线性模型与主成分分析在异常检测中的应用

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"中讨论的子空间方法可以-a primer on memory consistency and cache coherence" 这篇文档主要探讨了在处理数据集时使用子空间方法在异常值检测中的应用,特别是在线性模型和主成分分析中的作用。异常值分析是数据预处理的重要部分,尤其是在无监督学习任务如异常检测中。文档指出,不同数据集的属性子集可能需要不同模型来有效地捕捉其内在结构,而子空间方法可以提供一种有效的解决方案。 文档首先提到了简化模型,如线性模型和基于接近度的模型,它们在许多情况下能够简化问题,避免子空间方法的复杂性。线性模型主要分为两类:第一类是统计回归建模,它用于识别数据中的依赖关系,特别适用于某些属性能够自然预测其他属性的情况,例如时间序列预测。通过构建依赖变量和独立变量的模型,可以评估观测值与预测值之间的偏差,从而检测异常。即使在多维数据中,这种方法也可以被扩展到处理复杂的依赖关系。 第二类模型是主成分分析(PCA),它用于找到数据的低维表示,即子空间。PCA有助于降低数据的维度,同时保留大部分方差,这在异常检测中特别有用,因为它可以将高维数据转化为一系列回归问题,从而简化无监督异常值检测。 文档还强调了在异常检测的第一阶段进行探索性和可视化分析的重要性,因为这可以帮助确定特定数据模型是否适合特定数据集,尤其是在没有标签信息的情况下,需要测试不同模型的有效性。 作者Charu C. Aggarwal在《离群分析》第二版中提供了深入的见解,书中涵盖了异常检测的各种技术和理论,包括特征选择、极端值分析、概率统计模型以及各种线性模型和基于邻近度的模型。书中的内容旨在帮助读者理解和应用这些方法来解决实际的异常检测问题。 总结来说,这篇文档讨论了子空间方法在异常值检测中的应用,特别是在线性回归和主成分分析中的作用,强调了数据探索和模型选择的重要性,并引用了Charu C. Aggarwal的书籍作为进一步学习的资源。

优化代码SELECT SUM(IF(order_date BETWEEN '2022-10-31' AND '2022-11-11' AND is_new_customer = 1, 1, 0)) AS new_customer_count, SUM(IF(order_date BETWEEN '2022-10-31' AND '2022-11-11' AND is_new_customer = 0, 1, 0)) AS old_customer_count, SUM(IF(order_date BETWEEN '2022-10-31' AND '2022-11-11' AND is_new_customer = 1, payment_amount, 0)) AS new_customer_payment_amount, SUM(IF(order_date BETWEEN '2022-10-31' AND '2022-11-11' AND is_new_customer = 0, payment_amount, 0)) AS old_customer_payment_amount, SUM(IF(order_date BETWEEN '2022-10-31' AND '2022-11-11' AND category = 'A', 1, 0)) AS category_A_customer_count, SUM(IF(order_date BETWEEN '2022-10-31' AND '2022-11-11' AND category = 'A', payment_amount, 0)) AS category_A_payment_amount, SUM(IF(order_date BETWEEN '2022-10-31' AND '2022-11-11' AND category = 'B', 1, 0)) AS category_B_customer_count, SUM(IF(order_date BETWEEN '2022-10-31' AND '2022-11-11' AND category = 'B', payment_amount, 0)) AS category_B_payment_amount, SUM(IF(order_date BETWEEN '2022-10-31' AND '2022-11-11' AND product_id = 'P1', 1, 0)) AS product_P1_customer_count, SUM(IF(order_date BETWEEN '2022-10-31' AND '2022-11-11' AND product_id = 'P1', payment_amount, 0)) AS product_P1_payment_amount FROM orders o LEFT JOIN (SELECT DISTINCT order_date FROM orders WHERE order_date BETWEEN '2022-10-31' AND '2022-11-11') d1 ON o.order_date = d1.order_date LEFT JOIN (SELECT DISTINCT order_date FROM orders WHERE order_date BETWEEN '2021-10-31' AND '2022-10-30' AND order_date NOT IN (SELECT order_date FROM orders WHERE order_date BETWEEN '2022-10-31' AND '2022-11-11')) d2 ON o.order_date = d2.order_date LEFT JOIN (SELECT DISTINCT order_date FROM orders WHERE order_date BETWEEN '2021-11-12' AND '2022-10-30' AND order_date IN (SELECT order_date FROM orders WHERE order_date BETWEEN '2022-10-31' AND '2022-11-11')) d3 ON o.order_date = d3.order_date WHERE d1.order_date IS NOT NULL OR d2.order_date IS NOT NULL OR d3.order_date IS NOT NULL;

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优化代码,并提供新脚本SELECT SUM(CASE WHEN order_date BETWEEN '2022-10-31' AND '2022-11-11' AND is_new_customer = 1 THEN 1 ELSE 0 END) AS new_customer_count, SUM(CASE WHEN order_date BETWEEN '2022-10-31' AND '2022-11-11' AND is_new_customer = 0 THEN 1 ELSE 0 END) AS old_customer_count, SUM(CASE WHEN order_date BETWEEN '2022-10-31' AND '2022-11-11' AND is_new_customer = 1 THEN payment_amount ELSE 0 END) AS new_customer_payment_amount, SUM(CASE WHEN order_date BETWEEN '2022-10-31' AND '2022-11-11' AND is_new_customer = 0 THEN payment_amount ELSE 0 END) AS old_customer_payment_amount, SUM(CASE WHEN order_date BETWEEN '2022-10-31' AND '2022-11-11' THEN CASE WHEN category = 'A' THEN 1 ELSE 0 END ELSE 0 END) AS category_A_customer_count, SUM(CASE WHEN order_date BETWEEN '2022-10-31' AND '2022-11-11' THEN CASE WHEN category = 'A' THEN payment_amount ELSE 0 END ELSE 0 END) AS category_A_payment_amount, SUM(CASE WHEN order_date BETWEEN '2022-10-31' AND '2022-11-11' THEN CASE WHEN category = 'B' THEN 1 ELSE 0 END ELSE 0 END) AS category_B_customer_count, SUM(CASE WHEN order_date BETWEEN '2022-10-31' AND '2022-11-11' THEN CASE WHEN category = 'B' THEN payment_amount ELSE 0 END ELSE 0 END) AS category_B_payment_amount, SUM(CASE WHEN order_date BETWEEN '2022-10-31' AND '2022-11-11' THEN CASE WHEN product_id = 'P1' THEN 1 ELSE 0 END ELSE 0 END) AS product_P1_customer_count, SUM(CASE WHEN order_date BETWEEN '2022-10-31' AND '2022-11-11' THEN CASE WHEN product_id = 'P1' THEN payment_amount ELSE 0 END ELSE 0 END) AS product_P1_payment_amount FROM orders WHERE (order_date BETWEEN '2022-10-31' AND '2022-11-11') OR (order_date BETWEEN '2021-10-31' AND '2022-10-30' AND order_date NOT IN (SELECT order_date FROM orders WHERE order_date BETWEEN '2022-10-31' AND '2022-11-11')) OR (order_date BETWEEN '2021-11-12' AND '2022-10-30' AND order_date IN (SELECT order_date FROM orders WHERE order_date BETWEEN '2022-10-31' AND '2022-11-11'))

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