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NCA-ADS - Data Manipulation and Preparation - Section 1.6

Apply dimensionality reduction.

Apply dimensionality reduction methods such as PCA and UMAP to reduce feature space while preserving variance or local structure. Distinguish between linear and non-linear approaches and select each based on the data geometry and downstream task.

Practice question for this objective

Free sampleData Manipulation and Preparationmedium

A data scientist has a 500-feature dataset and wants to reduce it to two dimensions for a scatter-plot visualisation to explore cluster structure in the data. Training time is not a major concern, but the two-dimensional layout must faithfully preserve local neighbourhood relationships rather than global variance. Which technique is most appropriate?

  • APCA, retaining the top two principal components
  • BTruncated SVD applied to the feature matrix, keeping two components
  • CUMAP, configured for two output dimensions Correct
  • DFeature selection using variance thresholding, retaining the two highest-variance features
Distinguish between linear and non-linear dimensionality reduction methods and select the appropriate technique for cluster visualisation tasks. UMAP (Uniform Manifold Approximation and Projection) is a non-linear dimensionality reduction algorithm that constructs a high-dimensional graph of nearest neighbours and then optimises a low-dimensional layout to match that graph structure. Because it explicitly models local neighbourhood relationships rather than global variance, it is the preferred tool when the goal is a two-dimensional scatter plot that reveals cluster topology. PCA and truncated SVD are linear projections that maximise explained variance; they are appropriate for preprocessing and noise reduction but do not reliably separate non-linearly structured clusters in two dimensions. cuML provides a GPU-accelerated UMAP implementation via cuml.manifold.UMAP, which follows the same API as the reference implementation.

Why A is wrong: PCA is a linear method that maximises explained variance along orthogonal axes. It preserves global variance structure but often collapses distinct local clusters into overlapping regions in a two-dimensional projection, making it poorly suited for cluster visualisation tasks.

Why B is wrong: Truncated SVD is algebraically equivalent to PCA for centred data and shares the same linear, variance-maximising objective. It does not model non-linear manifold structure, so local cluster topology in high-dimensional space is not faithfully captured in the resulting two components.

Why C is correct: UMAP is a non-linear manifold technique that optimises for preserving local neighbourhood structure, producing two-dimensional embeddings where nearby points in high-dimensional space remain nearby. This makes it the standard choice for exploratory cluster visualisation.

Why D is wrong: Variance thresholding selects original features rather than constructing a lower-dimensional embedding. Keeping the two highest-variance raw features discards the vast majority of the signal encoded across all 500 features and cannot recover a meaningful two-dimensional representation of the full manifold.

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