Working Paper

Time-varying Lamperti Transformation and Clustering  Locally Asymptotically Self-similar Processes
​​with Qidi Peng, Nan Rao and Narn-Rueih Shieh

• We study the problems of clustering locally asymptotically self-similar processes, when the true number of clusters is given. A new concept "time-varying Lamperti transformation" is introduced to transform the processes to asymptotically stationary processes, from which the so-called approximately asymptotically consistent clustering algorithms are obtained. In a simulation study, clustering data sampled from multifractional Brownian motions is performed to illustrate the approximated asymptotic consistency of the proposed algorithms.

Publication

Cluster Analysis on Locally Asymptotically Self-similar Processes with Known Number of Clusters    [Journal] [ArVix] 
​with Qidi Peng and Nan Rao. Fractal and Fractional, 6(4): 222, 2022.​

Covariance-based Dissimilarity Measures Applied to Clustering Wide-sense Stationary Ergodic Processes    [Journal] [ArXiv] [Code]
with Qidi Peng and Nan Rao. Machine Learning, 108(12): 2159–2195, 2019. 

• UC Santa Barbara, SoCAMS 2018.​

Some Developments in Clustering Analysis on Stochastic Processes    [Journal] [ArXiv]
with Qidi Peng and Nan Rao. Biostatistics and Biometrics, 9(3): 72–77, 2019.​

Randomized Block Kaczmarz Method with Projection for Solving Least Squares    [Journal] [ArXiv]
with Deanna Needell and Anastasios Zouzias. Linear Algebra and its Applications, 484: 322–343, 2015.

A Comparison of Clustering and Missing Data Methods for Health Sciences    [ArXiv] 
with Deanna Needell, Chris Johansen and Jerry Grenard. IEEE 48th Asilomar Conference on Signals, Systems and Computers,1041-1045, 2014.

• ​Asilomar Conference on Signals, Systems, and Computers 2014.