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PCA and senate voting data
In this problem, we are given the data matrix with entries in , where each
row corresponds to a senator and each column to a bill. We first import this data, print some
relevant values, and normalize it as necessary to ready it for further computation.
To run this code, you'll need a number of standard Python libraries, all of which are installable
via or . We highly recommend using a virtual environment
(https://realpython.com/python-virtual-environments-a-primer/)
, for this class and in general.
Lastly, ensure that all data files (
senator_pca_data_matrix.csv
and
senator_pca_politician_labels.txt
) are located in the same folder as the notebook.
Places you will need to modify this code are enclosed in a block. You should not need to modify code outside these blocks to
complete the problems. Questions that you are expected to answer
in text are marked in red
. For solution files, solutions will be
presented in blue
.
#
In [1]:
In [2]:
We observe that the number of rows, , is the number of senators and is equal to 100. The
number of columns, , is the number of bills and is equal to 542.
X.shape: (100, 542)
# import the necessary packages for data manipulation, computation and PCA import
pandas as
pd
import
numpy as
np
import
scipy as
sp
from
numpy import
linalg as
LA
import
matplotlib.pyplot as
plt
from
sklearn.decomposition import
PCA
%
matplotlib inline
np.random.seed(
7
)
# import the data matrix
senator_df =
pd.read_csv(
'senator_pca_data_matrix.csv'
)
affiliation_file =
open
(
'senator_pca_politician_labels.txt'
, 'r'
)
affiliations =
[line.split(
'\n'
)[
0
].split(
' '
)[
1
] for
line in
affiliation_file
X =
np.array(senator_df.values[:, 3
:].T, dtype
=
'float64'
) # transpose to get s
print
(
'X.shape: '
, X.shape)
n =
X.shape[
0
] # number of senators
d =
X.shape[
1
] # number of bills
# this is just used for plotting, feel free to ignore
assert
set
(affiliations) ==
{
"Red"
, "Blue"
, "Yellow"
}
# assign a marker and hatch to each affiliation
markers =
[(
"Red"
, "o"
, "/"
), (
"Blue"
, "^"
, "-"
), (
"Yellow"
, "D"
, "+"
)]
In [3]:
A row of consists of 542 entries -1 (senator voted against), 1 (senator voted for), or 0
(senator abstained), one for each bill.
In [4]:
(542,)
[ 1. 1. 1. -1. -1. 1. 1. 1. 1. -1. 1. -1. -1. 1. 1. -1. 1. 1.
1. 1. 1. -1. 1. 1. 1. -1. 1. -1. 1. 1. 1. 1. 1. -1. 1. -1.
-1. -1. -1. 1. 1. -1. -1. -1. -1. 1. 1. 1. -1. 1. 1. -1. 1. 1.
-1. 1. 1. 1. 1. -1. 1. -1. -1. -1. 1. 1. 1. 1. 1. 1. 1. 1.
1. 1. -1. 0. -1. 1. 1. 1. -1. -1. 1. 1. -1. -1. 1. 1. 1. -1.
1. -1. 1. -1. 1. 1. -1. -1. -1. 1. 1. 1. -1. -1. -1. -1. -1. -1.
1. -1. 1. 1. -1. -1. -1. 1. -1. 1. -1. 1. 0. 0. 1. 1. -1. 1.
1. -1. 1. 1. -1. 1. -1. -1. 1. 1. 1. 1. 0. -1. -1. 1. 1. -1.
1. 1. 1. 1. 1. 0. 1. 0. 1. 1. 1. 1. 1. 1. 1. -1. 1. 1.
-1. 1. -1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. -1. 1.
1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 0. 1. -1. -1. 1. 1. 1.
1. 1. 1. 1. 1. 1. 1. 1. -1. 1. 1. 1. 1. 1. 1. 1. 1. -1.
1. 1. 0. 1. 0. -1. 1. 1. 1. 1. 1. 1. -1. 1. 1. 1. 1. 1.
1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.
1. -1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. -1. 1. 1. 1. -1.
1. 1. 1. 1. 1. 1. -1. -1. -1. 1. 1. -1. 1. -1. -1. 1. 1. 1.
-1. 1. 1. 1. -1. 1. -1. 1. -1. -1. 1. -1. -1. 1. 1. 1. -1. 1.
1. 1. 1. 1. -1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. -1. -1.
1. -1. 1. -1. -1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.
1. 1. 1. 1. 1. 1. 1. 1. 1. -1. 1. 1. 1. 1. 1. -1. 1. -1.
1. 1. 1. 1. 1. 1. -1. 1. -1. -1. -1. -1. 1. 1. 1. 1. 1. 1.
1. 1. 1. -1. 1. 1. 1. 1. 1. 1. 1. -1. -1. 1. -1. 1. 1. 1.
1. 1. -1. 1. -1. 1. -1. 1. 1. -1. 1. 1. 1. 1. 1. 1. 1. 1.
1. 0. 1. -1. 1. 1. 1. 1. 1. -1. -1. -1. 1. 1. 0. 1. 1. 1.
1. 1. 1. 1. -1. -1. 0. 0. 0. 0. 0. 0. 0. 1. 1. -1. -1. 1.
1. 1. 1. 1. 1. 1. 1. 1. 1. -1. 1. -1. 1. 1. 1. 1. -1. -1.
1. 1. 1. 1. -1. -1. 1. 1. -1. 1. 1. 1. 1. 1. 1. 1. 1. 1.
1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. -1. 1. 1. 1.
-1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.
1. 1. -1. -1. -1. 1. 1. 1. 1. -1. -1. 1. 1. -1. 1. 1. 1. 1.
1. 1.]
(100,)
[ 1. 1. 1. 1. 1. 1. 1. -1. 1. -1. 1. -1. 1. -1. -1. -1. 1. 1.
-1. 1. 1. -1. 1. -1. 1. 1. 1. -1. -1. 1. 1. 1. -1. 1. 1. 1.
-1. -1. -1. -1. 1. -1. -1. 1. 1. -1. -1. -1. -1. -1. 1. 1. -1. -1.
1. 1. -1. -1. -1. -1. -1. 1. 1. 1. 1. 1. -1. -1. -1. 1. -1. -1.
1. -1. -1. 1. 1. 1. -1. -1. -1. 1. 1. -1. 1. -1. 1. 1. 1. -1.
-1. -1. -1. -1. 1. 1. 1. -1. -1. -1.]
# print an example row of the data matrix
typical_row =
X[
0
]
print
(typical_row.shape)
print
(typical_row)
# print an example column of the data matrix
typical_column =
X[:,
0
]
print
(typical_column.shape)
print
(typical_column)
A column of consists of 100 entries in {-1, 0, 1}, one for each senator that voted on the bill.
In [5]:
We observe that the mean of the columns is not zero, so we center the data by subtracting the
mean of each bill's vote from its respective column.
In [6]:
a) Maximizing In this problem, you are asked to find a unit-norm vector maximizing the empirical
variance .
We first provide a function to calculate the scores, .
# compute the mean vote on each bill
X_mean =
np.mean(X, axis =
0
)
plt.plot(X_mean)
plt.title(
'means of each column of X'
)
plt.xlabel(
'column/bill'
)
plt.ylabel(
'mean vote'
)
plt.show()
# center the data matrix
X_original =
X.copy() # save a copy for part (d) and (e)
X =
X -
np.mean(X, axis =
0
)
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- Use python machine learning. A group of data scientists want to analyze some data. They already cleaned up the data, with the result being a Dataframe called X_train. The Dataframe X_train has 1058 rows and 13 columns. It has the below columns (picture attached on how it looks like): 'LotFrontage','LotArea','BsmtFinSF1', 'BsmtFinSF2', 'BsmtUnfSF','TotalBsmtSF','1stFlrSF', '2ndFlrSF', 'LowQualFinSF', 'GrLivArea','TotRmsAbvGrd','GarageArea','OpenPorchSF' Answer the following questions: 1. Transform X_train using PCA. Assign the output to a variable X_train_pca. 2. What is wrong with above approach? Scale the data, then repeat the above.arrow_forwardUsing a csv file attached (https://file.io/NMvbdnv4E3r0), Create a program on python that use the csv file. The program should accept a user's input of a compound. It should output the molar mass (in 2 decimal places only) of the compound.by using the csv file to compute for the atomic mass at name of the elements. Furthermore, if the "elements involved" are wrong an invallid message should be outputted and only existing chemical symbols are the output. The same goes for wrong input of the "number of atoms" wherein a wrong an invallid message should be outputted and only integers are to be inputted by the user. Program should look like this: Enter compound: C6H12O6 Enter elements involved: C,H,O Enter no. of Carbon atoms: AA Enter no. of Hydrogen atoms: 12 Enter no. of Oxygen atoms: 6 Wrong input of number of atoms! Try again. or Enter compound: C6H12O6 Enter elements involved: C,H,O Enter no. of Carbon atoms: 6 Enter no. of Hydrogen atoms: 12 Enter no. of Oxygen atoms: 6…arrow_forwardThe task is to implement part of a linter program using python. Specifically, you must be able to scan for grouping symbols ( "()", "[]", "{}” ) and ensure that there are no hanging open symbols or stray closing symbols in the source file. The implementation must involve recursion in terms of scanning for the scope. If a different closing symbol is encountered or the end of file is reached, the error message "Line : missing closing symbol for "" should be displayed. For stray closing tags, the message "Line : stray closing symbol for "". Note: Do not use "stack" in your code.arrow_forward
- Answer it. Help me out?arrow_forwardThe task is to implement part of a linter program using python. Specifically, you must be able to scan for grouping symbols ( "()", "[]", "{}") and ensure that there are no hanging open symbols or stray closing symbols in the source file. There will be files you will need to scan so you need the open() in your code. Also, you can use the read() or readlines() to know which lines has no opening or stray closing symbols. Example: You scan this code from a file, and you notice that there is a stray closing symbol ")". 1 int main(void) { . 123 2 3 4 printf("Hello world")); return 0; } The implementation must involve recursion in terms of scanning for the scope. If a different closing symbol is encountered or the end of file is reached, the error message "Line : missing closing symbol for "" should be displayed. For stray closing tags, the message "Line : stray closing symbol for "". Do not use "stack" in your code.arrow_forwardPython Question The campus is pretty big. There are n buildings scattered around it, numbered from 0 to n-1. These buildings are so far away from each other that the only way to get from one to another is to take a campus bus. There are m campus bus routes. The i-th one (0 <= i < m) takes you from building u_i to building v_i (but not the other way around). These buses run very frequently. Professor Zingaro is deciding where to hold his CS lectures. He believes a building x is accessible from a building y if you can get from y to x taking at most two buses. For his students’ convenience, he wants to hold his lectures in the most accessible building. Help him out by telling him how many buildings the most accessible building is accessible from. In addition, list all buildings that are the most accessible. Input The first line of the input contains two space-separated integers n and m, denoting the number of buildings and bus routes, respectively. m lines follow. The i-th one…arrow_forward
- I need the code from start to end with no errors and the explanation for the code ObjectivesJava refresher (including file I/O)Use recursionDescriptionFor this project, you get to write a maze solver. A maze is a two dimensional array of chars. Walls are represented as '#'s and ' ' are empty squares. The maze entrance is always in the first row, second column (and will always be an empty square). There will be zero or more exits along the outside perimeter. To be considered an exit, it must be reachable from the entrance. The entrance is not an exit.Here are some example mazes:mazeA7 9# # ###### # # ## # # #### # ## ##### ## ########## RequirementsWrite a MazeSolver class in Java. This program needs to prompt the user for a maze filename and then explore the maze. Display how many exits were found and the positions (not indices) of the valid exits. Your program can display the valid exits found in any order. See the examples below for exact output requirements. Also, record…arrow_forwardWrite a Python program, in a file called forest_map.py, to solve the following problem: Hansel and Gretel are abandoned in a forest with only a bag of breadcrumbs and must find their way home. The forest is laid out in a grid pattern. They can only take a step at a time through the forest, going either South or East. They cannot move diagonally, they cannot move North, and they cannot move West. As they leave a space, they will leave a breadcrumb (“*”) behind just in case -- if they have any breadcrumbs left. They do not leave a breadcrumb in the space where the path ends. If they don’t have enough breadcrumbs, they still move on to the next space, leaving their current space as it was. Given (as input) the number of breadcrumbs Hansel and Gretel have, and given the forest layout (as a fixed, but changeable, two-dimensional list in your code), determine whether Hansel and Gretel have just enough, more than enough, or not enough, breadcrumbs to leave in the path to get to the end. If…arrow_forwardPlease help with creating the code as follows: Task 2(a): Implement the FFT algorithm using the above pseudocode as the function FFT(). Notethat we have introduced a sign parameter in the FFT pseudocode to specify the sign of the exponent in ωn.If sign is 1, ωn = e2πi/n. If sign is -1, ωn = e−2πi/n.Task 2(b): Then implement the inverse FFT as the function IFFT() that calls the FFT function youwrote with the appropriate inputs, and then normalizes the output by n. Example Task 2(a): Fast Fourier Transform FFT <input_file.txt> <output_file.txt>where input_file.txt contains the coefficients of the polynomial, this query should read thenumbers from input_file.txt, compute the FFT, and output the result to output_file.txt.Note: This FFT query has the same name as the FFT function in the pseudocode. It should beclear from the context which one we are referring to.Example 1:task2a_input1.txt1.0002.0003.000FFT task2a_input1.txt…arrow_forward
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ISBN:9781337102087
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Publisher:Cengage Learning