ML Interview Q Series: Explain One-Hot Encoding and Label Encoding. Does the dimensionality of the dataset increase or decrease after applying these techniques?

📚 Browse the full ML Interview series here.

Comprehensive Explanation

One-Hot Encoding and Label Encoding are both techniques for converting categorical variables into numerical form, allowing machine learning algorithms to handle them properly. Despite sharing the same goal, they work very differently and have distinct impacts on a dataset's dimensionality.

Label Encoding

Label Encoding replaces each category in a feature with a single integer. For example, if the categories are {"Red", "Green", "Blue"}, they might be mapped to 0, 1, 2, respectively. This approach preserves the dimensionality of the data because you are converting one column of categorical data into one column of integers. However, it imposes an ordinal relationship among categories that may not exist in reality.

• The dimensionality typically remains the same (one categorical column transforms into one integer-based column).

• It can inadvertently imply that one category is "less" or "more" than another (e.g., "Green" > "Red"), which can be problematic for some models, especially linear models.

One-Hot Encoding

One-Hot Encoding creates new binary features for each unique category in a feature. If a feature has K possible categories, one-hot encoding (in its simplest form) generates K new columns. Each new column corresponds to one category, and a row will have a 1 in the column of the category it belongs to and 0 in all others.

To represent the encoding mathematically, assume x is a categorical variable that can take values in {1, 2, ..., K}. The encoded vector v(x) in R^K is given by:

$$ v_j(x) = \begin{cases}

1 & \text{if } x = j \ 0 & \text{otherwise} \end{cases} $$

Here, v_j(x) is the j-th component of the resulting one-hot vector, x is the actual category (an integer label you might have assigned internally to each category), and j runs from 1 to K (the total number of unique categories).

This encoding greatly increases dimensionality when K is large because each categorical column with K categories may become K separate columns in the transformed dataset. However, it avoids imposing any ordinal relationship among the categories.

Effect on Dimensionality

• Label Encoding does not change dimensionality. A single column of categories becomes a single column of numeric codes.

• One-Hot Encoding usually increases dimensionality because a single categorical column with many unique categories may explode into many binary indicator columns.

When deciding which method to use, it is crucial to consider the type of model and whether your categorical feature is truly ordinal. For certain models (e.g., tree-based methods), label encoding is often acceptable because the model can learn split points effectively. For methods sensitive to the numeric scale or ordering (e.g., linear or distance-based models), one-hot encoding is often preferred unless the feature is inherently ordinal (e.g., "Low", "Medium", "High").

Example Code

Below is a simple Python code snippet using scikit-learn demonstrating label encoding and one-hot encoding on a small dataset:

import pandas as pd
from sklearn.preprocessing import LabelEncoder, OneHotEncoder

# Sample Data
data = {'Color': ['Red', 'Green', 'Blue', 'Red', 'Green']}
df = pd.DataFrame(data)

# Label Encoding
label_enc = LabelEncoder()
df['Color_LabelEncoded'] = label_enc.fit_transform(df['Color'])

# One-Hot Encoding using pandas get_dummies
df_one_hot = pd.get_dummies(df['Color'], prefix='Color')
df = pd.concat([df, df_one_hot], axis=1)

print(df)

Here, Color_LabelEncoded is the label-encoded column, while the Color_Red, Color_Green, and Color_Blue columns form the one-hot encoding. Notice how a single categorical column expanded into multiple columns under one-hot encoding.

Why Dimensionality Might Matter

Higher dimensionality can increase computational costs and can sometimes lead to the curse of dimensionality in certain algorithms. On the other hand, label encoding could mislead algorithms that rely on the numeric scale of a feature. Thus, the choice between these techniques depends on data size, the nature of the categorical features, and the algorithms you intend to use.

Potential Follow-Up Questions

How do we choose between Label Encoding and One-Hot Encoding in practice?

It generally depends on:

• Nature of the categorical variable: If the categories are ordinal (like Grade A < Grade B < Grade C), then label encoding can capture that ordering. If the categories are nominal (Color or CityName), ordinal encoding may not be meaningful.

• Model type: Tree-based models (like Random Forests) can handle label-encoded features without a problem. Linear models typically need one-hot encoding to avoid implying numeric relationships among categories.

• Cardinality of categories: Very high cardinality with one-hot encoding can create extremely sparse matrices, increasing both memory usage and computational complexity.

Are there scenarios where One-Hot Encoding is detrimental?

One-hot encoding can be detrimental if the categorical variables have extremely large cardinality (e.g., thousands of unique categories). It will create a huge number of columns, leading to:

• High memory usage

• Potential overfitting if many dummy columns end up rarely used

• Slower training times

Techniques like target encoding, hashing tricks, or feature hashing might be more suitable in high-cardinality scenarios.

Why can Label Encoding be problematic for nominal variables?

Label encoding converts categories into an integer range that introduces a spurious ordinal relationship. For nominal features like Color, the numeric codes 0, 1, 2 might cause some algorithms to treat 2 as greater than 0 and 1, implying a distance between categories that is not valid for a nominal feature.

How do tree-based models handle Label Encoding without issues?

Tree-based methods (like Decision Trees, Random Forests, and Gradient Boosted Trees) primarily split on thresholds. For instance, if a label-encoded feature has codes {0, 1, 2}, the tree can learn splits such as "Is code < 1?" which effectively separates category 0 from {1, 2}. It does not necessarily interpret 2 as "greater" in a meaningful ordinal sense; it only uses the numeric value to partition data. Thus, the tree-based model does not get confused by the artificial ordering as easily as linear or distance-based algorithms might.

How to handle unseen categories at inference time?

When using Label Encoding or One-Hot Encoding, if new (unseen) categories appear during inference, the encoder may fail (e.g., it has no mapping for the new category). Possible strategies include:

• Training the encoder with a "dummy" category to capture all new categories.

• Using robust encoders like scikit-learn's OneHotEncoder(handle_unknown='ignore').

• Using more sophisticated encodings (like hashing) that can handle unseen strings gracefully.

Could we combine these techniques with dimension reduction?

If the resulting one-hot encoded feature space is too large, one might consider principal component analysis (PCA) or other dimensionality reduction techniques to manage high dimensionality. However, one must be cautious about interpretability and the risk of losing the direct meaning of one-hot vectors.

Implementation Details in Real-World Pipelines

In production pipelines:

• It’s common to fit an encoder (LabelEncoder or OneHotEncoder) on the training data.

• Persist the fitted encoder.

• Apply the same fitted encoder to the test or inference data to ensure consistent encoding.

• Watch out for memory constraints and model complexity when dealing with a high number of unique categories.

All of these considerations guide the choice between one-hot and label encoding, ensuring the encoded data is both computationally feasible and suitable for the model type in question.

Below are additional follow-up questions

What is the difference between One-Hot Encoding and Dummy Encoding, and why might we drop one category column?

One-Hot Encoding creates a binary indicator variable for every possible category, whereas Dummy Encoding typically creates one fewer indicator variable than the number of categories. When we use One-Hot Encoding with K categories, we end up with K new columns. With Dummy Encoding, we drop one of those columns, resulting in K-1 columns.

Dropping one column helps avoid perfect multicollinearity (often called the dummy variable trap) in models like linear regression. In a scenario where you have a bias term in your model, creating K dummy variables for a feature with K categories makes the data linearly dependent. One category can be perfectly inferred if you know all other indicator variables. By dropping one category, you remove this redundancy.

A potential pitfall is interpretability. If you drop the “Red” category column for a Color feature with categories “Red,” “Green,” and “Blue,” you must remember that when all other dummy columns are 0, it indicates “Red.” While this approach is perfectly valid, teams sometimes forget about the dropped category, leading to confusion when interpreting model outputs.

When do we consider feature embeddings for categorical variables instead of One-Hot or Label Encoding?

Feature embeddings are typically used when the number of unique categories is extremely large, and traditional encodings would be infeasible or not expressive enough. In deep learning contexts—especially in natural language processing tasks or recommendation systems—embeddings transform categorical entries into dense, low-dimensional vectors. These embeddings capture similarity relationships among categories in a more nuanced way than standard encodings.

For example, if you have a feature representing thousands of distinct items in an e-commerce dataset, one-hot encoding would produce a massive, sparse vector. In that scenario, an embedding table can learn meaningful representations of each item without exploding your dimensionality. However, embeddings require a neural network or a framework that can learn the vector representations jointly with the task objective.

A potential pitfall is ensuring you have enough data to learn stable embeddings. If certain categories are rare, their embeddings may not receive sufficient gradient updates. Another subtle issue arises if your dataset constantly introduces new categories; this may require a more flexible approach to handle unknown tokens.

Is it beneficial to combine multiple categorical columns into a single column before encoding? Under what conditions might that help?

Sometimes we create a combined categorical feature by merging multiple features. For instance, if you have separate features “City” and “Month,” you might create a combined category “City_Month.” This approach can help certain models learn interactions between features that are not captured by simple one-hot encoding of each feature separately.

This technique can be helpful when:

• There is a known interaction between the features (e.g., city-based seasonality).

• You have enough data to avoid overly sparse categories. A combined feature might produce many unique pairs, leading to very sparse data if each combination rarely occurs.

The major pitfall is dimensional explosion and severe sparsity. If “City” has 100 unique values and “Month” has 12, a combined feature could produce 1200 categories. If the dataset isn’t large enough to provide meaningful samples for every combination, many of those categories end up rarely or never used.

How do we handle missing values in categorical data before encoding?

For categorical data, common strategies to handle missing values include:

• Treating missing values as an additional category (e.g., “Unknown” or “NaN”).

• Imputing with the most frequent category, though this can bias distributions if the missing data is not random.

• Using model-based or algorithm-based imputation, where predictions fill in likely categories.

A potential edge case arises if you create a new “missing” category but the data truly has meaningful distinctions among different missing reasons (e.g., “not applicable,” “data not collected,” or “prefer not to answer”). Combining them all under one “missing” label may lose valuable information. If your chosen encoding approach automatically throws errors for unseen labels (e.g., scikit-learn’s OneHotEncoder default), you must ensure you handle missing values before encoding or allow the encoder to ignore unknown labels.

What if our dataset contains extremely large cardinality, and we cannot use standard One-Hot or Label Encoding effectively?

When the cardinality (number of unique categories) is very high (for instance, thousands or even millions of categories), standard encodings can become problematic:

• One-Hot Encoding leads to huge, sparse matrices, slowing down training and using excessive memory.

• Label Encoding may not be meaningful if the numeric ordering is entirely spurious.

Several strategies can help:

• Hashing Trick (Feature Hashing): Convert each category name into a fixed number of “hash buckets,” reducing dimensionality but introducing some collisions. This is widely used in large-scale text or recommendation systems.

• Frequency/Target Encoding: Replace the category with its frequency or average target value. This can collapse many categories into a single numeric value but runs the risk of target leakage if not carefully handled with proper cross-validation folds.

• Embedding Layers: If you have a neural network pipeline, learn a lower-dimensional representation of the categorical feature.

A subtle issue with hashing is the possibility of collisions—distinct categories may end up in the same hash bucket, potentially obscuring signals. For target or frequency encoding, you need to ensure you do not inadvertently reveal the target in the encoding process.

What happens if some categories occur very rarely? Does this affect the encoding choice?

Categories that occur infrequently can pose several challenges:

• One-Hot Encoding might create a column that almost always has zeros, yielding little value for the model and increasing sparsity.

• Label Encoding a rare category may not hurt as much for tree-based methods, but linear models can end up with coefficients that don’t generalize well.

One approach is to collapse rare categories into an “Other” bin. For example, if you have a feature “Country” and 1% of rows come from countries not in the top 10, you can combine those smaller groups into a single category like “Other.” This reduces the dimensionality for one-hot encoding and provides more robust statistical properties. A pitfall is losing the distinction between those rare categories, which could be relevant in some specific cases.

What is the effect of One-Hot Encoding and Label Encoding on distance-based models, such as K-Nearest Neighbors?

Distance-based models compute pairwise distances between data points. For example, K-Nearest Neighbors uses Euclidean or other distance measures. Consider the following differences in encodings:

• Label Encoding: It can mislead distance metrics because a small numeric difference might be interpreted as similarity. But there’s no inherent guarantee that category coded as 1 is more similar to the category coded as 2 than to the category coded as 10.

• One-Hot Encoding: This can produce very high-dimensional vectors, which may lead to the curse of dimensionality. However, each category remains equidistant to each other if only one feature is considered (assuming they all become equally distant in the one-hot space). This is typically less misleading but can be inefficient and possibly drown out signals when combined with numeric features in the same distance calculation.

A subtle pitfall is that if you have many such one-hot-encoded categorical features, the distance might be overwhelmed by the sum of zero-or-one differences, making it harder for continuous variables to play their role in determining distances.

Should we standardize or normalize label-encoded columns, and how do we interpret that in practice?

Standardizing label-encoded columns is seldom helpful for ordinal or nominal data because the numeric assignments are somewhat arbitrary. Scaling a label-encoded column from 0 to 1 or giving it a mean of 0 might not fix the inherent issue that the numeric scale imposes a false sense of continuity or distance.

In practice:

• For nominal variables (categories without an intrinsic order), normalizing the label codes doesn’t solve the problem of spurious ordering.

• For ordinal variables (e.g., “Low < Medium < High”), scaling might occasionally be useful if the difference between “Low” and “Medium” should have less influence than the difference between “Medium” and “High,” or vice versa. But even then, the assignment of codes is subjective.

A rare but subtle pitfall is that standardizing label-encoded categories can lead to confusion in interpretability. If your scaling turns categories into non-integer values, it becomes harder to map back to the original categories unless you store extra metadata.

When might we need multi-label or multi-hot encoding, and how does it differ from the usual one-hot encoding?

Multi-label or multi-hot encoding is relevant when a single instance can belong to multiple categories simultaneously. For example, a movie could be labeled with multiple genres, such as “Action,” “Adventure,” “Sci-Fi.” In this case, instead of forcing each row to have exactly one “1,” multiple entries in the encoded vector can be “1.”

A standard one-hot encoding assumes exactly one category per feature (e.g., color is either “Red,” “Green,” or “Blue”). For multi-label data, one-hot encoding is not enough. Each feature corresponding to a label is set to 1 if that instance has that label, and 0 otherwise.

An edge case is that some models do not inherently handle multi-label outputs. If your data has a multi-label structure, you need a learning algorithm that can process multi-hot vectors properly (e.g., multi-output classifiers or special activation functions in neural networks). Another subtlety is the potential overlap or correlation among categories. If certain labels almost always appear together, the model may need to learn these interdependencies.

How do we interpret model coefficients or feature importances after we apply encoding?

Interpretation after encoding depends heavily on the model type:

• Linear Models: Each one-hot column typically has its own coefficient. If you used dummy encoding (dropping one category), the coefficient for each category column is interpreted relative to the dropped baseline category. A coefficient’s sign and magnitude suggest how much that category differs in effect from the baseline.

• Tree-Based Models: Feature importance measures (like Gini importance or gain-based importance) will treat each encoded column as a separate feature. Categories that appear most often in splits might indicate they have higher predictive power.

A subtle pitfall in interpretation is the possibility of correlated categories. For instance, if you have multiple features that together encode certain business logic, you might incorrectly attribute importance to one feature that is simply correlated with another. Moreover, if you keep all K one-hot columns for a K-category feature, the sum of the importances of those columns might be more meaningful than looking at any single column in isolation.