Defining Features within Datasets

Before we examine how autoencoders learn new representations from data, it's essential to first understand what we mean by "features" within a dataset. Think of features as the individual, measurable properties or characteristics of the data you're working with. They are the building blocks that describe each piece of information, and machine learning models use these features to make predictions or find patterns.

Features in Tabular Data: Columns as Characteristics

Perhaps the most straightforward way to understand features is by looking at structured data, often organized in tables, like a spreadsheet. In such a table:

• Each row typically represents a single observation or item (e.g., a customer, a product, a patient, a house).
• Each column represents a specific feature or attribute of these items.

For instance, if you have a dataset about customers, the features might include:

• Age (e.g., 34 years)
• Annual Income (e.g., $50,000)
• City of Residence (e.g., "New York")
• Has Subscribed (e.g., True/False)

Each of these columns provides a distinct piece of information (a feature) about each customer. A machine learning model could use these features to, for example, predict whether a new customer is likely to subscribe to a service.

Consider the following simple representation of a dataset:

In this housing dataset example, "Square Footage," "No. of Bedrooms," and "Distance to City Center" are features that describe each house. "Price" might be what we want to predict.

Features in Other Types of Data

Features aren't limited to neat columns in a table.

• Image Data: For an image, the most basic features are the pixel values. A grayscale image of size 28x28 pixels (like those in the MNIST dataset of handwritten digits) has $28 \times 28 = 784$ features, where each feature is the intensity value of a specific pixel. For a color image, you'd typically have three values (Red, Green, Blue) for each pixel, so a 100x100 color image would have $100 \times 100 \times 3 = 30,000$ raw features.
• Text Data: In text, features can be individual words, the frequency of words (a "bag-of-words" model), sequences of words (n-grams), or more complex representations like word embeddings (which we'll see can be learned). For example, in a sentiment analysis task, the presence or absence of words like "happy" or "disappointed" could be important features.
• Audio Data: For sound, features might be derived from the waveform, such as Mel-frequency cepstral coefficients (MFCCs) which represent the short-term power spectrum of a sound.

The common thread is that features are the numerical or categorical inputs derived from raw data that a machine learning algorithm uses to perform its task.

Why Understanding Features is Important

The selection and quality of features are fundamental to the success of any machine learning project.

1. Input to Models: Features are the direct input that models "see." If the features don't contain relevant information for the task at hand, even the most sophisticated model will perform poorly.
2. Dimensionality: The number of features determines the dimensionality of your data. Having too many features (especially irrelevant ones) can sometimes make learning harder (this is often called the "curse of dimensionality"). This is one area where autoencoders can help, as we'll discuss later in the context of dimensionality reduction.
3. Interpretability: Well-chosen or well-learned features can sometimes make the model's decisions more understandable.

In essence, features are the lens through which a machine learning model views the data.

As we proceed through this chapter, we'll see that autoencoders don't just work with predefined features; their strength lies in their ability to learn new, often more compact and informative, features from the initial raw input features. The bottleneck layer in an autoencoder, which we've discussed previously, is where these learned features reside. Having a clear understanding of what "features" are in their basic sense provides the foundation for appreciating how autoencoders transform them.