# Multi-way Graph Signal Processing on Tensors: Integrative analysis of irregular geometries

Graph signal processing (GSP) is an important methodology for studying data residing on irregular structures.

# Baseline Drift Estimation for Air Quality Data Using Quantile Trend Filtering

Through simulation studies and our motivating application to low cost air quality sensor data, we demonstrate that our model provides better quantile trend estimates than existing methods and improves signal classification of low-cost air quality sensor output.

Methodology Applications Computation

1

# Co-manifold learning with missing data

We propose utilizing this coupled structure to perform co-manifold learning: uncovering the underlying geometry of both the rows and the columns of a given matrix, where we focus on a missing data setting.

# Recovering Trees with Convex Clustering

no code implementations28 Jun 2018,

Convex clustering refers, for given $\left\{x_1, \dots, x_n\right\} \subset \mathbb{R}^p$, to the minimization of \begin{eqnarray*} u(\gamma) & = & \underset{u_1, \dots, u_n }{\arg\min}\;\sum_{i=1}^{n}{\lVert x_i - u_i \rVert^2} + \gamma \sum_{i, j=1}^{n}{w_{ij} \lVert u_i - u_j\rVert},\\ \end{eqnarray*} where $w_{ij} \geq 0$ is an affinity that quantifies the similarity between $x_i$ and $x_j$.

# Provable Convex Co-clustering of Tensors

Our convex co-clustering (CoCo) estimator enjoys stability guarantees and its computational and storage costs are polynomial in the size of the data.

# Generalized Linear Model Regression under Distance-to-set Penalties

Estimation in generalized linear models (GLM) is complicated by the presence of constraints.

# An MM Algorithm for Split Feasibility Problems

no code implementations16 Dec 2016, , ,

Furthermore, we show that the Euclidean norm appearing in the proximity function of the non-linear split feasibility problem can be replaced by arbitrary Bregman divergences.

# Shape Constrained Tensor Decompositions using Sparse Representations in Over-Complete Libraries

1 code implementation16 Aug 2016, ,

We consider $N$-way data arrays and low-rank tensor factorizations where the time mode is coded as a sparse linear combination of temporal elements from an over-complete library.

2

# Convex Biclustering

In the biclustering problem, we seek to simultaneously group observations and features.

# Splitting Methods for Convex Clustering

no code implementations1 Apr 2013,

In contrast to previously considered algorithms, our ADMM and AMA formulations provide simple and unified frameworks for solving the convex clustering problem under the previously studied norms and open the door to potentially novel norms.

# Distance Majorization and Its Applications

no code implementations16 Nov 2012, ,

The problem of minimizing a continuously differentiable convex function over an intersection of closed convex sets is ubiquitous in applied mathematics.

# On Tensors, Sparsity, and Nonnegative Factorizations

no code implementations11 Dec 2011,

We present a new algorithm for Poisson tensor factorization called CANDECOMP-PARAFAC Alternating Poisson Regression (CP-APR) that is based on a majorization-minimization approach.

Numerical Analysis

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