Rutgers, The State University of New Jersey

Iterative Embedding with Robust Correction using Feedback of Error Observed

Praneeth Vepakomma1

Ahmed Elgammal2

Department of Statistics, Rutgers1,

Department of Computer Science, Rutgers2

Electrical & Computer Engineering, FIU1

Smart Public Safety Solutions, Motorola Solutions1

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Introduction

• Iterative Manifold Learning• Interleaving Iterative Embedding

& Feedback from Error• Damping Effect of Outliers• M-Estimation

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Interleaved Approach:

Manifold Learning

M-Estimation

At Iteration t:

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Feedback Loop With Adjustment of Weights:

Big Picture

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Majorization Minimization:

• Uses a surrogate objective• The surrogate bounds the original objective• Exception: Touches the original objective at only one point• Incremental Optimization (Monotonic Convergence)

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Proposed Majorization Function:

Linear Constraint:

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MM Routine:

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Robust Multiplicative Updates:

M-Estimation with Geman Mcclure Function:

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We Show Existence of Sharpest Majorizer:

Implicit Positivity Constraints

Majorization Function

Condition:

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