Introduction: In this project, we will explore binary classification using machine learning techniques, specifically logistic regression with the sigmoid function. We’ll apply this methodology to the song “California Love” by 2Pac, aiming to predict whether a song belongs to the rap or pop genre based on its tempo and lyrical content.
Imagine you’re building a model to classify songs as either “rap” or “pop” based on certain features like tempo, lyrical content, and beat style. Let’s take 2Pac’s song “California Love” as an example.
- Features as Tempo and Lyrical Content:
- You have two features: tempo (fast, slow) represented by 𝑥1x1 and lyrical content (explicit, positive) represented by 𝑥2x2.
- Linear Combination of Features:
- Your model combines these features using a linear equation: 𝑧=𝛽0+𝛽1𝑥1+𝛽2𝑥2z=β0+β1x1+β2x2 Here, 𝑧z is like a score that combines tempo and lyrical content, weighted by coefficients 𝛽0,𝛽1,β0,β1, and 𝛽2β2.
- Logistic Function (Sigmoid):
- The logistic function transforms this score 𝑧z into probabilities: Probability of being rap=𝜎(𝑧)=11+𝑒−𝑧Probability of being rap=σ(z)=1+e−z1 This formula converts the linear score into a probability value between 0 and 1. For example, if 𝜎(𝑧)=0.8σ(z)=0.8, it means there’s an 80% chance the song is rap.
- Interpretation with “California Love”:
- Suppose the model predicts 𝜎(𝑧)=0.9σ(z)=0.9 for “California Love.” This high probability suggests that based on tempo and lyrical content, the song is likely categorized as rap by the model.
- Training the Model:
- During training, the model adjusts coefficients 𝛽0,𝛽1,β0,β1, and 𝛽2β2 using labeled data (rap and pop songs) to improve predictions. It learns which tempo and lyrical features are more indicative of rap songs.
So, in this scenario, the logistic regression model with the sigmoid function acts like a “rap-or-pop” classifier, using features like tempo and lyrical content to probabilistically determine whether a song, such as “California Love” by 2Pac, is more likely to be categorized as rap or pop.