用数学方法优化CLIP的图像描述，让分类更准且更快。
Koo-Fu CLIP: Closed-Form Adaptation of Vision-Language Models via Fukunaga-Koontz Linear Discriminant Analysis
- 在白化空间中用福克纳-库恩茨线性判别分析，直接计算最优投影。
- ImageNet-1K上分类准确率从75.1%提至79.1%，大类数下仍有效。
- 压缩10-12倍几乎不丢精度，适合高效大规模图像检索。
视觉语言模型如CLIP提供强大的通用表征，但其原始嵌入未针对监督分类优化，常存在类别分离度低和维度过高问题。我们提出Koo-Fu CLIP，一种基于福克纳-库恩茨线性判别分析（Fukunaga-Koontz Linear Discriminant Analysis）的监督型CLIP适配方法，在白化嵌入空间中抑制类内差异并增强类间区分度。该方法通过闭式线性投影重构CLIP嵌入的几何结构，提升类别可分性的同时实现有效的降维，提供轻量且高效的CLIP表示适配。在大规模ImageNet基准测试中，基于最近视觉原型的分类在Koo-Fu CLIP空间中将ImageNet-1K的top-1准确率从75.1%提升至79.1%，且在扩展至14K和21K类时仍保持一致增益。该方法支持高达10-12倍的压缩，几乎无精度损失，适用于高效的大规模分类与检索任务。
原文摘要 · Abstract (English)
Visual-language models such as CLIP provide powerful general-purpose representations, but their raw embeddings are not optimized for supervised classification, often exhibiting limited class separation and excessive dimensionality. We propose Koo-Fu CLIP, a supervised CLIP adaptation method based on Fukunaga-Koontz Linear Discriminant Analysis, which operates in a whitened embedding space to suppress within-class variation and enhance between-class discrimination. The resulting closed-form linear projection reshapes the geometry of CLIP embeddings, improving class separability while performing effective dimensionality reduction, and provides a lightweight and efficient adaptation of CLIP representations. Across large-scale ImageNet benchmarks, nearest visual prototype classification in the Koo-Fu CLIP space improves top-1 accuracy from 75.1% to 79.1% on ImageNet-1K, with consistent gains persisting as the label space expands to 14K and 21K classes. The method supports substantial compression by up to 10-12x with little or no loss in accuracy, enabling efficient large-scale classification and retrieval.
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