These days I’m coding with the K-means clustring. In this algorithm, we often need to calculate the distance between 2 vectors. The expression of disctace between vector x and y is:
$$ d=\sqrt{\sum{(x{i}-y{i})^{2}}} $$

Depend on this expression, we can write our code as:

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import numpy as np
x=np.array([1,2,3,4])
y=np.array([0,1,0,1])
d = np.sqrt(((x-y)**2).sum())
print(d)

This code works well, but we can also use the numpy.linalg.norm to calculate the distance:

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import numpy as np
x=np.array([1,2,3,4])
y=np.array([0,1,0,1])
d = np.linalg.norm(x-y)
print(d)

For those guys who are struggling with the math, maybe the norm is a better choice ;)

Actually numpy.linalg.norm is very powerful. It can calculate different kind of normalisations by giving different value to the ord parameter. Here is the doc of norm

L2 norm is $$ L{2}=\sqrt {\sum{1}^{i} (x_i^2)} $$
For example, if x = (1,-1,2) the L2 norm of x is $$\sqrt{(1+1+4)} = \sqrt{6} $$

By dividing x’s each element from L2 we normalise x into unit L2
$$ \frac{x{i}}{L{2}}, \forall x $$
For example after normalisation, $$ x=(\frac{1}{\sqrt{6}},\frac{-1}{\sqrt{6}}, \frac{2}{\sqrt{6}}) $$

CSR Sparse Matrix

In CSR model, a m*n sparse matrix is organised by 3 vectors:
(i is both the index of the indptr vector and the index of the row )

• indptr: The indptr vector is a record that how to read the data from indices and data
• indices: The column index of all non-zero numbers in each row. Column indices for row i are stored in indices[indptr[i]:indptr[i+1]]. (Read the indptr[i] but not read the [indptr[i+1]])
• data: the corresponding data of all non-zero numbers in each row. The data of row i are stored in indices[indptr[i]:indptr[i+1]]. (Read the indptr[i] but not read the [indptr[i+1]]).
  Noticed that:

1. The length of the indptr vector is equal to the (number of rows - 1)

   1	m=len(indptr)-1

2. The lenght of data is equal to the length of the indices

   1	len(indices)==len(data)

Illustrated as the banner of the game Atletico vs Leverkusen.

Match Thread (in Chinese)

Ant System

Formulas

$$ P{ij}=\frac{[\tau{ij}(t)]^\alpha[\eta{ij}]^\beta}{\sum{k\in Ni}[\tau{ij}(t)]^\alpha[\eta_{ij}]^\beta} $$

• $$ \tau_{ij}(t) $$ : The amount of pheromon on the arc(i, j) at time t
• $$ \eta_{ij} $$ : The heuristic value of moving from i to j.
• $$ \eta{ij}=Q/d{ij} $$, Q is a real number. Some books/papers set Q=1, but in the tutorial Q=100. Q can arrange the weight of the distance when compute the posibility.
• $$ \alpha, \beta $$

• To be continiued *

Install

Hexo supports the TeX or the LaTex by plugin MathJax. We only need 3 steps to install it:

1. npm install hexo-math --save
2. cd to the dictionary of your local blog, input:hexo math install
3. Add plugins: hexo-math into the _config.yml
   Read more »

How to use Markdown

Markdown (MD) is a simple markup language. The grammar of MD is briefer and easier than HTML/XML. To be fair, everyone can understand how to use MD in 10 minutes. :) That’s why MD is becoming more and more popular in nearly years.

Actually there are lots of perfect tutorials about Markdown and this one might be the worst one. I write this just for my own practice. Hope it can help. ;P

The official site of Markdown is here

对于一个球员，或者希望自己前程似锦的人们来说，“实在是因为运气不好”这个理由，可以算是最稀奇的理由了。通常来说，我们喜欢上一个球员，大抵是因为他是我们主队的明星，或是因为我们欣赏他踢球的风格，但有时，忠诚与偏爱都是次要的。有时，球员们那不堪回首的黑历史，会让他的其他一切都黯然失色，融入背景，再不见痕迹。

而其中的一些黑历史则会让人觉得，他们经历了这么多的苦难，理应获得成功。不让他们享受到无上的荣光，则会显得天道不公。

而马竞的新人，安赫尔-科雷亚（Angel Correa），就是这样的一名球员。

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