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Last updated on 2024年7月6日

How do you pick the best dimensionality reduction method?

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Dimensionality reduction is a process of transforming a high-dimensional data set into a lower-dimensional one, while preserving as much of the relevant information as possible. It can help you simplify your data, reduce noise and redundancy, improve visualization and interpretation, and speed up your analysis. But how do you choose the best method for your data and goals? In this article, you will learn about some common criteria and techniques for selecting the most suitable dimensionality reduction method.

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Sébastien Ragot

Swiss and European Patent Attorney, Representative before the UPC, PhD.
Reza Bagheri

Data Scientist | 3x LinkedIn Top Voice | Author
Tyriek W.

Analyst | SQL | Python | R | Tableau | Power BI | Excel

1 Data type and structure

The first thing you need to consider is the type and structure of your data. Different methods may work better for different kinds of data, such as numerical, categorical, text, image, or mixed. For example, if your data is numerical and continuous, you may want to use methods based on linear algebra, such as principal component analysis (PCA) or singular value decomposition (SVD). If your data is categorical or discrete, you may want to use methods based on distance or similarity measures, such as multidimensional scaling (MDS) or t-distributed stochastic neighbor embedding (t-SNE). If your data is text or image, you may want to use methods based on feature extraction or learning, such as latent semantic analysis (LSA) or autoencoders.

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Reza Bagheri

Data Scientist | 3x LinkedIn Top Voice | Author
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A breakdown of some popular dimensionality reduction methods: PCA: reduces dimensions by projecting data onto orthogonal components. Assumes linear relationships between variables, which may not always hold in complex datasets. It requires feature scaling. t-SNE: Non-linear technique that preserves local similarities in high-dimensional data. It has a high computational cost. LDA: Supervised technique that maximizes class separability for classification tasks. Assumes Normality and Homoscedasticity and is vulnerable to overfitting. Autoencoders: Neural network-based technique for learning efficient representations of data. Training deep autoencoders can be computationally intensive and requires large amounts of data.

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Tyriek W.

Analyst | SQL | Python | R | Tableau | Power BI | Excel
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Quite frankly, you should always think about the data type and data structure before your analysis. This informs data collection, data pre-processing, continuous data cleansing, etc. In order to ensure that your dimensionality reduction technique is effective, you must ensure that it will retain the fundamental characteristics of the data that is to be analyzed (the data's intrinsic dimension). For structured data, common statistical techniques such as PCA are quite easy to apply. Non-structured or semi-structured data require further nuance and there is no one right to work with these data types. You should think about your business use case (and maybe even consider transforming the data into an easier to use format).

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2 Dimensionality and sparsity

The second thing you need to consider is the dimensionality and sparsity of your data. Dimensionality refers to the number of features or variables in your data, while sparsity refers to the proportion of zeros or missing values in your data. High dimensionality and sparsity can pose challenges for some methods, such as computational complexity, overfitting, or loss of information. For example, if your data has many features but few observations, you may want to use methods that can handle the curse of dimensionality, such as random projection or factor analysis. If your data has many zeros or missing values, you may want to use methods that can handle the sparsity, such as sparse PCA or non-negative matrix factorization (NMF).

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Sébastien Ragot

Swiss and European Patent Attorney, Representative before the UPC, PhD.
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<To be inserted before the last sentence> Beyond dimensionality-reduction techniques based on learning, other methods can be contemplated, such as the Hadamard method. This method does not learn from the data but instead attempts to approximate a random projection. It can be computationally efficient for datasets having a large number of features, even though the resulting embeddings may not be as good as with learning-based methods.

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3 Variance and correlation

The third thing you need to consider is the variance and correlation of your data. Variance refers to the amount of variation or dispersion in your data, while correlation refers to the degree of linear or nonlinear relationship between your features or variables. High variance and correlation can affect the performance and interpretation of some methods, such as noise reduction, feature selection, or clustering. For example, if your data has high variance and low correlation, you may want to use methods that can capture the maximum variance, such as PCA or SVD. If your data has low variance and high correlation, you may want to use methods that can capture the minimum correlation, such as independent component analysis (ICA) or kernel PCA.

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4 Visualization and interpretation

The fourth thing you need to consider is the visualization and interpretation of your data. Visualization refers to the ability to display your data in a graphical or visual form, while interpretation refers to the ability to explain or understand your data in a meaningful or intuitive way. Different methods may have different advantages and disadvantages for visualization and interpretation, such as dimensionality, shape, distance, or orientation. For example, if you want to visualize your data in a two-dimensional or three-dimensional space, you may want to use methods that can reduce the dimensionality to two or three, such as PCA, MDS, or t-SNE. If you want to interpret your data in terms of the original features or variables, you may want to use methods that can preserve the interpretability, such as factor analysis, ICA, or LSA.

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5 Evaluation and validation

The fifth thing you need to consider is the evaluation and validation of your data. Evaluation refers to the ability to measure or assess the quality or performance of your data, while validation refers to the ability to verify or confirm the reliability or accuracy of your data. Different methods may have different criteria and techniques for evaluation and validation, such as variance explained, reconstruction error, cluster quality, or stability. For example, if you want to evaluate your data in terms of how much variance is explained by the reduced dimensions, you may want to use methods that can provide the variance explained, such as PCA, SVD, or factor analysis. If you want to validate your data in terms of how well the reduced dimensions reconstruct the original data, you may want to use methods that can provide the reconstruction error, such as PCA, SVD, or autoencoders.

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6 Experimentation and comparison

The sixth thing you need to consider is the experimentation and comparison of your data. Experimentation refers to the ability to try or test different methods or parameters on your data, while comparison refers to the ability to contrast or compare the results or outcomes of different methods or parameters on your data. Different methods may have different options and settings for experimentation and comparison, such as number of dimensions, distance metric, kernel function, or random seed. For example, if you want to experiment with different methods or parameters on your data, you may want to use methods that can allow you to adjust or tune the options and settings, such as PCA, MDS, or t-SNE. If you want to compare different methods or parameters on your data, you may want to use methods that can allow you to visualize or quantify the differences or similarities, such as scatter plots, heat maps, or correlation coefficients.

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7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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Sébastien Ragot

Swiss and European Patent Attorney, Representative before the UPC, PhD.
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At the end of the day, dimension reduction is as much an art as it is a science. Choosing the most appropriate dimension reduction technique depends largely on your assumptions about the data. And beyond dimension reduction methods based on learning, other methods could be contemplated, such as the Hadamard method.

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How do you pick the best dimensionality reduction method?

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2

3

4

5

6

7

1 Data type and structure

2 Dimensionality and sparsity

3 Variance and correlation

4 Visualization and interpretation

5 Evaluation and validation

6 Experimentation and comparison

7 Here’s what else to consider

Statistics

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How do you pick the best dimensionality reduction method?

1

2

3

4

5

6

7

1 Data type and structure

2 Dimensionality and sparsity

3 Variance and correlation

4 Visualization and interpretation

5 Evaluation and validation

6 Experimentation and comparison

7 Here’s what else to consider

Statistics

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