RAandTinLSKM

摘要部分

1. 核方法优势：通过使用核技巧可以把线性模型直接拓展到非线性应用场景

2. 然鹅， 核方法的naive使用的计算复杂度是很高的，scales cubically w.r.t. 训练样本的数量

   表示不赞同，我现有层面的知识恰恰是能避免高维计算 (或许是不同的角度？)

3. 这篇文章回归了最近的处理大规模数据的核方法

Outline

Chapter 1

1. Vector spaces: Basis, linear independence
2. Normed spaces: Norm, convergence, equivalent norms
3. Topology of normed spaces: Open, closed, bounded, compact, and dense sets
4. Banach spaces: Cauchy sequences, completeness, convergent and absolutely convergent series
5. Linear mappings: Continuity, boundedness, the norm of a linear mapping

Chapter 3

1. Inner product spaces: Inner product, norm, Schwarz’s Inequality, Parallelogram Law, orthogonality, Pythagorean Formula, strong and weak convergence, Hilbert spaces, isomorphic Hilbert spaces
2. Orthonomal systems: Orthogonal and orthonormal systems, Gram-Schmidt orthonormalization process, Pythagorean Formula, Bessel’s equality and inequality, the best approximation, complete orthonormal sequences and equivalent conditions, Parseval’s Formula, separable Hilbert spaces
3. Orthogonal Complements and Projections: Orthogonal sets, orthogonal complement, the closest point property, orthogonal decompositions, orthogonal projections
4. Linear functionals: The norm of a linear functional, the Riesz Representation Theorem

First of all, thanks Dr. Charles Russell Severance

Why I write this summary?

• gained certificate from last winter vacation(2019)
• need to apply this knowledge for data access

Here we summarize the geospatial data visualization.

The Synthetic Power Grid Data Set will be used as an example. [Download here]

Before all the things, let’s import some basic tools:

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import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
%matplotlib inline
plt.style.use('ggplot')