# Deep Compact Polyhedral Conic Classifier for Open and Closed Set Recognition

arXiv: https://arxiv.org/abs/2102.12570 · HTML: https://mlsanity.com/paper/2102.12570/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 39 references that are in the map.
- First posted on arXiv 24 Feb 2021.

## Builds on (most cited first, 17 of 17)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [CosFace: Large Margin Cosine Loss for Deep Face Recognition](https://mlsanity.com/paper/1801.09414/) (2018)
- [SphereFace: Deep Hypersphere Embedding for Face Recognition](https://mlsanity.com/paper/1704.08063/) (2017)
- [MS-Celeb-1M: A Dataset and Benchmark for Large-Scale Face Recognition](https://mlsanity.com/paper/1607.08221/) (2016)
- [Towards Open Set Deep Networks](https://mlsanity.com/paper/1511.06233/) (2015)
- [Learning Face Representation from Scratch](https://mlsanity.com/paper/1411.7923/) (2014)
- [Deep metric learning using Triplet network](https://mlsanity.com/paper/1412.6622/) (2014)
- [Large-Margin Softmax Loss for Convolutional Neural Networks](https://mlsanity.com/paper/1612.02295/) (2016)
- [Generative OpenMax for Multi-Class Open Set Classification](https://mlsanity.com/paper/1707.07418/) (2017)
- [C2AE: Class Conditioned Auto-Encoder for Open-set Recognition](https://mlsanity.com/paper/1904.01198/) (2019)
- [Range Loss for Deep Face Recognition with Long-tail](https://mlsanity.com/paper/1611.08976/) (2016)
- [The Extreme Value Machine](https://mlsanity.com/paper/1506.06112/) (2015)
- [Driver Anomaly Detection: A Dataset and Contrastive Learning Approach](https://mlsanity.com/paper/2009.14660/) (2020)
- [Contrastive-center loss for deep neural networks](https://mlsanity.com/paper/1707.07391/) (2017)
- [Minimum Margin Loss for Deep Face Recognition](https://mlsanity.com/paper/1805.06741/) (2018)

## Built on by (most cited first, 5 of 5)

- [Towards Accurate Open-Set Recognition via Background-Class Regularization](https://mlsanity.com/paper/2207.10287/) (2022)
- [Deep Open-Set Recognition for Silicon Wafer Production Monitoring](https://mlsanity.com/paper/2208.14071/) (2022)
- [Deep Simplex Classifier for Maximizing the Margin in Both Euclidean and Angular Spaces](https://mlsanity.com/paper/2212.11747/) (2022)
- [Polyhedral Conic Classifier for CTR Prediction](https://mlsanity.com/paper/2406.03892/) (2024)
- [Data-Driven Hierarchical Open Set Recognition](https://mlsanity.com/paper/2411.02635/) (2024)

## Abstract (arXiv)

In this paper, we propose a new deep neural network classifier that simultaneously maximizes the inter-class separation and minimizes the intra-class variation by using the polyhedral conic classification function. The proposed method has one loss term that allows the margin maximization to maximize the inter-class separation and another loss term that controls the compactness of the class acceptance regions. Our proposed method has a nice geometric interpretation using polyhedral conic function geometry. We tested the proposed method on various visual classification problems including closed/open set recognition and anomaly detection. The experimental results show that the proposed method typically outperforms other state-of-the art methods, and becomes a better choice compared to other tested methods especially for open set recognition type problems.