What are the best ways to generate new features in feature engineering?

Domain knowledge is indeed a crucial aspect of feature engineering, allowing data scientists to leverage their understanding of the underlying domain to create meaningful and informative features. By drawing on domain knowledge, data scientists can identify relevant variables, interactions, and transformations that may not be apparent from the raw data alone. This enables them to design features that capture important relationships and patterns in the data, ultimately improving the performance of machine learning models. Additionally, domain knowledge can help in selecting appropriate feature engineering techniques and ensuring that the generated features align with the specific requirements and objectives of the problem at hand.

Domain knowledge is paramount in feature engineering, the art of creating informative variables for machine learning models. Domain experts have an intimate understanding of the problem at hand and the underlying relationships within the data. This knowledge allows them to identify subtle patterns that pure statistical analysis might miss. They can suggest transformations, combinations, and aggregations of existing data points to reveal crucial insights. For example, in healthcare, domain knowledge could lead to crafting features like the ratio of specific blood test results or durations between medical events, which hold much more predictive power than raw values alone.

Domain knowledge enriches feature engineering by leveraging expertise relevant to the problem domain. It enables the identification of key variables and transformations, enhancing data representation. For instance, in weather prediction, utilizing domain knowledge can lead to features like wind chill or heat index, enriching model insights and predictive accuracy.

Needless to say, domain knowledge is the first and most obvious way to generate features. I think what is required is to look at non-domain knowledge to extract features. We need to remember that we have Machine Learning Capability at our disposal and even if we are wrong in selecting some feature, it doesn't cost us too much. One should play around and not be tied down by domain knowledge.

There are many mathematical operations that prove effective in converting raw data into informative features. Techniques like polynomial features delve into non-linear relationships through power and interaction terms, offering a nuanced view of data patterns. Scaling and normalization, like Z-score and Min-Max methods, help achieve consistency across feature scales, a step that can't be overlooked when feature magnitude directly impacts performance. Logarithmic and exponential transformations have dual purposes, either normalizing data to reduce skewness or amplifying variances to highlight data trends. The strategy chosen should be based on the specific characteristics of the data itself and the requirements of the model used.

Mathematical operations offer a straightforward and effective way to derive new features, enhancing the predictive power of machine learning models. Simple additions, subtractions, multiplications, and divisions can uncover latent relationships within the data. For instance, subtracting a product's cost from its selling price reveals profit margins. Ratios and proportions normalize features, making them less sensitive to scale. However, relying solely on basic mathematical operations can be limiting. Sophisticated feature engineering often needs more complex transformations like logarithmic conversions to handle skewed distributions, binning to categorize continuous variables, or domain-specific calculations.

Mathematical operations can be used for performing linear(addition, subtraction etc) or non-linear(exponential, logarithm or square root etc) operations on the numerical field. Mathematical operations can be used in the following scenarios 1) Right skewed distribution- If the variable has right skewed distribution, then log or square root operation can be used. 2) Left skewed distribution- If the variable has left skewed distribution then we use square or cube operation. 3) Change in the unit- If we want to change the unit of the variable. E.g. Celsius is converted to Fahrenheit. 4) Mathematical or financial formula is used to compute financial ratios. Mathematical ops are important but they can increase multicollinearity.

Applying mathematical operations to existing features enriches feature sets by capturing nonlinear relationships and scaling variations. Operations like addition, subtraction, multiplication, and division enable the creation of features such as price per square foot or area ratio, enhancing model insights and predictive capabilities, particularly in problems like house price prediction.

Statistical methods play a pivotal role in crafting new features within machine learning. They provide a data-driven approach to uncovering hidden relationships and patterns. Techniques like correlation analysis identify features strongly associated with target outcomes. Statistical distributions help transform data by normalization or scaling, improving model performance. Principal Component Analysis (PCA) reduces dimensionality by creating powerful combinations of existing features. Statistical methods offer quantifiable insights into data characteristics, leading to more informative features that ultimately boost model accuracy and predictive power.

In Statistics, the statistical moments describe a specific property of distribution. - Mean is defined as first moment and standard deviation is defined as second moment. - Skewness is defined as a third moment. If data is skewed, we can use log, square root, square transformation. - kurtosis is the fourth moment in statistics. It is used to measure tailedness in data. If data has long tail then we can remove outliers. Z-score is used for identifying outliers. Standardization and normalization are used for feature transformation. Standardization is used for Gaussian distribution. If the data distribution is not known then standardization can be used.

Metrics like mean, median, and standard deviation enable the creation of features such as average purchase amount or customer lifetime value, crucial in customer segmentation problems. These methods enhance data representation and provide valuable insights for model training and interpretation.

Tried and tested statistical techniques like factoring etc. can help us find new features and test them. Of course, a lot of this comes from domain knowledge. A word of caution here is still in order - do not read too much into correlation.

Categorical encoding transforms categories (like "red", "blue") into numbers machine learning models understand. Common methods include one-hot encoding and label encoding. This is necessary for model input but doesn't directly create new insights. Feature engineering for new features is more creative. It might involve combining existing features (e.g., calculating ratios), extracting patterns from text data, or using domain knowledge to derive entirely new attributes. Categorical encoding plays a supporting role, preparing categorical data for use within these more complex feature generation techniques.

According to me, Selecting the appropriate encoding method depends on the nature and quantity of categories. For instance, in sentiment analysis, categorical encoding can generate features like word count or sentiment score, facilitating model training and interpretation.

Feature selection focuses on identifying the most relevant existing features for a machine learning model, reducing dimensionality and potential overfitting. In contrast, the core of feature engineering is creating new features from existing data. Techniques like combining features, applying mathematical transformations (e.g., logarithms, ratios), or extracting information from text or time-series data generate novel features with a potentially stronger impact on model performance than the original feature set. Feature selection complements this process, ensuring that newly created features, along with original ones, are truly beneficial for the machine learning task.

Techniques like filter, wrapper, or embedded methods streamline data complexity and noise, optimizing model performance. For instance, in spam detection, feature selection can generate informative features like spam score, keyword frequency, or sender reputation, improving model efficacy in identifying spam emails.

Techniques like principal component analysis, linear discriminant analysis, or autoencoders uncover latent variables effectively. For instance, in face recognition, feature extraction can generate eigenfaces, fisherfaces, or deep features, facilitating accurate identification by capturing distinctive facial characteristics.

Feature extraction plays a significant role in feature engineering, especially when raw data is too complex for direct use by machine learning models. This is often the case with images, audio, or text. Feature extraction transforms this raw data into numerical representations that algorithms can process. For instance, it might extract color histograms from images or word frequencies from text. While valuable, it's important to note that feature extraction isn't always the best approach. Techniques like feature construction (manually crafting features based on domain knowledge) or feature selection (picking the most relevant existing features) also hold great importance in machine learning workflows.

One thing I have found useful in applying feature engineering to multiple domains like finance, real estate, e-commerce and education is to be open to experimentation. The whole idea of using AI is to uncover hidden patterns and features so one need not hold themselves back while doing feature engineering.

One rare but effective way to generate new features in feature engineering is through the use of advanced techniques such as autoencoders or generative adversarial networks (GANs). These methods involve training neural networks to learn and generate new representations of the data, which can then be used as additional features for predictive modeling.