https://www.chenk.top/zh/tags/dimensionality-reduction/Recent content in Dimensionality Reduction on Chen Kai BlogHugozh-CNThu, 05 Feb 2026 09:00:00 +0000https://www.chenk.top/zh/ml-math-derivations/17-%E9%99%8D%E7%BB%B4%E4%B8%8E%E4%B8%BB%E6%88%90%E5%88%86%E5%88%86%E6%9E%90/Thu, 05 Feb 2026 09:00:00 +0000https://www.chenk.top/zh/ml-math-derivations/17-%E9%99%8D%E7%BB%B4%E4%B8%8E%E4%B8%BB%E6%88%90%E5%88%86%E5%88%86%E6%9E%90/<h2 id="你将学到什么" class="heading-anchor">你将学到什么<a href="#%e4%bd%a0%e5%b0%86%e5%ad%a6%e5%88%b0%e4%bb%80%e4%b9%88" class="heading-link" aria-label="Permalink to this section" title="Copy link to this section">#</a> </h2><p>给聚类算法输入 10,000 维的数据，它大概率会失败——问题不在于算法本身，而在于<strong>高维空间对基于距离的学习方法天然不友好</strong>。体积几乎都集中在球壳上，最近邻和最远邻的距离比值趋近于 <span class="math-inline">$1$</span> ，“近”这个概念变得毫无意义。降维的目的正是将数据投影到低维空间，同时保留其关键结构。</p>https://www.chenk.top/zh/linear-algebra/09-%E5%A5%87%E5%BC%82%E5%80%BC%E5%88%86%E8%A7%A3svd/Wed, 26 Feb 2025 09:00:00 +0000https://www.chenk.top/zh/linear-algebra/09-%E5%A5%87%E5%BC%82%E5%80%BC%E5%88%86%E8%A7%A3svd/<h2 id="一为什么-svd-配得上皇冠二字" class="heading-anchor">一、为什么 SVD 配得上“皇冠”二字<a href="#%e4%b8%80%e4%b8%ba%e4%bb%80%e4%b9%88-svd-%e9%85%8d%e5%be%97%e4%b8%8a%e7%9a%87%e5%86%a0%e4%ba%8c%e5%ad%97" class="heading-link" aria-label="Permalink to this section" title="Copy link to this section">#</a> </h2><p><a href="https://www.chenk.top/zh/linear-algebra/08-%e5%af%b9%e7%a7%b0%e7%9f%a9%e9%98%b5%e4%b8%8e%e4%ba%8c%e6%ac%a1%e5%9e%8b/">第 8 章</a> 的谱定理给出了 <span class="math-inline">$A = Q\Lambda Q^{\!\top}$</span> ，形式简洁优美，但有个硬性限制：<strong>仅适用于对称矩阵</strong>。而现实中遇到的矩阵大多不对称，甚至根本不是方阵：</p>