Nyström Approximation¶

Kernel methods often require an (n \times n) kernel matrix. For large data sets, storing and manipulating the full matrix can become the main computational bottleneck.

TorchKM supports a Nyström approximation for larger problems. This provides a lower-rank representation of the kernel matrix using a subset of landmark points.

Basic usage¶

The recommended scikit-learn-style API sets the Nyström options in the constructor:

clf = TorchKMSVC(
    kernel="rbf",
    Cs=Cs,
    cv=5,
    device=device,
    low_rank=True,
    num_landmarks=40,
    nys_k=20,
    max_iter=40,
    probability=True,
)
clf.fit(Xtr, ytr)

For convenience, the same options can also be supplied at fit time:

clf = TorchKMSVC(kernel="rbf", Cs=Cs, cv=5, device=device, probability=True)
clf.fit(Xtr, ytr, low_rank=True, num_landmarks=40, nys_k=20)

Important parameters¶

Parameter	Meaning
`low_rank`	Enables the Nyström approximation
`num_landmarks`	Number of landmark points used to build the approximation
`nys_k`	Rank used in the low-rank representation
`device`	CPU or GPU device
`kernel`	The high-level low-rank path currently supports RBF-kernel workflows

When to use¶

Use low_rank=True when:

the full kernel matrix is too large for memory;
training with the exact kernel is too slow;
an approximate solution is acceptable;
the data set is large enough that full-kernel methods become impractical.

Practical advice¶

Start with a modest number of landmarks, then increase num_landmarks and nys_k if accuracy is not sufficient. Larger values may improve approximation quality but increase memory use and runtime.

The high-level low-rank classifier path requires raw feature input and does not support kernel="precomputed".