NCA-ADS - Data Manipulation and Preparation (23% of the exam) - 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
lock_openFree 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 dimensionscheck_circle 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.
Answers that look right on this material and are not. Each one is a distractor from a different question in the NCA-ADS bank for this domain.
Fit a cuML PCA estimator to retain 30 principal components, because PCA captures the directions of greatest variance and therefore reconstructs curved manifolds accurately.
errorWhy it is wrong: PCA is tempting because it is the default reduction tool and does produce a learned transform applicable to new rows, but PCA is a linear projection and cannot follow a curved manifold, so it fails the non-linear requirement.
t-SNE, reducing the feature space to 50 dimensions before training
errorWhy it is wrong: t-SNE is designed for visualisation at very low target dimensions such as 2 or 3. It does not preserve global distances reliably, is non-deterministic, and scales poorly to 50 output dimensions; using it as a preprocessing step ahead of supervised training discards global structure needed for generalisation.
t-SNE, because it scales linearly to millions of rows and produces a stored mapping that can be reapplied to each new streaming batch without refitting.
errorWhy it is wrong: t-SNE is tempting because it is a well-known reduction method, but it does not produce a reusable mapping for new rows and its cost grows steeply with sample size, so it cannot serve streaming batches in production.