on the isolated feature vector `x` and the binarized target labels `y`. This optimization process computes the optimal weight ($w$) and bias ($b$) parameters that minimize the loss function. - - -```python -from sklearn.linear_model import LogisticRegression -mylr = LogisticRegression(solver='lbfgs', random_state=42) -mylr.fit(x,y) -``` - - - - -

- - - - -```python -Xnew = np.linspace(-1,3,100).reshape(-1,1) -yPred = mylr.predict_proba(Xnew) -#plt.plot(Xnew, yPred[:,0], label= 'No Iris') -plt.plot(Xnew, yPred[:,1], label= 'Yes Iris') -plt.legend() -plt.plot(x,y,'*g') -plt.show() -``` - - - -![png](README_files/README_20_0.png) - - - -This plot visualizes the trained model's Sigmoid prediction curve over the experimental dataset samples: - -* **Sample Distribution (Green Stars):** Represents the real dataset. Small petal widths (0.1 - 0.6 cm) belong to *Iris setosa* ($y=1$), while larger widths (1.0 - 2.5 cm) belong to the other species ($y=0$). -* **Sigmoid Mapping (Blue Curve):** Displays an inverted logistic curve. It demonstrates the mathematical relationship: as petal width increases, the probability of the flower being *Iris setosa* drops sharply from 1.0 to 0.0. -* **Decision Boundary Threshold:** The curve crosses the 0.5 probability threshold at approximately 0.75 cm. This inflection point defines the exact baseline boundary separating both classifications. - -### Model 2: Iris-Setosa Classifier based on petal length - -#### Feature Shift – Petal Length Isolation - -The model configuration is updated to evaluate a different morphological predictor: -* **Feature Vector ($X$):** Slicing index `[:, 2:3]` isolates **Petal Length** as the independent variable. -* **Target Continuity ($y$):** The classification objective remains focused on **Iris setosa** (`iris.target == 0`) to compare the separation power of petal length against the previous petal width baseline. - - -```python -x = iris.data[:, 2:3] -y = (iris.target == 0).astype(int) - -``` - - -```python -from sklearn.linear_model import LogisticRegression -mylr = LogisticRegression(solver='lbfgs', random_state=42) -mylr.fit(x,y) -``` - - - - -
LogisticRegression(random_state=42)
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- - - - -```python -Xnew = np.linspace(0,8,100).reshape(-1,1) -yPred = mylr.predict_proba(Xnew) -#plt.plot(Xnew, yPred[:,0], label= 'No Iris') -plt.plot(Xnew, yPred[:,1], label= 'Yes Iris') -plt.legend() -plt.plot(x,y,'*g') -plt.axis([1.5, 5, -0.5, 1.5]) -plt.show() -``` - - - -![png](README_files/README_26_0.png) - - - -This plot illustrates the performance of the second univariable model using **Petal Length**: - -* **Sample Distribution:** Samples with short petal lengths (1.0 - 2.0 cm) are correctly clustered as *Iris setosa* ($y=1$), while samples with larger lengths ($>3.0$ cm) map to $y=0$. -* **Sigmoid Mapping:** The descending blue curve demonstrates that as petal length increases, the probability of the sample being *Iris setosa* drops sharply from 1.0 to 0.0. -* **Decision Boundary:** The curve crosses the 0.5 probability threshold at approximately 2.5 cm, marking the exact inflection point that separates the target class from the rest of the dataset. - -### Model 3: Iris-Setosa Classifier based on Sepal length - -#### Feature Shift – Sepal Length Isolation - -The model evaluates a third morphological predictor independently: -* **Feature Vector ($X$):** Slicing index `[:, 0:1]` isolates **Sepal Length** as the continuous independent variable. -* **Target Continuity ($y$):** The objective remains focused on **Iris setosa** ($y=1$) to compare the separation power of sepal dimensions against the previous petal metrics. - - -```python -x = iris.data[:, 0:1] -y = (iris.target == 0).astype(int) -from sklearn.linear_model import LogisticRegression -mylr = LogisticRegression(solver='lbfgs', random_state=42) -mylr.fit(x,y) -``` - - - - -
LogisticRegression(random_state=42)
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- - - - -```python -Xnew = np.linspace(0,8,100).reshape(-1,1) -yPred = mylr.predict_proba(Xnew) -#plt.plot(Xnew, yPred[:,0], label= 'No Iris') -plt.plot(Xnew, yPred[:,1], label= 'Yes Iris') -plt.legend() -plt.plot(x,y,'*g') -plt.axis([3.5, 7, -0.1, 1.1]) -plt.show() -``` - - - -![png](README_files/README_31_0.png) - - - -This plot displays the performance of the third univariable model using **Sepal Length**: - -* **Sample Distribution:** Samples representing *Iris setosa* ($y=1$) are concentrated at shorter lengths, but show a much higher spatial overlap with non-setosa samples ($y=0$) compared to the previous petal features. -* **Sigmoid Mapping:** The descending curve shows the probability dropping as sepal length increases. Due to this significant data overlap, the slope is less steep, indicating a more gradual and less aggressive probabilistic transition. -* **Decision Boundary:** The inflection point at $\sigma = 0.5$ establishes the final threshold. This boundary carries more classification uncertainty because sepal dimensions are naturally less distinct between these species. - -### Model 4: Multiple features classifier - -#### Multi-Class Spatial Mapping (Sepal Features) - -This cell upgrades the initial exploratory plot by adding the ground-truth class labels to the 2D sepal feature space: - -* **Feature Interaction:** Maps Sepal Length (`sl`) against Sepal Width (`sw`) simultaneously to analyze their combined distribution. -* **Class Color-Coding:** Differentiates the three original species using distinct markers: Green for *Setosa*, Red for *Versicolor*, and Blue for *Virginica*. -* **Visual Separability Analysis:** Allows immediate observation of the data structure, showing that while *Setosa* forms a perfectly isolated cluster, *Versicolor* and *Virginica* exhibit significant spatial overlap, justifying the need for optimization models. - - -```python -import matplotlib.pyplot as plt -sl = iris.data[:,0:1] -sw = iris.data[:,1:2] -tg = iris.target -plt.plot(sl[tg==0,0], sw[tg==0,0],'.g' ,label='Set') -plt.plot(sl[tg==1,0], sw[tg==1,0],'.r', label='Ver') -plt.plot(sl[tg==2,0], sw[tg==2,0],'.b', label='Vir') -plt.legend() -plt.show() -``` - - - -![png](README_files/README_35_0.png) - - - -#### Bivariate Model Training for Iris Virginica - -This cell configures and trains a multi-feature logistic regression model utilizing tuned optimization parameters: - -* **Bivariate Data Selection:** * **Features (`X`):** Slices index `[:, 0:2]` to combine **Sepal Length** and **Sepal Width** into a two-dimensional feature space. - * **Target (`y`):** Shifts the positive class focus exclusively to **Iris virginica** (`iris.target == 2`). -* **Hyperparameter Tuning (`mylrvir`):** - * **`solver='newton-cg'`**: Uses the Newton-Conjugate Gradient method to compute accurate optimization paths. - * **`C=100` & `tol=1e-5`**: Applies high cost (low regularization) to allow a tighter fit to the data, paired with a strict tolerance for precise convergence. -* **`mylrvir.fit(X, y)`**: Trains the system to find the optimal weight vector $w = [w_1, w_2]$ and bias ($b$), establishing the multi-variable benchmark line. - - -```python -X = iris.data[:,0:2] -y = (iris.target==2).astype(int) -mylrvir = LogisticRegression( - random_state=22, - tol=1e-5, - C=100, - max_iter=100, - solver='newton-cg' -) -mylrvir.fit(X,y) -``` - - - - -
LogisticRegression(C=100, random_state=22, solver='newton-cg', tol=1e-05)
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- - - -#### Coordinate Grid Generation & Probability Mapping - -This block builds the mathematical testing grid used to map out the complete probability landscape: - -* **`np.meshgrid`**: Generates a dense $100 \times 100$ coordinate grid across the sepal feature space (Length: 3–8 cm, Width: 0–6 cm). -* **`Xnew` (`np.c_`)**: Flattens and couples the grid matrices into a matrix of 10,000 discrete 2D spatial coordinates. -* **`predict_proba(Xnew)`**: Evaluates the trained model across the entire grid, computing the continuous probabilities needed to render the decision contours and 3D surfaces. - - -```python -x0, x1 = np.meshgrid( - np.linspace(3,8,100).reshape(-1,1), - np.linspace(0,6,100).reshape(-1,1) -) -Xnew = np.c_[x0.ravel(), x1.ravel()] -yPred = mylrvir.predict_proba(Xnew) -``` - - -```python -plt.figure(figsize=(10,4)) -plt.plot(X[y==0,0], X[y==0,1],'bs',label='No Virg') -plt.plot(X[y==1,0], X[y==1,1],'g^',label='Virginica') -zz=yPred[:,1].reshape(x0.shape) -contour=plt.contour(x0,x1,zz) -plt.clabel(contour, inline=1,fontsize=15) -plt.xlabel("Sepal Length") -plt.ylabel("Sepal Width") -plt.legend() -plt.show() -``` - - - -![png](README_files/README_40_0.png) - - - -This plot visualizes the continuous probability space generated by the trained bivariate model: - -* **Sample Distribution:** Blue squares represent non-virginica samples ($y=0$), and green triangles represent *Iris virginica* ($y=1$) mapped across Sepal Length and Sepal Width. -* **Probability Contours (`plt.contour`):** The labeled contour lines map specific probability thresholds. They show how the model's prediction confidence transitions across the 2D space. -* **Decision Boundary:** The contour line labeled **0.5** marks the exact geometric threshold. Any sample falling past this line is classified as *Iris virginica*, capturing the spatial trade-off between both sepal measurements. - - -```python -fig, ax =plt.subplots(subplot_kw={"projection": "3d"}) -surf = ax.plot_surface(x0,x1,zz, cmap='jet') -ax.scatter(iris.data[:,0:1], iris.data[:,1:2], y, 'or') -``` - - - - - - - - - - -![png](README_files/README_42_1.png) - - - -This cell projects the bivariate logistic regression model into a 3D coordinate space to visualize the complete probability landscape: - -* **Axis Dimensions:** The horizontal axes represent **Sepal Length** ($x_1$) and **Sepal Width** ($x_2$), while the vertical axis ($Z$) tracks the continuous model probability $\sigma(z) \in [0, 1]$. -* **Probability Surface (`plot_surface`):** The Sigmoid function is rendered as a 3D sheet using the `jet` colormap. It displays the non-linear S-curve transition dynamically stretched across the two-dimensional feature plane. -* **True Labels Spatial Scatter (`ax.scatter`):** The red markers plot the actual samples at their exact spatial coordinates and true binary height ($z = 1$ for *Iris virginica*, $z = 0$ for others). This highlights how the optimized surface splits the space to fit the data points. - -### Modelo 5: Multiple features and muticlass classifier - -#### Multi-Feature & Multi-Class Model Training - -This cell configures and trains the final baseline model to handle all three species simultaneously within a two-dimensional feature space: - -* **Bivariate Inputs (`X`):** Slices index `[:, 0:2]` to utilize both **Sepal Length** and **Sepal Width** as the predictor variables. -* **Multi-Class Target (`y`):** Retains the original multi-class target labels (`0`, `1`, `2`) without applying binarization, expanding the task from a single boundary to a three-class decision space. -* **`LogisticRegression(C=100, solver='lbfgs')`:** Trains a multinomial classifier. The algorithm optimizes a distinct set of weights and biases for each target category, preparing the model to partition the 2D plane into three distinct classification zones. - - -```python -X = iris.data[:,0:2] -y = iris.target -lrmc = LogisticRegression( - solver='lbfgs', - C=100, - random_state=22 -) -lrmc.fit(X,y) -``` - - - - -
LogisticRegression(C=100, random_state=22)
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- - - -#### Multi-Class Grid Generation and Probability Evaluation - -This cell sets up the coordinate testing matrix to evaluate the multi-class prediction behavior across the entire sepal feature space: - -* **`np.meshgrid`**: Constructs a dense $100 \times 100$ coordinate grid bounding the Sepal Length (3–8 cm) and Sepal Width (0–6 cm) ranges. -* **`Xnew` (`np.c_`)**: Flattens and pairs the grid elements into a matrix of 10,000 distinct 2D spatial coordinates. -* **`lrmc.predict_proba(Xnew)`**: Computes a three-column probability matrix for each point. This mapping determines the exact multi-class boundaries by evaluating the localized likelihood for *Setosa*, *Versicolor*, and *Virginica* simultaneously. - - -```python -x0, x1 = np.meshgrid( - np.linspace(3,8,100).reshape(-1,1), - np.linspace(0,6,100).reshape(-1,1) -) -Xnew = np.c_[x0.ravel(), x1.ravel()] -yPred = lrmc.predict_proba(Xnew) -``` - - -```python -plt.figure(figsize=(10,4)) -plt.plot(X[y==0,0], X[y==0,1],'.b',label='Setosa') -plt.plot(X[y==1,0], X[y==1,1],'+g',label='Versi') -plt.plot(X[y==2,0], X[y==2,1],'*m',label='Virgi') -zz=yPred[:,1].reshape(x0.shape) -contour=plt.contour(x0,x1,zz) -plt.clabel(contour, inline=1,fontsize=15) -plt.xlabel("Sepal Length") -plt.ylabel("Sepal Width") -plt.legend() -plt.show() -``` - - - -![png](README_files/README_49_0.png) - - - -This plot maps the continuous probability distribution of the middle class within the multi-class decision space: - -* **Three-Class Distribution:** Displays all species simultaneously using distinct markers: blue dots for *Setosa* ($y=0$), green pluses for *Versicolor* ($y=1$), and magenta stars for *Virginica* ($y=2$). -* **Target Class Extraction (`yPred[:, 1]`):** Slicing the second column of the probability matrix isolates and tracks the specific localized likelihood of a sample being **Iris versicolor**. -* **Localized Probability Ridge:** Unlike the linear boundaries seen in binary classification, the multinomial model creates a bounded peak or "ridge" to isolate the middle class. The highest contour line (**0.90**) tightly encapsulates the core *Versicolor* cluster, dropping off systematically as the features move toward *Setosa* (left) or *Virginica* (right) territories. - - -```python -yPred = lrmc.predict(Xnew) -plt.figure(figsize=(10,6)) -plt.plot(X[y==0,0], X[y==0,1],'bs',label='Setosa') -plt.plot(X[y==1,0], X[y==1,1],'g^',label='Versi') -plt.plot(X[y==2,0], X[y==2,1],'*m',label='Virgi') -zz=yPred.reshape(x0.shape) -contour=plt.contourf(x0,x1,zz, cmap='jet', alpha=0.3) -plt.clabel(contour, inline=1,fontsize=15) -plt.xlabel("Sepal Length") -plt.ylabel("Sepal Width") -plt.legend() -plt.show() -``` - - - -![png](README_files/README_51_0.png) - - - -This plot visualizes the ultimate classification boundaries by partitioning the entire 2D feature space into hard decision zones: - -* **Hard Class Assignment (`lrmc.predict`):** Converts continuous probabilities into discrete class verdicts (`0`, `1`, or `2`) by applying an *argmax* function (selecting the class with the highest probability for each point). -* **Filled Decision Regions (`plt.contourf`):** Shades the coordinate plane into three distinct, solid zones using the `jet` colormap: - * **Blue Region:** Absolute classification space for *Iris setosa*. - * **Green Region:** Absolute classification space for *Iris versicolor*. - * **Red/Orange Region:** Absolute classification space for *Iris virginica*. -* **Boundary Analysis:** The sharp geometric intersections between the colored blocks define the definitive decision thresholds. This layout explicitly reveals how the linear multi-class model manages the regional trade-offs and handles the spatial overlap between the *Versicolor* and *Virginica* samples. - - -```python -fig, ax =plt.subplots(subplot_kw={"projection": "3d"}) -surf = ax.plot_surface(x0,x1,zz, cmap='jet') -ax.scatter(iris.data[:,0:1], iris.data[:,1:2], y, 'or') -``` - - - - - - - - - - -![png](README_files/README_53_1.png) - - - -This cell integrates the actual dataset samples into the 3D hard decision space to visually evaluate the multi-class model's accuracy: - -* **Discrete Vertical Alignment ($Z$):** Both the staircase surface and the scatter markers use the integer multi-class taxonomy ($0$ for *Setosa*, $1$ for *Versicolor*, and $2$ for *Virginica*) instead of continuous probabilities. -* **Stepped Surface (`plot_surface`):** Represents the geometric boundaries computed by the model. Each level dictates the categorical verdict zone based on the combination of sepal features. -* **True Labels Scatter (`ax.scatter`):** Plots the real flower samples at their actual feature coordinates and true species height. This allows immediate visual verification of performance: samples resting on their matching colored step are correctly classified, while those caught on the wrong tier highlight the exact instances of classification error caused by spatial overlap.