alignment {mtlgmm}

Align the initializations.

Description

Align the initializations. This function implements the two alignment algorithms (Algorithms 2 and 3) in Tian, Y., Weng, H., & Feng, Y. (2022). This function is mainly for people to align the single-task initializations manually. The alignment procedure has been automatically implemented in function mtlgmm and tlgmm. So there is no need to call this function when fitting MTL-GMM or TL-GMM.

Usage

alignment(mu1, mu2, method = c("exhaustive", "greedy"))

Arguments

mu1

the initializations for mu1 of all tasks. Should be a matrix of which each column is a mu1 estimate of a task.

mu2

the initializations for mu2 of all tasks. Should be a matrix of which each column is a mu2 estimate of a task.

method

alignment method. Can be either "exhaustive" (Algorithm 2 in Tian, Y., Weng, H., & Feng, Y. (2022)) or "greedy" (Algorithm 3 in Tian, Y., Weng, H., & Feng, Y. (2022)). Default: "exhaustive"

Value

the index of two clusters to become well-aligned, i.e. the "r_k" in Section 2.4.2 of Tian, Y., Weng, H., & Feng, Y. (2022). The output can be passed to function alignment_swap to obtain the well-aligned intializations.

Note

For examples, see part "fit signle-task GMMs" of examples in function mtlgmm.

References

Tian, Y., Weng, H., & Feng, Y. (2022). Unsupervised Multi-task and Transfer Learning on Gaussian Mixture Models. arXiv preprint arXiv:2209.15224.

See Also

mtlgmm, tlgmm, predict_gmm, data_generation, initialize, alignment_swap, estimation_error, misclustering_error.