T-distributed Stochastic Neighbor Embedding is a two-stage non-linear manifold learning algorithm based on Batch Gradient Descent that seeks to maintain the distances between samples in low-dimensional space. During the first stage (early stage) the distances are exaggerated to encourage more pronounced clusters. Since the t-SNE cost function (KL Divergence) has a rough gradient, momentum is employed to help escape bad local minima.
Note: T-SNE is implemented using the exact method which scales quadratically in the number of samples. Therefore, it is recommended to subsample datasets larger than a few thousand samples.
Data Type Compatibility: Depends on distance kernel
|1||dimensions||2||int||The number of dimensions of the target embedding.|
|2||rate||100.0||float||The learning rate that controls the global step size.|
|3||perplexity||30||int||The number of effective nearest neighbors to refer to when computing the variance of the distribution over that sample.|
|4||exaggeration||12.0||float||The factor to exaggerate the distances between samples during the early stage of embedding.|
|5||epochs||1000||int||The maximum number of times to iterate over the embedding.|
|6||min gradient||1e-7||float||The minimum norm of the gradient necessary to continue embedding.|
|7||window||10||int||The number of epochs without improvement in the training loss to wait before considering an early stop.|
|8||kernel||Euclidean||Distance||The distance kernel to use when measuring distances between samples.|
Return the magnitudes of the gradient at each epoch from the last embedding:
public steps() : array
use Rubix\ML\Embedders\TSNE; use Rubix\ML\Kernels\Manhattan; $embedder = new TSNE(3, 10.0, 30, 12.0, 500, 1e-6, 10, new Manhattan());
- L. van der Maaten et al. (2008). Visualizing Data using t-SNE.
- L. van der Maaten. (2009). Learning a Parametric Embedding by Preserving Local Structure.