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anothertimdrakestan · 4 years

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Tiktok Inspired Pranks On Batboys/YJ Characters HC! PART TWO!

SOME OF THESE ARE SEXUAL SO THIS IS A WARNING

omg the requests for part two were AMAZINGGG shout-out to the anons who recommended two different Jason ideas and a Bart one that is to die for! I threw in a Tim because he’s my bb boi and cannot be left out! Hope you enjoy!

Jason Todd - Bl0wjob Prank

- after being tagged in a million videos of girls tying their hair up then getting on their knees in front of their boyfriend only to pick something up you knew Jason would go berserk

- In the back of a car driving the two of you home from a gala you knew it was time

- luckily it was just you and Jason in the back while the driver had closed the front seat from the back so you knew it was private enough

- you were resting your head on his shoulder when you sat up, pulling your hair up making direct eye contact with him while he looked confused

- lightly biting your lip while finishing putting your hair up Jason’s confused look turned in to a little bit of a smirk as you pulled your hair into it’s signature d*ck sucking style

- you were aiming for the water bottle in the seat’s lower pocket, reaching for it would place you perfectly on Jason’s lap

- for even more tension you carefully took out your earrings, being sure not to break eye contact

- slowly you leaned over his lap, dragging you hand over his lap, pausing to put pressure on him while he sucked in a breath and reached to undo his seat belt and belt buckle

- right before he could do anything you reached forward, grabbing the water bottle, sitting up cooly and unscrewing the lid before taking a sip as if nothing had happened

- “you’re fucking kidding me” Jason whispered and you looked at him with innocent eyes “hm? I wanted water” you grinned. “well when we get home I want something else” his eyes narrowed with a smirk making you squirm in your seat.

- Jason knocked on the driver’s window “how much cash do I need to give you to speed?” giving you a wink before whispering “not much longer princess” his hand gripping your thigh the rest of the ride home

Bart Allen - Letting Go Of His Hand

- your friends sent you the video saying you had to do it to Bart

- Bart is constantly touch deprived, he’s always hanging all over you 24/7 whether it’s holding your hand, playing with your hair, toying with the material of your shirt, rubbing your back, or literally anything else he could think of to be close to you

- that’s why refusing to hold his hand would be hilarious, especially in a grocery store where he had holding you down to a science

- as usual he had your hand clasped in his while he carried a basket with his other as you picked stuff to put in it

- holding in a laugh you tugged your hand out of his and started towards the produce, Bart stood completely baffled in the middle of the aisle then he quickly sped up next to you grabbing your hand again as you pretended not to notice

- him getting more frustrated as you let go again to turn a 180 and look at some apples

- he gave up on the hand and slipped his hand around your waist, pulling you in for a quick kiss while you swerved to look at avocados

- que the whining “babeee, Y/N, why don’t you love meeee”

- “I do love you B!” you held up an onion with a smile as the pouting increased

- “if you loved me you’d hold my hand like always” he had the most adorable puppy eyes

- “Mhm in a minute!” you were shaking trying to hold in a laugh, pretending to be infatuated with the lettuce

- “Now!” he’d come up behind you, taking your hand and squeezing it, looking at you with the most confused, sincere look

- “I give up, it was just prank B” you laughed, intertwining your fingers with his as he smiled “terrible prank, wasn’t even funny” he’d make sure you made it up to him later with cuddles only then would he admit it was pretty funny

Tim Drake - I Want A Baby

- you had no idea what would happen with this one, but you knew Tim’s reaction would be priceless

- you’d decided the perfect time was your after dinner cuddles when the two of you would usually watch a movie or something before he went on patrol or began working on cases

- laying in Tim’s lap as he mindlessly ran his hands through your hair while scrolling through his phone you broke the silence “can we talk real quick?”

- he froze and put his phone down “uh yeah... what’s up are you okay?” his worrying nature kicking in

- “everything’s good! Better than good actually, perfect. So perfect that maybe we can spread all our love to someone else?” you tried to hint but Tim looked beyond confused

- “Someone else? Like another person?” you realized where he was going and stopped “no no! not like that, our own person, a baby!”

- it took everything to hold in a guttural laugh as Tim’s entire face flushed and his eyes frantically searched yours “you, want, a child? Like our own kid?” Tim was processing and you could see him panicking

- “Yeah! Like a mini you or me! You’d have your own sidekick or Wayne Enterprise CEO in like 20 years!” you were biting the inside of your cheeks so hard to keep in laughter as Tim looked petrified

- “Y/N like now? You want a baby now? Like a literal child? In our home?” you nodded while he began taking deep breaths before continuing

- “You know I love you and we can totally have kids later in life but right now?! I’m always busy with WE and Red Robin and you’re still making a name for yourself! Shouldn’t we be established first? I mean there’s nothing I’d love more than having a bunch of min Y/N’s but-” it was adorable watching Tim spin out

- “Timmy I’m just kidding, when we’re older we can talk for real but I was just teasing” you sat up a little to place a kiss on his lips to help him stop hyperventilating “oh thank god” was all he said before kissing you back

- “You know our kids would be adorable though” you teased “yeah in like 10 years!” he replied as he calmed down, making you promise to give him a couple months before you pulled another ‘prank’

Jason Todd - Walking Out Naked

- in the 21st century Jason totally plays COD or R6 and gets really into it

- after a shower you had a towel wrapped around you and decided you wanted Jay’s undivided attention

- creeping out you can hear profanities being screamed at whoever he’s playing against drowning out your footsteps up behind him

- dropping the towel and coming into his view

- jaw: dropped. headset: off. Jason: horny.

- screaming something about an emergency he is fucking lightning fast scooping you up

- “babe you sure you don’t wanna keep playing your game” you teased, biting your lip as Jason was using inhuman speed to get you to the bedroom

- “I’d much rather play other games with you babe”

- the plan worked - Jason was totally focused on you for hours in every way you could’ve imagined possible, maybe this should be a weekly thing...

#jason todd #jason todd x you #jason todd x reader #jason todd fluff #jason todd hot #jason todd smut #bart allen #bart allen x reader #tim drake #tim drake x reader #red hood #red hood x reader #red robin #kid flash #batboys #batboys headcanons #kid flash x you #tim drake x you #dc fluf

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abhomachinelearning · 4 years

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K-means Cluster Analysis

Clustering is a broad set of techniques for finding subgroups of observations within a data set. When we cluster observations, we want observations in the same group to be similar and observations in different groups to be dissimilar. Because there isn’t a response variable, this is an unsupervised method, which implies that it seeks to find relationships between the nn observations without being trained by a response variable. Clustering allows us to identify which observations are alike, and potentially categorize them therein. K-means clustering is the simplest and the most commonly used clustering method for splitting a dataset into a set of k groups.

tl;dr:

This tutorial serves as an introduction to the k-means clustering method.

Replication Requirements: What you’ll need to reproduce the analysis in this tutorial

Data Preparation: Preparing our data for cluster analysis

Clustering Distance Measures: Understanding how to measure differences in observations

K-Means Clustering: Calculations and methods for creating K subgroups of the data

Determining Optimal Clusters: Identifying the right number of clusters to group your data

Replication Requirements

To replicate this tutorial’s analysis you will need to load the following packages:

library(tidyverse) # data manipulation

library(cluster) # clustering algorithms

library(factoextra) # clustering algorithms & visualization

Data Preparation:

To perform a cluster analysis in R, generally, the data should be prepared as follows:

Rows are observations (individuals) and columns are variables

Any missing value in the data must be removed or estimated.

The data must be standardized (i.e., scaled) to make variables comparable. Recall that, standardization consists of transforming the variables such that they have mean zero and standard deviation one.1

Here, we’ll use the built-in R data set USArrests, which contains statistics in arrests per 100,000 residents for assault, murder, and rape in each of the 50 US states in 1973. It includes also the percent of the population living in urban areas

df <- USArrests

To remove any missing value that might be present in the data, type this:

df <- na.omit(df)

As we don’t want the clustering algorithm to depend to an arbitrary variable unit, we start by scaling/standardizing the data using the R function scale:

df <- scale(df)

head(df)

## Murder Assault UrbanPop Rape

## Alabama 1.24256408 0.7828393 -0.5209066 -0.003416473

## Alaska 0.50786248 1.1068225 -1.2117642 2.484202941

## Arizona 0.07163341 1.4788032 0.9989801 1.042878388

## Arkansas 0.23234938 0.2308680 -1.0735927 -0.184916602

## California 0.27826823 1.2628144 1.7589234 2.067820292

## Colorado 0.02571456 0.3988593 0.8608085 1.864967207

Clustering Distance Measures:

The classification of observations into groups requires some methods for computing the distance or the (dis)similarity between each pair of observations. The result of this computation is known as a dissimilarity or distance matrix. There are many methods to calculate this distance information; the choice of distance measures is a critical step in clustering. It defines how the similarity of two elements (x, y) is calculated and it will influence the shape of the clusters.

The choice of distance measures is a critical step in clustering. It defines how the similarity of two elements (x, y) is calculated and it will influence the shape of the clusters. The classical methods for distance measures are Euclidean and Manhattan distances, which are defined as follow:

Euclidean distance:

deuc(x,y)=

⎷n∑i=1(xi−yi)2(1)(1)deuc(x,y)=∑i=1n(xi−yi)2

Manhattan distance:

dman(x,y)=n∑i=1|(xi−yi)|(2)(2)dman(x,y)=∑i=1n|(xi−yi)|

Where, x and y are two vectors of length n.

Other dissimilarity measures exist such as correlation-based distances, which is widely used for gene expression data analyses. Correlation-based distance is defined by subtracting the correlation coefficient from 1. Different types of correlation methods can be used such as:

Pearson correlation distance:

dcor(x,y)=1−∑ni=1(xi−¯x)(yi−¯y)√∑ni=1(xi−¯x)2∑ni=1(yi−¯y)2(3)(3)dcor(x,y)=1−∑i=1n(xi−x¯)(yi−y¯)∑i=1n(xi−x¯)2∑i=1n(yi−y¯)2

Spearman correlation distance:

The spearman correlation method computes the correlation between the rank of x and the rank of y variables.

dspear(x,y)=1−∑ni=1(x′i−¯x′)(y′i−¯y′)√∑ni=1(x′i−¯x′)2∑ni=1(y′i−¯y′)2(4)(4)dspear(x,y)=1−∑i=1n(xi′−x¯′)(yi′−y¯′)∑i=1n(xi′−x¯′)2∑i=1n(yi′−y¯′)2

Where x′i=rank(xi)xi′=rank(xi) and y′i=rank(yi)yi′=rank(yi).

Kendall correlation distance:

Kendall correlation method measures the correspondence between the ranking of x and y variables. The total number of possible pairings of x with y observations is n(n − 1)/2, where n is the size of x and y. Begin by ordering the pairs by the x values. If x and y are correlated, then they would have the same relative rank orders. Now, for each yiyi, count the number of yj>yiyj>yi (concordant pairs (c)) and the number of yj<yiyj<yi (discordant pairs (d)).

Kendall correlation distance is defined as follow:

dkend(x,y)=1−nc−nd12n(n−1)(5)(5)dkend(x,y)=1−nc−nd12n(n−1)

The choice of distance measures is very important, as it has a strong influence on the clustering results. For most common clustering software, the default distance measure is the Euclidean distance. However, depending on the type of the data and the research questions, other dissimilarity measures might be preferred and you should be aware of the options.

Within R it is simple to compute and visualize the distance matrix using the functions get_dist and fviz_dist from the factoextra R package. This starts to illustrate which states have large dissimilarities (red) versus those that appear to be fairly similar (teal).

get_dist: for computing a distance matrix between the rows of a data matrix. The default distance computed is the Euclidean; however, get_dist also supports distanced described in equations 2-5 above plus others.

fviz_dist: for visualizing a distance matrix

distance <- get_dist(df)

fviz_dist(distance, gradient = list(low = "#00AFBB", mid = "white", high = "#FC4E07"))

K-Means Clustering:

K-means clustering is the most commonly used unsupervised machine learning algorithm for partitioning a given data set into a set of k groups (i.e. k clusters), where k represents the number of groups pre-specified by the analyst. It classifies objects in multiple groups (i.e., clusters), such that objects within the same cluster are as similar as possible (i.e., high intra-class similarity), whereas objects from different clusters are as dissimilar as possible (i.e., low inter-class similarity). In k-means clustering, each cluster is represented by its center (i.e, centroid) which corresponds to the mean of points assigned to the cluster.

The Basic Idea:

The basic idea behind k-means clustering consists of defining clusters so that the total intra-cluster variation (known as total within-cluster variation) is minimized. There are several k-means algorithms available. The standard algorithm is the Hartigan-Wong algorithm (1979), which defines the total within-cluster variation as the sum of squared distances Euclidean distances between items and the corresponding centroid:

W(Ck)=∑xi∈Ck(xi−μk)2(6)(6)W(Ck)=∑xi∈Ck(xi−μk)2

where:

xixi is a data point belonging to the cluster CkCk

μkμk is the mean value of the points assigned to the cluster CkCk

Each observation (xixi) is assigned to a given cluster such that the sum of squares (SS) distance of the observation to their assigned cluster centers (μkμk) is minimized.

We define the total within-cluster variation as follows:

tot.withiness=k∑k=1W(Ck)=k∑k=1∑xi∈Ck(xi−μk)2(7)(7)tot.withiness=∑k=1kW(Ck)=∑k=1k∑xi∈Ck(xi−μk)2

The total within-cluster sum of square measures the compactness (i.e goodness) of the clustering and we want it to be as small as possible.

K-means Algorithm:

The first step when using k-means clustering is to indicate the number of clusters (k) that will be generated in the final solution. The algorithm starts by randomly selecting k objects from the data set to serve as the initial centers for the clusters. The selected objects are also known as cluster means or centroids. Next, each of the remaining objects is assigned to it’s closest centroid, where closest is defined using the Euclidean distance (Eq. 1) between the object and the cluster mean. This step is called “cluster assignment step”. After the assignment step, the algorithm computes the new mean value of each cluster. The term cluster “centroid update” is used to design this step. Now that the centers have been recalculated, every observation is checked again to see if it might be closer to a different cluster. All the objects are reassigned again using the updated cluster means. The cluster assignment and centroid update steps are iteratively repeated until the cluster assignments stop changing (i.e until convergence is achieved). That is, the clusters formed in the current iteration are the same as those obtained in the previous iteration.

K-means algorithm can be summarized as follows:

Specify the number of clusters (K) to be created (by the analyst)

Select randomly k objects from the data set as the initial cluster centers or means

Assigns each observation to their closest centroid, based on the Euclidean distance between the object and the centroid

For each of the k clusters update the cluster centroid by calculating the new mean values of all the data points in the cluster. The centroid of a Kth cluster is a vector of length p containing the means of all variables for the observations in the kth cluster; p is the number of variables.

Iteratively minimize the total within sum of square (Eq. 7). That is, iterate steps 3 and 4 until the cluster assignments stop changing or the maximum number of iterations is reached. By default, the R software uses 10 as the default value for the maximum number of iterations.

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