##### Department of Mathematics,

University of California San Diego

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### Math 278C - Optimization and Data Science Seminar

## Kaizheng Wang

#### Columbia University

## Clustering via uncoupled regression

##### Abstract:

In this talk we consider a canonical clustering problem where one receives unlabeled samples drawn from a balanced mixture of two elliptical distributions and aims for a classifier to estimate the labels. Many popular methods including PCA and k-means require individual components of the mixture to be somewhat spherical, and perform poorly when they are stretched. To overcome this issue, we propose a non-convex program seeking for an affine transform to turn the data into a one-dimensional point cloud concentrating around -1 and 1, after which clustering becomes easy. Our theoretical contributions are two-fold: (1) we show that the non-convex loss function exhibits desirable geometric properties when the sample size exceeds some constant multiple of the dimension, and (2) we leverage this to prove that an efficient first-order algorithm achieves near-optimal statistical precision without good initialization. We also propose a general methodology for clustering with flexible choices of feature transforms and loss objectives.

Host: Jiawang Nie

### March 3, 2021

### 2:00 PM

### Meeting ID: 982 9781 6626 Password: 278CWn21

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