# What is Dimensionality Reduction? Overview, Objectives, and Popular Techniques

• What is Dimensionality
• Reduction
• Why Dimensionality Reduction is Important
• Dimensionality Reduction Methods and Approaches
• Dimensionality Reduction Techniques
• Dimensionality Reduction Example

Learning by machine is not an easy task. Okay, so that’s a lesser statement. Artificial Intelligence and machine learning represent a major step in making computers think like humans, but both concepts are challenging to understand. Fortunately, the profit is worth the effort.

Today we are dealing with the process of reducing size, analyzing a key component in machine learning. We will cover its meaning, why it is important, how to do it, and give you a related example to illustrate the point.

Once you are done, you will have a solid understanding of size reduction, something that may be helpful during the interview. You will also know how to answer in-depth study interview questions or machine learning interview questions with great confidence and accuracy.

#### What is Dimensionality Reduction

Before we can give a clear definition of size reduction, we first need to understand the magnitude. If you have too many different inputs, the performance of the machine learning algorithm may decrease. Suppose you use rows and columns, such as those commonly found in a spreadsheet, to represent your ML data. In that case, columns that become input variables (also called features) are fed to the model that predicts the target variable.

Additionally, we can treat data columns as n-dimensional feature size, while data lines are points found in space. This process is known as translating geometric data.

Unfortunately, if too much space resides in the feature area, that results in a large amount of space. Thus, space points and data lines may represent only a small, non-representative sample. This imbalance may adversely affect the performance of the machine learning algorithm. This condition is known as the “curse of greatness.” An important point, a set of data with multiple input features includes predictive modeling function, which puts performance and accuracy at risk.

Here is an example to help you visualize a problem. Imagine walking a straight line 50 yards, and somewhere along that line, down a quarter. You will probably find it soon. But now, suppose your search area spans 50 by 50 yards. Now your search will take days! But we are not finished yet. Now, make that search space a 50 by 50 yard cube for 50 yards. You may want to say “goodbye” that quarter! The size involved, the more difficult it is and the more distant it is to search.

How do we raise the curse of greatness? By reducing the number of input elements, thereby reducing the size of the size in the feature space. Therefore, “reducing size.”

To make a long story short, to reduce the size means to reduce the size of your feature set.

#### Why Dimensionality Reduction is Important

• Fewer features mean less complexity
• You will need less storage space because you have fewer data
• Fewer features require less computation time
• Model accuracy improves due to less misleading data
• Algorithms train faster thanks to fewer data
• Reducing the data set’s feature dimensions helps visualize the data faster
• It removes noise and redundant features

#### Dimensionality Reduction Methods and Approaches

Now that we have figured out how many size reduction benefits the machine learns, what is the best way to do it? Here are some suggestions on how to look or get an appointment for antique items. This series of methods and techniques are also known as Dimensionality Reduction Algorithms.

#### Feature Selection.

Feature selection is a way to select the appropriate, appropriate features for the data set to install and remove non-essential features.

• Sorting methods. This method filters the data set to the appropriate subset.
• Wrapping methods. This method uses a machine learning model to test the performance of the components included in it. Performance determines whether it is better to maintain or remove features to improve model accuracy. This method is more accurate than filtering but also more complex.
• Embedded methods. The embedded process evaluates the various training of the machine learning model and assesses the value of each feature.
• Feature Extraction.

This method transforms the space containing too many dimensions into a space with fewer dimensions. This process is useful for keeping the whole information while using fewer resources during information processing. Here are three of the more common extraction techniques.

• Linear discriminant analysis. LDA is commonly used for dimensionality reduction in continuous data. LDA rotates and projects the data in the direction of increasing variance. Features with maximum variance are designated the principal components.
• Kernel PCA. This process is a nonlinear extension of PCA that works for more complicated structures that cannot be represented in a linear subspace in an easy or appropriate manner. KPCA uses the “kernel trick” to construct nonlinear mappings.
• Quadratic discriminant analysis. This technique projects data in a way that maximizes class separability. The projection puts examples from the same class close together, and examples from different classes are placed farther apart.

#### Dimensionality Reduction Techniques

Here are some techniques machine learning professionals use.

• Principal Component Analysis.

PCA extracts a new set of variables from an existing, more extensive set. The new set is called “principal components.”

• Backward Feature Elimination.

This five-step technique defines the optimal number of features required for a machine learning algorithm by choosing the best model performance and the maximum tolerable error rate.

• Forward Feature Selection.

This technique follows the inverse of the backward feature elimination process. Thus, we don’t eliminate the feature. Instead, we find the best features that produce the highest increase in the model’s performance.

• Missing Value Ratio.

This technique sets a threshold level for missing values. If a variable exceeds the threshold, it’s dropped.

• Low Variance Filter.

Like the Missing Value Ratio technique, the Low Variance Filter works with a threshold. However, in this case, it’s testing data columns. The method calculates the variance of each variable. All data columns with variances falling below the threshold are dropped since low variance features don’t affect the target variable.

• High Correlation Filter.

This method applies to two variables carrying the same information, thus potentially degrading the model. In this method, we identify the variables with high correlation and use the Variance Inflation Factor (VIF) to choose one. You can remove variables with a higher value (VIF > 5).

• Decision Trees.

Decision trees are a popular supervised learning algorithm that splits data into homogenous sets based on input variables. This approach solves problems like data outliers, missing values, and identifying significant variables.

• Random Forest.

This method is like the decision tree strategy. However, in this case, we generate a large set of trees (hence “forest”) against the target variable. Then we find feature subsets with the help of each attribute’s usage statistics of each attribute.

• Factor Analysis.

This method places highly correlated variables into their own group, symbolizing a single factor or construct.

## Dimensionality Reduction Example

Here is an example of dimensionality reduction using the PCA method mentioned earlier. You want to classify a database full of emails into “not spam” and “spam.” To do this, you build a mathematical representation of every email as a bag-of-words vector. Each position in this binary vector corresponds to a word from an alphabet. For any single email, each entry in the bag-of-words vector is the number of times the corresponding word appears in the email (with a zero, meaning it doesn’t appear at all).

Now let’s say you’ve constructed a bag-of-words from each email, giving you a sample of bag-of-words vectors, x1…xm. However, not all your vector’s dimensions (words) are useful for the spam/not spam classification. For instance, words like “credit,” “bargain,” “offer,” and “sale” would be better candidates for spam classification than “sky,” “shoe,” or “fish.” This is where PCA comes in.

You should construct an m-by-m covariance matrix from your sample and compute its eigenvectors and eigenvalues. Then sort the resulting numbers in decreasing order and choose the p top eigenvalues. By applying PCA to your vector sample, you project them onto eigenvectors corresponding to the top p eigenvalues. Your output data is now a projection of the original data onto p eigenvectors. Thus, the projected data dimension has been reduced to p.

After you have computed your bag-of-words vector’s low-dimensional PCA projections, you can use the projection with various classification algorithms to classify the emails instead of using the original emails. Projections are smaller than the original data, so things move along faster.

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