Logistic classification (logistic regression) is used to classify data when the goal is to predict the probability that an input belongs to a particular class, typically for binary classification problems (two classes such as 0/1, yes/no). The classification occurs by applying a logistic (sigmoid) function to a linear combination of input features, which outputs a probability between 0 and 1. When this probability crosses a threshold (usually 0.5), the data point is assigned to a class.
When to use logistic classification for classifying data:
- When the dependent variable is categorical and usually binary.
- When the task is to classify data points into two discrete categories.
- When the output needs to be a probability mapping to a class label.
- Often used in fields like medical diagnosis (e.g., disease/no disease), spam detection, and any other binary classification tasks.
How logistic classification works:
- Transform input features through a linear combination parametrized by weights and bias.
- Use the logistic sigmoid function σ(z)=11+e−z\sigma(z)=\frac{1}{1+e^{-z}}σ(z)=1+e−z1 to map this linear combination zzz into a probability.
- Classify the input data based on whether the probability exceeds a threshold.
Summary of the classification process:
- Collect input features matrix XXX.
- Compute linear combination z=w⋅X+bz=w\cdot X+bz=w⋅X+b.
- Apply sigmoid function σ(z)\sigma(z)σ(z) to get a probability.
- Assign class based on thresholding the probability.
This approach works well when the relationship between features and the log- odds of the class is linear, and it is a widely used method in supervised machine learning for classification problems.
