Main Requirements for Cluster Analysis

Following Han, Kamber & Pei (Data Mining: Concepts and Techniques), the key requirements that a good clustering method should satisfy are:

1. Scalability

The method must work efficiently on large databases — ideally near-linear (or sub-quadratic) in the number of objects $n$. Many classic algorithms degrade badly on millions of tuples.

2. Ability to deal with different types of attributes

Real data contains numerical, categorical (binary/nominal), ordinal, and mixed attributes. The clustering method should handle all these types (often by using an appropriate dissimilarity matrix).

3. Discovery of clusters of arbitrary shape

Clusters are not always spherical/ball-like. A good method should find clusters of arbitrary shape (e.g., elongated, concave, "C"-shaped) — density-based methods (DBSCAN, OPTICS) do this well, whereas k-Means cannot.

4. Minimal requirements for domain knowledge / input parameters

Clustering should require as few user-supplied parameters as possible (e.g., $k$ for k-Means, $\varepsilon$/MinPts for DBSCAN), because guessing them needs domain knowledge and a wrong guess harms the result. Ideally parameters should be easy to determine.

5. Ability to deal with noisy data

Real data contains noise and outliers. The method should be robust so that noise does not seriously distort the discovered clusters, and outliers should be handled (detected or tolerated).

6. Insensitivity to input order / incremental updatability

The same result should be obtained no matter the order in which input records are presented, and the method should support incremental updates when new data arrive (important for data warehouses that get refreshed).

7. High dimensionality

Distances concentrate in high-dimensional spaces ("curse of dimensionality"). A suitable method should either work well in high dimensions or use subspace/feature-selection strategies.

8. Interpretability and usability

The resulting clusters should be interpretable, comprehensible, and usable — the user must be able to understand and act on the discovered grouping.

9. Constraint-based clustering

Real applications often impose constraints (must-link / cannot-link, or spatial/budget constraints); the method should be able to incorporate them to produce domain-appropriate clusters.

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Summary: a good clustering algorithm must be scalable, robust to noise, general (arbitrary shapes, mixed data types), minimal-parameter, order-insensitive, high-dimensionality-aware, and interpretable.