MATH 427: Principal Component Analysis (PCA)

Eric Friedlander

Computational Set-Up

library(tidyverse)
library(tidymodels)
library(knitr)
library(kableExtra)

tidymodels_prefer()

set.seed(427)

Data: mnist

• MNIST Database: Modified National Institute of Standards and Technology Database
• Large database of handwritten digits
  • 60,000 training images
  • 10,000 test images
• Each image:
  • 28x28 black and white pixels
  • \(28\times 28\times 1 = 784\)

Loading data

library(dslabs)
mnist <- read_mnist()
mnist_train <- mnist$train$images
mnist_train |> head() |> kable()

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Digits

image(x = 1:28, y = 1:28,
      z = matrix(mnist_train[1,], nrow = 28, byrow=FALSE)[,28:1],
      col=gray((0:255)/255))

Digits

image(x = 1:28, y = 1:28,
      z = matrix(mnist_train[2,], nrow = 28, byrow=FALSE)[,28:1],
      col=gray((0:255)/255))

Digits

image(x = 1:28, y = 1:28,
      z = matrix(mnist_train[3,], nrow = 28, byrow=FALSE)[,28:1],
      col=gray((0:255)/255))

Digits

image(x = 1:28, y = 1:28,
      z = matrix(mnist_train[4,], nrow = 28, byrow=FALSE)[,28:1],
      col=gray((0:255)/255))

Unsupervised Learning & Dimensionality Reduction

• Unsupervised Learning: ML for unlabeled data (i.e. no response variables)
  • Goal: Uncover patterns/structure within data
  • Tasks:
    • Clustering: finding sub-groups within our data
    • Dimensionality Reduction: reducing the number of columns in our data set… why?

Dimensionality Reduction

• Goal phrasing 1: Reduce the number of columns, while losing as little information as possible
• Goal phrasing 2: Extract lower-dimensional structure from our data

Last Time

• Vectors and Projects

Principal Component Analysis (PCA)

PCA Vocabulary

• Principal Component (PC1): direction in \(p\)-dimensional space (e.g. \(\langle 1, 1, 2\rangle\))
• Scores: our new variables (e.g. \((-0.56\times 1 + -0.996\times 1 + -1.56\times 2)/6 = -0.778\))
• Loadings: For direction above’
  • Loading on \(x\) is 1
  • Loading on \(y\) is 1
  • Loading on \(z\) is 2

Recall: Variance

• What is variance?
• Intuitively: what does variance measure?
• Variance: \(\frac{1}{n-1}\sum_{i=1}^n(x_i - \bar{x})^2\)
  • Average of the squared distance from zero of each observation

Idea behind PCA

• Select first PC so variance of scores is the maximum
• Iteratively:
  • Select next PC so variance of scores is maximize AND new PC is orthogonal to all other PCs

• What does orthogonal mean?

Easy Example

• Exercise: What should the first and second PCs be?

How much variance is explained by each of the PC’s?

var_exp <- easy_ex |> 
  mutate(PC1 = x,
         PC2 = y) |> 
  summarize(var1 = var(PC1), 
            var2 = var(PC2))

var_exp |> kable()

var1	var2
0.9834589	0.0637151

What proportion of variance is explained by each of the PC’s?

var_exp |> 
  pivot_longer(everything()) |> 
  mutate(proportion = value/sum(value)) |> 
  kable()

name	value	proportion
var1	0.9834589	0.9391552
var2	0.0637151	0.0608448

• 93% of our variance (information) is contained in our first PC

Harder Example

• Exercise: What should the first and second PCs be?

How much variance is explained by each of the PC’s?

var_exp <- harder_ex |> 
  mutate(PC1 = (x + y)/2,
         PC2 = (x-y)/2) |> 
  summarize(var1 = var(PC1), 
            var2 = var(PC2))

var_exp |> kable()

var1	var2
1.021035	0.0159288

Question?

• Will our PCs depend on the scale of our data?
• What does this mean we should do?

How is PCA actually accomplished

• Compute Variance-Covariance Matrix
• Compute Eigen-decomposition of variance-covariance matrix
  • Eigen-vectors = Principal components
  • Eigen-values = Variance explained by corresponding component

PCA in R

Recipe

• Documentation for step_normalize

pca_recipe <- recipe(~ ., data = mnist_train) |> 
  step_normalize(all_numeric_predictors()) |> 
  step_pca(all_numeric_predictors(), num_comp = 20)

Prepping and Baking recipes

• If we want to apply a recipe to a data set outside of a workflow:
  • First, prep using training set: this estimates any necessary quantities
  • Second, bake this applies the recipe to a new data set (in our case the new data set in the same data set)

Applying recipe to training data

prepped_pca <- pca_recipe |> prep(mnist_train)
mnist_pca <- prepped_pca |> bake(new_data = mnist_train)

Using the results

• Three things of interest
  • New scores: this is our new data… use for plotting and analysis
  • PCs: these are our new directions… by looking at loadings we can interpret structure
  • Eigenvalues: this will tell us how much information is lost

How many PCs Should We Use?

prepped_pca |> 
  tidy(2, type = "variance") |> 
  filter(terms == "variance") |> 
  kable()

terms	value	component	id
variance	40.4869603	1	pca_XZ5Kg
variance	29.2412102	2	pca_XZ5Kg
variance	26.8113576	3	pca_XZ5Kg
variance	20.6862734	4	pca_XZ5Kg
variance	18.0763488	5	pca_XZ5Kg
variance	15.7329156	6	pca_XZ5Kg
variance	13.7903793	7	pca_XZ5Kg
variance	12.5173805	8	pca_XZ5Kg
variance	11.0066118	9	pca_XZ5Kg
variance	10.0503295	10	pca_XZ5Kg
variance	9.6202975	11	pca_XZ5Kg
variance	8.6308297	12	pca_XZ5Kg
variance	7.9914637	13	pca_XZ5Kg
variance	7.8147519	14	pca_XZ5Kg
variance	7.3754149	15	pca_XZ5Kg
variance	7.1304687	16	pca_XZ5Kg
variance	6.7138681	17	pca_XZ5Kg
variance	6.6038974	18	pca_XZ5Kg
variance	6.4059417	19	pca_XZ5Kg
variance	6.2372735	20	pca_XZ5Kg
variance	5.9321928	21	pca_XZ5Kg
variance	5.7605025	22	pca_XZ5Kg
variance	5.4839422	23	pca_XZ5Kg
variance	5.3185086	24	pca_XZ5Kg
variance	5.1286499	25	pca_XZ5Kg
variance	4.9605418	26	pca_XZ5Kg
variance	4.9052549	27	pca_XZ5Kg
variance	4.7083565	28	pca_XZ5Kg
variance	4.5291221	29	pca_XZ5Kg
variance	4.3946352	30	pca_XZ5Kg
variance	4.2751505	31	pca_XZ5Kg
variance	4.2139267	32	pca_XZ5Kg
variance	4.0983125	33	pca_XZ5Kg
variance	4.0317442	34	pca_XZ5Kg
variance	3.9770700	35	pca_XZ5Kg
variance	3.8604597	36	pca_XZ5Kg
variance	3.8085767	37	pca_XZ5Kg
variance	3.7255722	38	pca_XZ5Kg
variance	3.6438747	39	pca_XZ5Kg
variance	3.4416399	40	pca_XZ5Kg
variance	3.4161882	41	pca_XZ5Kg
variance	3.3637292	42	pca_XZ5Kg
variance	3.2576820	43	pca_XZ5Kg
variance	3.2361493	44	pca_XZ5Kg
variance	3.2047276	45	pca_XZ5Kg
variance	3.1790572	46	pca_XZ5Kg
variance	3.1420049	47	pca_XZ5Kg
variance	3.0858372	48	pca_XZ5Kg
variance	3.0607145	49	pca_XZ5Kg
variance	3.0375491	50	pca_XZ5Kg
variance	2.9016712	51	pca_XZ5Kg
variance	2.8640379	52	pca_XZ5Kg
variance	2.8497604	53	pca_XZ5Kg
variance	2.8236951	54	pca_XZ5Kg
variance	2.7662834	55	pca_XZ5Kg
variance	2.7177360	56	pca_XZ5Kg
variance	2.6916372	57	pca_XZ5Kg
variance	2.6584628	58	pca_XZ5Kg
variance	2.6166512	59	pca_XZ5Kg
variance	2.5761851	60	pca_XZ5Kg
variance	2.5265801	61	pca_XZ5Kg
variance	2.4936804	62	pca_XZ5Kg
variance	2.4694291	63	pca_XZ5Kg
variance	2.4368544	64	pca_XZ5Kg
variance	2.4087941	65	pca_XZ5Kg
variance	2.4011323	66	pca_XZ5Kg
variance	2.3794627	67	pca_XZ5Kg
variance	2.3160961	68	pca_XZ5Kg
variance	2.2677059	69	pca_XZ5Kg
variance	2.2459613	70	pca_XZ5Kg
variance	2.2279444	71	pca_XZ5Kg
variance	2.2029316	72	pca_XZ5Kg
variance	2.1862348	73	pca_XZ5Kg
variance	2.1704822	74	pca_XZ5Kg
variance	2.1473098	75	pca_XZ5Kg
variance	2.1349476	76	pca_XZ5Kg
variance	2.1155197	77	pca_XZ5Kg
variance	2.0824414	78	pca_XZ5Kg
variance	2.0567589	79	pca_XZ5Kg
variance	2.0483094	80	pca_XZ5Kg
variance	2.0319621	81	pca_XZ5Kg
variance	2.0264366	82	pca_XZ5Kg
variance	2.0043811	83	pca_XZ5Kg
variance	2.0026194	84	pca_XZ5Kg
variance	1.9969826	85	pca_XZ5Kg
variance	1.9893557	86	pca_XZ5Kg
variance	1.9782088	87	pca_XZ5Kg
variance	1.9662099	88	pca_XZ5Kg
variance	1.9460140	89	pca_XZ5Kg
variance	1.9306153	90	pca_XZ5Kg
variance	1.9106927	91	pca_XZ5Kg
variance	1.8898779	92	pca_XZ5Kg
variance	1.8854346	93	pca_XZ5Kg
variance	1.8716125	94	pca_XZ5Kg
variance	1.8557891	95	pca_XZ5Kg
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variance	0.0939418	482	pca_XZ5Kg
variance	0.0934708	483	pca_XZ5Kg
variance	0.0931274	484	pca_XZ5Kg
variance	0.0927579	485	pca_XZ5Kg
variance	0.0918690	486	pca_XZ5Kg
variance	0.0910154	487	pca_XZ5Kg
variance	0.0907436	488	pca_XZ5Kg
variance	0.0901512	489	pca_XZ5Kg
variance	0.0896621	490	pca_XZ5Kg
variance	0.0892178	491	pca_XZ5Kg
variance	0.0887262	492	pca_XZ5Kg
variance	0.0880554	493	pca_XZ5Kg
variance	0.0880271	494	pca_XZ5Kg
variance	0.0874531	495	pca_XZ5Kg
variance	0.0873566	496	pca_XZ5Kg
variance	0.0862892	497	pca_XZ5Kg
variance	0.0861687	498	pca_XZ5Kg
variance	0.0855976	499	pca_XZ5Kg
variance	0.0852034	500	pca_XZ5Kg
variance	0.0846459	501	pca_XZ5Kg
variance	0.0844515	502	pca_XZ5Kg
variance	0.0836709	503	pca_XZ5Kg
variance	0.0830853	504	pca_XZ5Kg
variance	0.0825595	505	pca_XZ5Kg
variance	0.0818487	506	pca_XZ5Kg
variance	0.0816690	507	pca_XZ5Kg
variance	0.0811529	508	pca_XZ5Kg
variance	0.0806626	509	pca_XZ5Kg
variance	0.0804725	510	pca_XZ5Kg
variance	0.0798590	511	pca_XZ5Kg
variance	0.0795467	512	pca_XZ5Kg
variance	0.0787387	513	pca_XZ5Kg
variance	0.0784439	514	pca_XZ5Kg
variance	0.0780325	515	pca_XZ5Kg
variance	0.0777017	516	pca_XZ5Kg
variance	0.0773247	517	pca_XZ5Kg
variance	0.0768321	518	pca_XZ5Kg
variance	0.0767898	519	pca_XZ5Kg
variance	0.0766431	520	pca_XZ5Kg
variance	0.0762530	521	pca_XZ5Kg
variance	0.0757462	522	pca_XZ5Kg
variance	0.0754874	523	pca_XZ5Kg
variance	0.0751168	524	pca_XZ5Kg
variance	0.0746517	525	pca_XZ5Kg
variance	0.0740428	526	pca_XZ5Kg
variance	0.0738354	527	pca_XZ5Kg
variance	0.0735300	528	pca_XZ5Kg
variance	0.0732921	529	pca_XZ5Kg
variance	0.0729363	530	pca_XZ5Kg
variance	0.0722028	531	pca_XZ5Kg
variance	0.0717088	532	pca_XZ5Kg
variance	0.0715695	533	pca_XZ5Kg
variance	0.0710300	534	pca_XZ5Kg
variance	0.0708745	535	pca_XZ5Kg
variance	0.0707496	536	pca_XZ5Kg
variance	0.0698304	537	pca_XZ5Kg
variance	0.0696761	538	pca_XZ5Kg
variance	0.0692013	539	pca_XZ5Kg
variance	0.0689276	540	pca_XZ5Kg
variance	0.0685700	541	pca_XZ5Kg
variance	0.0681503	542	pca_XZ5Kg
variance	0.0678005	543	pca_XZ5Kg
variance	0.0674213	544	pca_XZ5Kg
variance	0.0673106	545	pca_XZ5Kg
variance	0.0665346	546	pca_XZ5Kg
variance	0.0662575	547	pca_XZ5Kg
variance	0.0662254	548	pca_XZ5Kg
variance	0.0660517	549	pca_XZ5Kg
variance	0.0651589	550	pca_XZ5Kg
variance	0.0647095	551	pca_XZ5Kg
variance	0.0642805	552	pca_XZ5Kg
variance	0.0636520	553	pca_XZ5Kg
variance	0.0633399	554	pca_XZ5Kg
variance	0.0630302	555	pca_XZ5Kg
variance	0.0627478	556	pca_XZ5Kg
variance	0.0627228	557	pca_XZ5Kg
variance	0.0622318	558	pca_XZ5Kg
variance	0.0617651	559	pca_XZ5Kg
variance	0.0611614	560	pca_XZ5Kg
variance	0.0607914	561	pca_XZ5Kg
variance	0.0606068	562	pca_XZ5Kg
variance	0.0605425	563	pca_XZ5Kg
variance	0.0603339	564	pca_XZ5Kg
variance	0.0600316	565	pca_XZ5Kg
variance	0.0596667	566	pca_XZ5Kg
variance	0.0588990	567	pca_XZ5Kg
variance	0.0588618	568	pca_XZ5Kg
variance	0.0585501	569	pca_XZ5Kg
variance	0.0579933	570	pca_XZ5Kg
variance	0.0578428	571	pca_XZ5Kg
variance	0.0576485	572	pca_XZ5Kg
variance	0.0572756	573	pca_XZ5Kg
variance	0.0568802	574	pca_XZ5Kg
variance	0.0563234	575	pca_XZ5Kg
variance	0.0561282	576	pca_XZ5Kg
variance	0.0560246	577	pca_XZ5Kg
variance	0.0556846	578	pca_XZ5Kg
variance	0.0553713	579	pca_XZ5Kg
variance	0.0548701	580	pca_XZ5Kg
variance	0.0543958	581	pca_XZ5Kg
variance	0.0542514	582	pca_XZ5Kg
variance	0.0541719	583	pca_XZ5Kg
variance	0.0535840	584	pca_XZ5Kg
variance	0.0534817	585	pca_XZ5Kg
variance	0.0532694	586	pca_XZ5Kg
variance	0.0526302	587	pca_XZ5Kg
variance	0.0525551	588	pca_XZ5Kg
variance	0.0520580	589	pca_XZ5Kg
variance	0.0520354	590	pca_XZ5Kg
variance	0.0514785	591	pca_XZ5Kg
variance	0.0514116	592	pca_XZ5Kg
variance	0.0510471	593	pca_XZ5Kg
variance	0.0505489	594	pca_XZ5Kg
variance	0.0499108	595	pca_XZ5Kg
variance	0.0497753	596	pca_XZ5Kg
variance	0.0495371	597	pca_XZ5Kg
variance	0.0494464	598	pca_XZ5Kg
variance	0.0489601	599	pca_XZ5Kg
variance	0.0486752	600	pca_XZ5Kg
variance	0.0484454	601	pca_XZ5Kg
variance	0.0484011	602	pca_XZ5Kg
variance	0.0481149	603	pca_XZ5Kg
variance	0.0478454	604	pca_XZ5Kg
variance	0.0476975	605	pca_XZ5Kg
variance	0.0471474	606	pca_XZ5Kg
variance	0.0469730	607	pca_XZ5Kg
variance	0.0467838	608	pca_XZ5Kg
variance	0.0464157	609	pca_XZ5Kg
variance	0.0460452	610	pca_XZ5Kg
variance	0.0458673	611	pca_XZ5Kg
variance	0.0454372	612	pca_XZ5Kg
variance	0.0451101	613	pca_XZ5Kg
variance	0.0449031	614	pca_XZ5Kg
variance	0.0444963	615	pca_XZ5Kg
variance	0.0443734	616	pca_XZ5Kg
variance	0.0441724	617	pca_XZ5Kg
variance	0.0438086	618	pca_XZ5Kg
variance	0.0435438	619	pca_XZ5Kg
variance	0.0433648	620	pca_XZ5Kg
variance	0.0431079	621	pca_XZ5Kg
variance	0.0429888	622	pca_XZ5Kg
variance	0.0425301	623	pca_XZ5Kg
variance	0.0423341	624	pca_XZ5Kg
variance	0.0420923	625	pca_XZ5Kg
variance	0.0419995	626	pca_XZ5Kg
variance	0.0415967	627	pca_XZ5Kg
variance	0.0415538	628	pca_XZ5Kg
variance	0.0410668	629	pca_XZ5Kg
variance	0.0408937	630	pca_XZ5Kg
variance	0.0406157	631	pca_XZ5Kg
variance	0.0404402	632	pca_XZ5Kg
variance	0.0403427	633	pca_XZ5Kg
variance	0.0401443	634	pca_XZ5Kg
variance	0.0399559	635	pca_XZ5Kg
variance	0.0398520	636	pca_XZ5Kg
variance	0.0394720	637	pca_XZ5Kg
variance	0.0393763	638	pca_XZ5Kg
variance	0.0389693	639	pca_XZ5Kg
variance	0.0386442	640	pca_XZ5Kg
variance	0.0383515	641	pca_XZ5Kg
variance	0.0382810	642	pca_XZ5Kg
variance	0.0378687	643	pca_XZ5Kg
variance	0.0374988	644	pca_XZ5Kg
variance	0.0372839	645	pca_XZ5Kg
variance	0.0371122	646	pca_XZ5Kg
variance	0.0367338	647	pca_XZ5Kg
variance	0.0365614	648	pca_XZ5Kg
variance	0.0361874	649	pca_XZ5Kg
variance	0.0359937	650	pca_XZ5Kg
variance	0.0359157	651	pca_XZ5Kg
variance	0.0354626	652	pca_XZ5Kg
variance	0.0354017	653	pca_XZ5Kg
variance	0.0350353	654	pca_XZ5Kg
variance	0.0348493	655	pca_XZ5Kg
variance	0.0346105	656	pca_XZ5Kg
variance	0.0345239	657	pca_XZ5Kg
variance	0.0343125	658	pca_XZ5Kg
variance	0.0341484	659	pca_XZ5Kg
variance	0.0339538	660	pca_XZ5Kg
variance	0.0333331	661	pca_XZ5Kg
variance	0.0330420	662	pca_XZ5Kg
variance	0.0330316	663	pca_XZ5Kg
variance	0.0328578	664	pca_XZ5Kg
variance	0.0324660	665	pca_XZ5Kg
variance	0.0323101	666	pca_XZ5Kg
variance	0.0321032	667	pca_XZ5Kg
variance	0.0317928	668	pca_XZ5Kg
variance	0.0315557	669	pca_XZ5Kg
variance	0.0313029	670	pca_XZ5Kg
variance	0.0311393	671	pca_XZ5Kg
variance	0.0308684	672	pca_XZ5Kg
variance	0.0306067	673	pca_XZ5Kg
variance	0.0300692	674	pca_XZ5Kg
variance	0.0299639	675	pca_XZ5Kg
variance	0.0297945	676	pca_XZ5Kg
variance	0.0294315	677	pca_XZ5Kg
variance	0.0292626	678	pca_XZ5Kg
variance	0.0288831	679	pca_XZ5Kg
variance	0.0286481	680	pca_XZ5Kg
variance	0.0285703	681	pca_XZ5Kg
variance	0.0283093	682	pca_XZ5Kg
variance	0.0278183	683	pca_XZ5Kg
variance	0.0277578	684	pca_XZ5Kg
variance	0.0274424	685	pca_XZ5Kg
variance	0.0273865	686	pca_XZ5Kg
variance	0.0270099	687	pca_XZ5Kg
variance	0.0268432	688	pca_XZ5Kg
variance	0.0265604	689	pca_XZ5Kg
variance	0.0261230	690	pca_XZ5Kg
variance	0.0260789	691	pca_XZ5Kg
variance	0.0256059	692	pca_XZ5Kg
variance	0.0254156	693	pca_XZ5Kg
variance	0.0251043	694	pca_XZ5Kg
variance	0.0248624	695	pca_XZ5Kg
variance	0.0244666	696	pca_XZ5Kg
variance	0.0242218	697	pca_XZ5Kg
variance	0.0239523	698	pca_XZ5Kg
variance	0.0237958	699	pca_XZ5Kg
variance	0.0235872	700	pca_XZ5Kg
variance	0.0233358	701	pca_XZ5Kg
variance	0.0229986	702	pca_XZ5Kg
variance	0.0222646	703	pca_XZ5Kg
variance	0.0216653	704	pca_XZ5Kg
variance	0.0214996	705	pca_XZ5Kg
variance	0.0210715	706	pca_XZ5Kg
variance	0.0202919	707	pca_XZ5Kg
variance	0.0189436	708	pca_XZ5Kg
variance	0.0183219	709	pca_XZ5Kg
variance	0.0138854	710	pca_XZ5Kg
variance	0.0071723	711	pca_XZ5Kg
variance	0.0065655	712	pca_XZ5Kg
variance	0.0000000	713	pca_XZ5Kg
variance	0.0000000	714	pca_XZ5Kg
variance	0.0000000	715	pca_XZ5Kg
variance	0.0000000	716	pca_XZ5Kg
variance	0.0000000	717	pca_XZ5Kg
variance	0.0000000	718	pca_XZ5Kg
variance	0.0000000	719	pca_XZ5Kg
variance	0.0000000	720	pca_XZ5Kg
variance	0.0000000	721	pca_XZ5Kg
variance	0.0000000	722	pca_XZ5Kg
variance	0.0000000	723	pca_XZ5Kg
variance	0.0000000	724	pca_XZ5Kg
variance	0.0000000	725	pca_XZ5Kg
variance	0.0000000	726	pca_XZ5Kg
variance	0.0000000	727	pca_XZ5Kg
variance	0.0000000	728	pca_XZ5Kg
variance	0.0000000	729	pca_XZ5Kg
variance	0.0000000	730	pca_XZ5Kg
variance	0.0000000	731	pca_XZ5Kg
variance	0.0000000	732	pca_XZ5Kg
variance	0.0000000	733	pca_XZ5Kg
variance	0.0000000	734	pca_XZ5Kg
variance	0.0000000	735	pca_XZ5Kg
variance	0.0000000	736	pca_XZ5Kg
variance	0.0000000	737	pca_XZ5Kg
variance	0.0000000	738	pca_XZ5Kg
variance	0.0000000	739	pca_XZ5Kg
variance	0.0000000	740	pca_XZ5Kg
variance	0.0000000	741	pca_XZ5Kg
variance	0.0000000	742	pca_XZ5Kg
variance	0.0000000	743	pca_XZ5Kg
variance	0.0000000	744	pca_XZ5Kg
variance	0.0000000	745	pca_XZ5Kg
variance	0.0000000	746	pca_XZ5Kg
variance	0.0000000	747	pca_XZ5Kg
variance	0.0000000	748	pca_XZ5Kg
variance	0.0000000	749	pca_XZ5Kg
variance	0.0000000	750	pca_XZ5Kg
variance	0.0000000	751	pca_XZ5Kg
variance	0.0000000	752	pca_XZ5Kg
variance	0.0000000	753	pca_XZ5Kg
variance	0.0000000	754	pca_XZ5Kg
variance	0.0000000	755	pca_XZ5Kg
variance	0.0000000	756	pca_XZ5Kg
variance	0.0000000	757	pca_XZ5Kg
variance	0.0000000	758	pca_XZ5Kg
variance	0.0000000	759	pca_XZ5Kg
variance	0.0000000	760	pca_XZ5Kg
variance	0.0000000	761	pca_XZ5Kg
variance	0.0000000	762	pca_XZ5Kg
variance	0.0000000	763	pca_XZ5Kg
variance	0.0000000	764	pca_XZ5Kg
variance	0.0000000	765	pca_XZ5Kg
variance	0.0000000	766	pca_XZ5Kg
variance	0.0000000	767	pca_XZ5Kg
variance	0.0000000	768	pca_XZ5Kg
variance	0.0000000	769	pca_XZ5Kg
variance	0.0000000	770	pca_XZ5Kg
variance	0.0000000	771	pca_XZ5Kg
variance	0.0000000	772	pca_XZ5Kg
variance	0.0000000	773	pca_XZ5Kg
variance	0.0000000	774	pca_XZ5Kg
variance	0.0000000	775	pca_XZ5Kg
variance	0.0000000	776	pca_XZ5Kg
variance	0.0000000	777	pca_XZ5Kg
variance	0.0000000	778	pca_XZ5Kg
variance	0.0000000	779	pca_XZ5Kg
variance	0.0000000	780	pca_XZ5Kg
variance	0.0000000	781	pca_XZ5Kg
variance	0.0000000	782	pca_XZ5Kg
variance	0.0000000	783	pca_XZ5Kg
variance	0.0000000	784	pca_XZ5Kg

prepped_pca |> 
  tidy(2, type = "variance") |> 
  filter(terms == "percent variance") |> 
  kable()

terms	value	component	id
percent variance	5.6467169	1	pca_XZ5Kg
percent variance	4.0782720	2	pca_XZ5Kg
percent variance	3.7393804	3	pca_XZ5Kg
percent variance	2.8851148	4	pca_XZ5Kg
percent variance	2.5211086	5	pca_XZ5Kg
percent variance	2.1942700	6	pca_XZ5Kg
percent variance	1.9233444	7	pca_XZ5Kg
percent variance	1.7457992	8	pca_XZ5Kg
percent variance	1.5350923	9	pca_XZ5Kg
percent variance	1.4017196	10	pca_XZ5Kg
percent variance	1.3417430	11	pca_XZ5Kg
percent variance	1.2037419	12	pca_XZ5Kg
percent variance	1.1145695	13	pca_XZ5Kg
percent variance	1.0899236	14	pca_XZ5Kg
percent variance	1.0286492	15	pca_XZ5Kg
percent variance	0.9944866	16	pca_XZ5Kg
percent variance	0.9363833	17	pca_XZ5Kg
percent variance	0.9210457	18	pca_XZ5Kg
percent variance	0.8934368	19	pca_XZ5Kg
percent variance	0.8699126	20	pca_XZ5Kg
percent variance	0.8273630	21	pca_XZ5Kg
percent variance	0.8034174	22	pca_XZ5Kg
percent variance	0.7648455	23	pca_XZ5Kg
percent variance	0.7417725	24	pca_XZ5Kg
percent variance	0.7152929	25	pca_XZ5Kg
percent variance	0.6918468	26	pca_XZ5Kg
percent variance	0.6841360	27	pca_XZ5Kg
percent variance	0.6566745	28	pca_XZ5Kg
percent variance	0.6316767	29	pca_XZ5Kg
percent variance	0.6129198	30	pca_XZ5Kg
percent variance	0.5962553	31	pca_XZ5Kg
percent variance	0.5877164	32	pca_XZ5Kg
percent variance	0.5715917	33	pca_XZ5Kg
percent variance	0.5623074	34	pca_XZ5Kg
percent variance	0.5546820	35	pca_XZ5Kg
percent variance	0.5384184	36	pca_XZ5Kg
percent variance	0.5311822	37	pca_XZ5Kg
percent variance	0.5196056	38	pca_XZ5Kg
percent variance	0.5082113	39	pca_XZ5Kg
percent variance	0.4800056	40	pca_XZ5Kg
percent variance	0.4764558	41	pca_XZ5Kg
percent variance	0.4691394	42	pca_XZ5Kg
percent variance	0.4543490	43	pca_XZ5Kg
percent variance	0.4513458	44	pca_XZ5Kg
percent variance	0.4469634	45	pca_XZ5Kg
percent variance	0.4433832	46	pca_XZ5Kg
percent variance	0.4382155	47	pca_XZ5Kg
percent variance	0.4303818	48	pca_XZ5Kg
percent variance	0.4268779	49	pca_XZ5Kg
percent variance	0.4236470	50	pca_XZ5Kg
percent variance	0.4046961	51	pca_XZ5Kg
percent variance	0.3994474	52	pca_XZ5Kg
percent variance	0.3974561	53	pca_XZ5Kg
percent variance	0.3938208	54	pca_XZ5Kg
percent variance	0.3858136	55	pca_XZ5Kg
percent variance	0.3790427	56	pca_XZ5Kg
percent variance	0.3754027	57	pca_XZ5Kg
percent variance	0.3707758	58	pca_XZ5Kg
percent variance	0.3649444	59	pca_XZ5Kg
percent variance	0.3593006	60	pca_XZ5Kg
percent variance	0.3523822	61	pca_XZ5Kg
percent variance	0.3477936	62	pca_XZ5Kg
percent variance	0.3444113	63	pca_XZ5Kg
percent variance	0.3398681	64	pca_XZ5Kg
percent variance	0.3359545	65	pca_XZ5Kg
percent variance	0.3348860	66	pca_XZ5Kg
percent variance	0.3318637	67	pca_XZ5Kg
percent variance	0.3230260	68	pca_XZ5Kg
percent variance	0.3162770	69	pca_XZ5Kg
percent variance	0.3132442	70	pca_XZ5Kg
percent variance	0.3107314	71	pca_XZ5Kg
percent variance	0.3072429	72	pca_XZ5Kg
percent variance	0.3049142	73	pca_XZ5Kg
percent variance	0.3027172	74	pca_XZ5Kg
percent variance	0.2994853	75	pca_XZ5Kg
percent variance	0.2977612	76	pca_XZ5Kg
percent variance	0.2950516	77	pca_XZ5Kg
percent variance	0.2904381	78	pca_XZ5Kg
percent variance	0.2868562	79	pca_XZ5Kg
percent variance	0.2856777	80	pca_XZ5Kg
percent variance	0.2833978	81	pca_XZ5Kg
percent variance	0.2826271	82	pca_XZ5Kg
percent variance	0.2795511	83	pca_XZ5Kg
percent variance	0.2793054	84	pca_XZ5Kg
percent variance	0.2785192	85	pca_XZ5Kg
percent variance	0.2774555	86	pca_XZ5Kg
percent variance	0.2759008	87	pca_XZ5Kg
percent variance	0.2742273	88	pca_XZ5Kg
percent variance	0.2714106	89	pca_XZ5Kg
percent variance	0.2692629	90	pca_XZ5Kg
percent variance	0.2664843	91	pca_XZ5Kg
percent variance	0.2635813	92	pca_XZ5Kg
percent variance	0.2629616	93	pca_XZ5Kg
percent variance	0.2610338	94	pca_XZ5Kg
percent variance	0.2588269	95	pca_XZ5Kg
percent variance	0.2561764	96	pca_XZ5Kg
percent variance	0.2538459	97	pca_XZ5Kg
percent variance	0.2504473	98	pca_XZ5Kg
percent variance	0.2478294	99	pca_XZ5Kg
percent variance	0.2450336	100	pca_XZ5Kg
percent variance	0.2423467	101	pca_XZ5Kg
percent variance	0.2420638	102	pca_XZ5Kg
percent variance	0.2388754	103	pca_XZ5Kg
percent variance	0.2374547	104	pca_XZ5Kg
percent variance	0.2356084	105	pca_XZ5Kg
percent variance	0.2330532	106	pca_XZ5Kg
percent variance	0.2279801	107	pca_XZ5Kg
percent variance	0.2261742	108	pca_XZ5Kg
percent variance	0.2228315	109	pca_XZ5Kg
percent variance	0.2224421	110	pca_XZ5Kg
percent variance	0.2181694	111	pca_XZ5Kg
percent variance	0.2172568	112	pca_XZ5Kg
percent variance	0.2142768	113	pca_XZ5Kg
percent variance	0.2119377	114	pca_XZ5Kg
percent variance	0.2109720	115	pca_XZ5Kg
percent variance	0.2073302	116	pca_XZ5Kg
percent variance	0.2047611	117	pca_XZ5Kg
percent variance	0.2043682	118	pca_XZ5Kg
percent variance	0.2024085	119	pca_XZ5Kg
percent variance	0.2004622	120	pca_XZ5Kg
percent variance	0.1988220	121	pca_XZ5Kg
percent variance	0.1952156	122	pca_XZ5Kg
percent variance	0.1937373	123	pca_XZ5Kg
percent variance	0.1921032	124	pca_XZ5Kg
percent variance	0.1917159	125	pca_XZ5Kg
percent variance	0.1898021	126	pca_XZ5Kg
percent variance	0.1870895	127	pca_XZ5Kg
percent variance	0.1865357	128	pca_XZ5Kg
percent variance	0.1813200	129	pca_XZ5Kg
percent variance	0.1800053	130	pca_XZ5Kg
percent variance	0.1791940	131	pca_XZ5Kg
percent variance	0.1789732	132	pca_XZ5Kg
percent variance	0.1769504	133	pca_XZ5Kg
percent variance	0.1761577	134	pca_XZ5Kg
percent variance	0.1747968	135	pca_XZ5Kg
percent variance	0.1729847	136	pca_XZ5Kg
percent variance	0.1720166	137	pca_XZ5Kg
percent variance	0.1687271	138	pca_XZ5Kg
percent variance	0.1685170	139	pca_XZ5Kg
percent variance	0.1668415	140	pca_XZ5Kg
percent variance	0.1647184	141	pca_XZ5Kg
percent variance	0.1645749	142	pca_XZ5Kg
percent variance	0.1642936	143	pca_XZ5Kg
percent variance	0.1614858	144	pca_XZ5Kg
percent variance	0.1604903	145	pca_XZ5Kg
percent variance	0.1589123	146	pca_XZ5Kg
percent variance	0.1574895	147	pca_XZ5Kg
percent variance	0.1559177	148	pca_XZ5Kg
percent variance	0.1556379	149	pca_XZ5Kg
percent variance	0.1546657	150	pca_XZ5Kg
percent variance	0.1540429	151	pca_XZ5Kg
percent variance	0.1516047	152	pca_XZ5Kg
percent variance	0.1502716	153	pca_XZ5Kg
percent variance	0.1487606	154	pca_XZ5Kg
percent variance	0.1475054	155	pca_XZ5Kg
percent variance	0.1468202	156	pca_XZ5Kg
percent variance	0.1458028	157	pca_XZ5Kg
percent variance	0.1455677	158	pca_XZ5Kg
percent variance	0.1447368	159	pca_XZ5Kg
percent variance	0.1428951	160	pca_XZ5Kg
percent variance	0.1410578	161	pca_XZ5Kg
percent variance	0.1399386	162	pca_XZ5Kg
percent variance	0.1397092	163	pca_XZ5Kg
percent variance	0.1395330	164	pca_XZ5Kg
percent variance	0.1393550	165	pca_XZ5Kg
percent variance	0.1392252	166	pca_XZ5Kg
percent variance	0.1387732	167	pca_XZ5Kg
percent variance	0.1383397	168	pca_XZ5Kg
percent variance	0.1378161	169	pca_XZ5Kg
percent variance	0.1368447	170	pca_XZ5Kg
percent variance	0.1361655	171	pca_XZ5Kg
percent variance	0.1358224	172	pca_XZ5Kg
percent variance	0.1337013	173	pca_XZ5Kg
percent variance	0.1329054	174	pca_XZ5Kg
percent variance	0.1310594	175	pca_XZ5Kg
percent variance	0.1302932	176	pca_XZ5Kg
percent variance	0.1293243	177	pca_XZ5Kg
percent variance	0.1282407	178	pca_XZ5Kg
percent variance	0.1274068	179	pca_XZ5Kg
percent variance	0.1268222	180	pca_XZ5Kg
percent variance	0.1253217	181	pca_XZ5Kg
percent variance	0.1240448	182	pca_XZ5Kg
percent variance	0.1229835	183	pca_XZ5Kg
percent variance	0.1216180	184	pca_XZ5Kg
percent variance	0.1215063	185	pca_XZ5Kg
percent variance	0.1200025	186	pca_XZ5Kg
percent variance	0.1190869	187	pca_XZ5Kg
percent variance	0.1188945	188	pca_XZ5Kg
percent variance	0.1176042	189	pca_XZ5Kg
percent variance	0.1167602	190	pca_XZ5Kg
percent variance	0.1162339	191	pca_XZ5Kg
percent variance	0.1147983	192	pca_XZ5Kg
percent variance	0.1137035	193	pca_XZ5Kg
percent variance	0.1127199	194	pca_XZ5Kg
percent variance	0.1120552	195	pca_XZ5Kg
percent variance	0.1094088	196	pca_XZ5Kg
percent variance	0.1085456	197	pca_XZ5Kg
percent variance	0.1070285	198	pca_XZ5Kg
percent variance	0.1064011	199	pca_XZ5Kg
percent variance	0.1054745	200	pca_XZ5Kg
percent variance	0.1046285	201	pca_XZ5Kg
percent variance	0.1036038	202	pca_XZ5Kg
percent variance	0.1032681	203	pca_XZ5Kg
percent variance	0.1020732	204	pca_XZ5Kg
percent variance	0.1008248	205	pca_XZ5Kg
percent variance	0.1001579	206	pca_XZ5Kg
percent variance	0.0997859	207	pca_XZ5Kg
percent variance	0.0991933	208	pca_XZ5Kg
percent variance	0.0977275	209	pca_XZ5Kg
percent variance	0.0968494	210	pca_XZ5Kg
percent variance	0.0958049	211	pca_XZ5Kg
percent variance	0.0956368	212	pca_XZ5Kg
percent variance	0.0947728	213	pca_XZ5Kg
percent variance	0.0946473	214	pca_XZ5Kg
percent variance	0.0943705	215	pca_XZ5Kg
percent variance	0.0926746	216	pca_XZ5Kg
percent variance	0.0917402	217	pca_XZ5Kg
percent variance	0.0908678	218	pca_XZ5Kg
percent variance	0.0897470	219	pca_XZ5Kg
percent variance	0.0891567	220	pca_XZ5Kg
percent variance	0.0887811	221	pca_XZ5Kg
percent variance	0.0878886	222	pca_XZ5Kg
percent variance	0.0869156	223	pca_XZ5Kg
percent variance	0.0862124	224	pca_XZ5Kg
percent variance	0.0860558	225	pca_XZ5Kg
percent variance	0.0845353	226	pca_XZ5Kg
percent variance	0.0840092	227	pca_XZ5Kg
percent variance	0.0835726	228	pca_XZ5Kg
percent variance	0.0824022	229	pca_XZ5Kg
percent variance	0.0820780	230	pca_XZ5Kg
percent variance	0.0812968	231	pca_XZ5Kg
percent variance	0.0810186	232	pca_XZ5Kg
percent variance	0.0791971	233	pca_XZ5Kg
percent variance	0.0783284	234	pca_XZ5Kg
percent variance	0.0778764	235	pca_XZ5Kg
percent variance	0.0771504	236	pca_XZ5Kg
percent variance	0.0766372	237	pca_XZ5Kg
percent variance	0.0750170	238	pca_XZ5Kg
percent variance	0.0743536	239	pca_XZ5Kg
percent variance	0.0738994	240	pca_XZ5Kg
percent variance	0.0732431	241	pca_XZ5Kg
percent variance	0.0727074	242	pca_XZ5Kg
percent variance	0.0725536	243	pca_XZ5Kg
percent variance	0.0716773	244	pca_XZ5Kg
percent variance	0.0711041	245	pca_XZ5Kg
percent variance	0.0702519	246	pca_XZ5Kg
percent variance	0.0694518	247	pca_XZ5Kg
percent variance	0.0694157	248	pca_XZ5Kg
percent variance	0.0679467	249	pca_XZ5Kg
percent variance	0.0678416	250	pca_XZ5Kg
percent variance	0.0676395	251	pca_XZ5Kg
percent variance	0.0671492	252	pca_XZ5Kg
percent variance	0.0663286	253	pca_XZ5Kg
percent variance	0.0655073	254	pca_XZ5Kg
percent variance	0.0651828	255	pca_XZ5Kg
percent variance	0.0644496	256	pca_XZ5Kg
percent variance	0.0641337	257	pca_XZ5Kg
percent variance	0.0636327	258	pca_XZ5Kg
percent variance	0.0632129	259	pca_XZ5Kg
percent variance	0.0627868	260	pca_XZ5Kg
percent variance	0.0624060	261	pca_XZ5Kg
percent variance	0.0620206	262	pca_XZ5Kg
percent variance	0.0609022	263	pca_XZ5Kg
percent variance	0.0605853	264	pca_XZ5Kg
percent variance	0.0598580	265	pca_XZ5Kg
percent variance	0.0591857	266	pca_XZ5Kg
percent variance	0.0583652	267	pca_XZ5Kg
percent variance	0.0580762	268	pca_XZ5Kg
percent variance	0.0575234	269	pca_XZ5Kg
percent variance	0.0572629	270	pca_XZ5Kg
percent variance	0.0569686	271	pca_XZ5Kg
percent variance	0.0563930	272	pca_XZ5Kg
percent variance	0.0558807	273	pca_XZ5Kg
percent variance	0.0556567	274	pca_XZ5Kg
percent variance	0.0551707	275	pca_XZ5Kg
percent variance	0.0550204	276	pca_XZ5Kg
percent variance	0.0544644	277	pca_XZ5Kg
percent variance	0.0540724	278	pca_XZ5Kg
percent variance	0.0538777	279	pca_XZ5Kg
percent variance	0.0532445	280	pca_XZ5Kg
percent variance	0.0529544	281	pca_XZ5Kg
percent variance	0.0526201	282	pca_XZ5Kg
percent variance	0.0522384	283	pca_XZ5Kg
percent variance	0.0518818	284	pca_XZ5Kg
percent variance	0.0514805	285	pca_XZ5Kg
percent variance	0.0508333	286	pca_XZ5Kg
percent variance	0.0507345	287	pca_XZ5Kg
percent variance	0.0503105	288	pca_XZ5Kg
percent variance	0.0500768	289	pca_XZ5Kg
percent variance	0.0497042	290	pca_XZ5Kg
percent variance	0.0492309	291	pca_XZ5Kg
percent variance	0.0482837	292	pca_XZ5Kg
percent variance	0.0479555	293	pca_XZ5Kg
percent variance	0.0476913	294	pca_XZ5Kg
percent variance	0.0476003	295	pca_XZ5Kg
percent variance	0.0471105	296	pca_XZ5Kg
percent variance	0.0466000	297	pca_XZ5Kg
percent variance	0.0458822	298	pca_XZ5Kg
percent variance	0.0456748	299	pca_XZ5Kg
percent variance	0.0449407	300	pca_XZ5Kg
percent variance	0.0446582	301	pca_XZ5Kg
percent variance	0.0442656	302	pca_XZ5Kg
percent variance	0.0438385	303	pca_XZ5Kg
percent variance	0.0438195	304	pca_XZ5Kg
percent variance	0.0432325	305	pca_XZ5Kg
percent variance	0.0430700	306	pca_XZ5Kg
percent variance	0.0424771	307	pca_XZ5Kg
percent variance	0.0421255	308	pca_XZ5Kg
percent variance	0.0419234	309	pca_XZ5Kg
percent variance	0.0415179	310	pca_XZ5Kg
percent variance	0.0413275	311	pca_XZ5Kg
percent variance	0.0410348	312	pca_XZ5Kg
percent variance	0.0408452	313	pca_XZ5Kg
percent variance	0.0403769	314	pca_XZ5Kg
percent variance	0.0401531	315	pca_XZ5Kg
percent variance	0.0398452	316	pca_XZ5Kg
percent variance	0.0395260	317	pca_XZ5Kg
percent variance	0.0392093	318	pca_XZ5Kg
percent variance	0.0390083	319	pca_XZ5Kg
percent variance	0.0386734	320	pca_XZ5Kg
percent variance	0.0386207	321	pca_XZ5Kg
percent variance	0.0383034	322	pca_XZ5Kg
percent variance	0.0379053	323	pca_XZ5Kg
percent variance	0.0376053	324	pca_XZ5Kg
percent variance	0.0375230	325	pca_XZ5Kg
percent variance	0.0370519	326	pca_XZ5Kg
percent variance	0.0366553	327	pca_XZ5Kg
percent variance	0.0363809	328	pca_XZ5Kg
percent variance	0.0359468	329	pca_XZ5Kg
percent variance	0.0358257	330	pca_XZ5Kg
percent variance	0.0355090	331	pca_XZ5Kg
percent variance	0.0353727	332	pca_XZ5Kg
percent variance	0.0352500	333	pca_XZ5Kg
percent variance	0.0348450	334	pca_XZ5Kg
percent variance	0.0345271	335	pca_XZ5Kg
percent variance	0.0341972	336	pca_XZ5Kg
percent variance	0.0338996	337	pca_XZ5Kg
percent variance	0.0336546	338	pca_XZ5Kg
percent variance	0.0334798	339	pca_XZ5Kg
percent variance	0.0332341	340	pca_XZ5Kg
percent variance	0.0330096	341	pca_XZ5Kg
percent variance	0.0328801	342	pca_XZ5Kg
percent variance	0.0324949	343	pca_XZ5Kg
percent variance	0.0323091	344	pca_XZ5Kg
percent variance	0.0321550	345	pca_XZ5Kg
percent variance	0.0319330	346	pca_XZ5Kg
percent variance	0.0314955	347	pca_XZ5Kg
percent variance	0.0311147	348	pca_XZ5Kg
percent variance	0.0309910	349	pca_XZ5Kg
percent variance	0.0308832	350	pca_XZ5Kg
percent variance	0.0306476	351	pca_XZ5Kg
percent variance	0.0304602	352	pca_XZ5Kg
percent variance	0.0302166	353	pca_XZ5Kg
percent variance	0.0300485	354	pca_XZ5Kg
percent variance	0.0297699	355	pca_XZ5Kg
percent variance	0.0296507	356	pca_XZ5Kg
percent variance	0.0294382	357	pca_XZ5Kg
percent variance	0.0290275	358	pca_XZ5Kg
percent variance	0.0289892	359	pca_XZ5Kg
percent variance	0.0287456	360	pca_XZ5Kg
percent variance	0.0285534	361	pca_XZ5Kg
percent variance	0.0283583	362	pca_XZ5Kg
percent variance	0.0282367	363	pca_XZ5Kg
percent variance	0.0280189	364	pca_XZ5Kg
percent variance	0.0277317	365	pca_XZ5Kg
percent variance	0.0276485	366	pca_XZ5Kg
percent variance	0.0272504	367	pca_XZ5Kg
percent variance	0.0270523	368	pca_XZ5Kg
percent variance	0.0270038	369	pca_XZ5Kg
percent variance	0.0266002	370	pca_XZ5Kg
percent variance	0.0265727	371	pca_XZ5Kg
percent variance	0.0262995	372	pca_XZ5Kg
percent variance	0.0260022	373	pca_XZ5Kg
percent variance	0.0259336	374	pca_XZ5Kg
percent variance	0.0255641	375	pca_XZ5Kg
percent variance	0.0253839	376	pca_XZ5Kg
percent variance	0.0253071	377	pca_XZ5Kg
percent variance	0.0251249	378	pca_XZ5Kg
percent variance	0.0249732	379	pca_XZ5Kg
percent variance	0.0248269	380	pca_XZ5Kg
percent variance	0.0244425	381	pca_XZ5Kg
percent variance	0.0244022	382	pca_XZ5Kg
percent variance	0.0243260	383	pca_XZ5Kg
percent variance	0.0242242	384	pca_XZ5Kg
percent variance	0.0237773	385	pca_XZ5Kg
percent variance	0.0237021	386	pca_XZ5Kg
percent variance	0.0236187	387	pca_XZ5Kg
percent variance	0.0234955	388	pca_XZ5Kg
percent variance	0.0233115	389	pca_XZ5Kg
percent variance	0.0230621	390	pca_XZ5Kg
percent variance	0.0229707	391	pca_XZ5Kg
percent variance	0.0229059	392	pca_XZ5Kg
percent variance	0.0227135	393	pca_XZ5Kg
percent variance	0.0225591	394	pca_XZ5Kg
percent variance	0.0224797	395	pca_XZ5Kg
percent variance	0.0224158	396	pca_XZ5Kg
percent variance	0.0221744	397	pca_XZ5Kg
percent variance	0.0221393	398	pca_XZ5Kg
percent variance	0.0220104	399	pca_XZ5Kg
percent variance	0.0218274	400	pca_XZ5Kg
percent variance	0.0217179	401	pca_XZ5Kg
percent variance	0.0216259	402	pca_XZ5Kg
percent variance	0.0214719	403	pca_XZ5Kg
percent variance	0.0213356	404	pca_XZ5Kg
percent variance	0.0211567	405	pca_XZ5Kg
percent variance	0.0210481	406	pca_XZ5Kg
percent variance	0.0208622	407	pca_XZ5Kg
percent variance	0.0207084	408	pca_XZ5Kg
percent variance	0.0206225	409	pca_XZ5Kg
percent variance	0.0203735	410	pca_XZ5Kg
percent variance	0.0202692	411	pca_XZ5Kg
percent variance	0.0199951	412	pca_XZ5Kg
percent variance	0.0199834	413	pca_XZ5Kg
percent variance	0.0198223	414	pca_XZ5Kg
percent variance	0.0198037	415	pca_XZ5Kg
percent variance	0.0196254	416	pca_XZ5Kg
percent variance	0.0195397	417	pca_XZ5Kg
percent variance	0.0190573	418	pca_XZ5Kg
percent variance	0.0189984	419	pca_XZ5Kg
percent variance	0.0189109	420	pca_XZ5Kg
percent variance	0.0188644	421	pca_XZ5Kg
percent variance	0.0187215	422	pca_XZ5Kg
percent variance	0.0185164	423	pca_XZ5Kg
percent variance	0.0184912	424	pca_XZ5Kg
percent variance	0.0183366	425	pca_XZ5Kg
percent variance	0.0180638	426	pca_XZ5Kg
percent variance	0.0179137	427	pca_XZ5Kg
percent variance	0.0179070	428	pca_XZ5Kg
percent variance	0.0177557	429	pca_XZ5Kg
percent variance	0.0176246	430	pca_XZ5Kg
percent variance	0.0176034	431	pca_XZ5Kg
percent variance	0.0175095	432	pca_XZ5Kg
percent variance	0.0173225	433	pca_XZ5Kg
percent variance	0.0173140	434	pca_XZ5Kg
percent variance	0.0171066	435	pca_XZ5Kg
percent variance	0.0170430	436	pca_XZ5Kg
percent variance	0.0170103	437	pca_XZ5Kg
percent variance	0.0168660	438	pca_XZ5Kg
percent variance	0.0168279	439	pca_XZ5Kg
percent variance	0.0166931	440	pca_XZ5Kg
percent variance	0.0165987	441	pca_XZ5Kg
percent variance	0.0165434	442	pca_XZ5Kg
percent variance	0.0164738	443	pca_XZ5Kg
percent variance	0.0163828	444	pca_XZ5Kg
percent variance	0.0163646	445	pca_XZ5Kg
percent variance	0.0162792	446	pca_XZ5Kg
percent variance	0.0161606	447	pca_XZ5Kg
percent variance	0.0160560	448	pca_XZ5Kg
percent variance	0.0159098	449	pca_XZ5Kg
percent variance	0.0157161	450	pca_XZ5Kg
percent variance	0.0156415	451	pca_XZ5Kg
percent variance	0.0155452	452	pca_XZ5Kg
percent variance	0.0153885	453	pca_XZ5Kg
percent variance	0.0153679	454	pca_XZ5Kg
percent variance	0.0152370	455	pca_XZ5Kg
percent variance	0.0151249	456	pca_XZ5Kg
percent variance	0.0149945	457	pca_XZ5Kg
percent variance	0.0149403	458	pca_XZ5Kg
percent variance	0.0149100	459	pca_XZ5Kg
percent variance	0.0147983	460	pca_XZ5Kg
percent variance	0.0147274	461	pca_XZ5Kg
percent variance	0.0147218	462	pca_XZ5Kg
percent variance	0.0146736	463	pca_XZ5Kg
percent variance	0.0144912	464	pca_XZ5Kg
percent variance	0.0143608	465	pca_XZ5Kg
percent variance	0.0143483	466	pca_XZ5Kg
percent variance	0.0143001	467	pca_XZ5Kg
percent variance	0.0141532	468	pca_XZ5Kg
percent variance	0.0141228	469	pca_XZ5Kg
percent variance	0.0140885	470	pca_XZ5Kg
percent variance	0.0139593	471	pca_XZ5Kg
percent variance	0.0139453	472	pca_XZ5Kg
percent variance	0.0138260	473	pca_XZ5Kg
percent variance	0.0137614	474	pca_XZ5Kg
percent variance	0.0136848	475	pca_XZ5Kg
percent variance	0.0136156	476	pca_XZ5Kg
percent variance	0.0134200	477	pca_XZ5Kg
percent variance	0.0133990	478	pca_XZ5Kg
percent variance	0.0133461	479	pca_XZ5Kg
percent variance	0.0131737	480	pca_XZ5Kg
percent variance	0.0131280	481	pca_XZ5Kg
percent variance	0.0131021	482	pca_XZ5Kg
percent variance	0.0130364	483	pca_XZ5Kg
percent variance	0.0129885	484	pca_XZ5Kg
percent variance	0.0129369	485	pca_XZ5Kg
percent variance	0.0128130	486	pca_XZ5Kg
percent variance	0.0126939	487	pca_XZ5Kg
percent variance	0.0126560	488	pca_XZ5Kg
percent variance	0.0125734	489	pca_XZ5Kg
percent variance	0.0125052	490	pca_XZ5Kg
percent variance	0.0124432	491	pca_XZ5Kg
percent variance	0.0123746	492	pca_XZ5Kg
percent variance	0.0122811	493	pca_XZ5Kg
percent variance	0.0122771	494	pca_XZ5Kg
percent variance	0.0121971	495	pca_XZ5Kg
percent variance	0.0121836	496	pca_XZ5Kg
percent variance	0.0120348	497	pca_XZ5Kg
percent variance	0.0120179	498	pca_XZ5Kg
percent variance	0.0119383	499	pca_XZ5Kg
percent variance	0.0118833	500	pca_XZ5Kg
percent variance	0.0118056	501	pca_XZ5Kg
percent variance	0.0117785	502	pca_XZ5Kg
percent variance	0.0116696	503	pca_XZ5Kg
percent variance	0.0115879	504	pca_XZ5Kg
percent variance	0.0115146	505	pca_XZ5Kg
percent variance	0.0114154	506	pca_XZ5Kg
percent variance	0.0113904	507	pca_XZ5Kg
percent variance	0.0113184	508	pca_XZ5Kg
percent variance	0.0112500	509	pca_XZ5Kg
percent variance	0.0112235	510	pca_XZ5Kg
percent variance	0.0111379	511	pca_XZ5Kg
percent variance	0.0110944	512	pca_XZ5Kg
percent variance	0.0109817	513	pca_XZ5Kg
percent variance	0.0109406	514	pca_XZ5Kg
percent variance	0.0108832	515	pca_XZ5Kg
percent variance	0.0108371	516	pca_XZ5Kg
percent variance	0.0107845	517	pca_XZ5Kg
percent variance	0.0107158	518	pca_XZ5Kg
percent variance	0.0107099	519	pca_XZ5Kg
percent variance	0.0106894	520	pca_XZ5Kg
percent variance	0.0106350	521	pca_XZ5Kg
percent variance	0.0105643	522	pca_XZ5Kg
percent variance	0.0105282	523	pca_XZ5Kg
percent variance	0.0104765	524	pca_XZ5Kg
percent variance	0.0104117	525	pca_XZ5Kg
percent variance	0.0103268	526	pca_XZ5Kg
percent variance	0.0102978	527	pca_XZ5Kg
percent variance	0.0102552	528	pca_XZ5Kg
percent variance	0.0102220	529	pca_XZ5Kg
percent variance	0.0101724	530	pca_XZ5Kg
percent variance	0.0100701	531	pca_XZ5Kg
percent variance	0.0100012	532	pca_XZ5Kg
percent variance	0.0099818	533	pca_XZ5Kg
percent variance	0.0099066	534	pca_XZ5Kg
percent variance	0.0098849	535	pca_XZ5Kg
percent variance	0.0098674	536	pca_XZ5Kg
percent variance	0.0097393	537	pca_XZ5Kg
percent variance	0.0097177	538	pca_XZ5Kg
percent variance	0.0096515	539	pca_XZ5Kg
percent variance	0.0096133	540	pca_XZ5Kg
percent variance	0.0095635	541	pca_XZ5Kg
percent variance	0.0095049	542	pca_XZ5Kg
percent variance	0.0094561	543	pca_XZ5Kg
percent variance	0.0094032	544	pca_XZ5Kg
percent variance	0.0093878	545	pca_XZ5Kg
percent variance	0.0092796	546	pca_XZ5Kg
percent variance	0.0092409	547	pca_XZ5Kg
percent variance	0.0092365	548	pca_XZ5Kg
percent variance	0.0092122	549	pca_XZ5Kg
percent variance	0.0090877	550	pca_XZ5Kg
percent variance	0.0090250	551	pca_XZ5Kg
percent variance	0.0089652	552	pca_XZ5Kg
percent variance	0.0088776	553	pca_XZ5Kg
percent variance	0.0088340	554	pca_XZ5Kg
percent variance	0.0087908	555	pca_XZ5Kg
percent variance	0.0087514	556	pca_XZ5Kg
percent variance	0.0087479	557	pca_XZ5Kg
percent variance	0.0086795	558	pca_XZ5Kg
percent variance	0.0086144	559	pca_XZ5Kg
percent variance	0.0085302	560	pca_XZ5Kg
percent variance	0.0084786	561	pca_XZ5Kg
percent variance	0.0084528	562	pca_XZ5Kg
percent variance	0.0084439	563	pca_XZ5Kg
percent variance	0.0084148	564	pca_XZ5Kg
percent variance	0.0083726	565	pca_XZ5Kg
percent variance	0.0083217	566	pca_XZ5Kg
percent variance	0.0082146	567	pca_XZ5Kg
percent variance	0.0082095	568	pca_XZ5Kg
percent variance	0.0081660	569	pca_XZ5Kg
percent variance	0.0080883	570	pca_XZ5Kg
percent variance	0.0080673	571	pca_XZ5Kg
percent variance	0.0080402	572	pca_XZ5Kg
percent variance	0.0079882	573	pca_XZ5Kg
percent variance	0.0079331	574	pca_XZ5Kg
percent variance	0.0078554	575	pca_XZ5Kg
percent variance	0.0078282	576	pca_XZ5Kg
percent variance	0.0078138	577	pca_XZ5Kg
percent variance	0.0077663	578	pca_XZ5Kg
percent variance	0.0077226	579	pca_XZ5Kg
percent variance	0.0076527	580	pca_XZ5Kg
percent variance	0.0075866	581	pca_XZ5Kg
percent variance	0.0075664	582	pca_XZ5Kg
percent variance	0.0075554	583	pca_XZ5Kg
percent variance	0.0074734	584	pca_XZ5Kg
percent variance	0.0074591	585	pca_XZ5Kg
percent variance	0.0074295	586	pca_XZ5Kg
percent variance	0.0073403	587	pca_XZ5Kg
percent variance	0.0073299	588	pca_XZ5Kg
percent variance	0.0072605	589	pca_XZ5Kg
percent variance	0.0072574	590	pca_XZ5Kg
percent variance	0.0071797	591	pca_XZ5Kg
percent variance	0.0071704	592	pca_XZ5Kg
percent variance	0.0071195	593	pca_XZ5Kg
percent variance	0.0070501	594	pca_XZ5Kg
percent variance	0.0069611	595	pca_XZ5Kg
percent variance	0.0069422	596	pca_XZ5Kg
percent variance	0.0069089	597	pca_XZ5Kg
percent variance	0.0068963	598	pca_XZ5Kg
percent variance	0.0068285	599	pca_XZ5Kg
percent variance	0.0067887	600	pca_XZ5Kg
percent variance	0.0067567	601	pca_XZ5Kg
percent variance	0.0067505	602	pca_XZ5Kg
percent variance	0.0067106	603	pca_XZ5Kg
percent variance	0.0066730	604	pca_XZ5Kg
percent variance	0.0066524	605	pca_XZ5Kg
percent variance	0.0065756	606	pca_XZ5Kg
percent variance	0.0065513	607	pca_XZ5Kg
percent variance	0.0065249	608	pca_XZ5Kg
percent variance	0.0064736	609	pca_XZ5Kg
percent variance	0.0064219	610	pca_XZ5Kg
percent variance	0.0063971	611	pca_XZ5Kg
percent variance	0.0063371	612	pca_XZ5Kg
percent variance	0.0062915	613	pca_XZ5Kg
percent variance	0.0062626	614	pca_XZ5Kg
percent variance	0.0062059	615	pca_XZ5Kg
percent variance	0.0061888	616	pca_XZ5Kg
percent variance	0.0061607	617	pca_XZ5Kg
percent variance	0.0061100	618	pca_XZ5Kg
percent variance	0.0060731	619	pca_XZ5Kg
percent variance	0.0060481	620	pca_XZ5Kg
percent variance	0.0060123	621	pca_XZ5Kg
percent variance	0.0059957	622	pca_XZ5Kg
percent variance	0.0059317	623	pca_XZ5Kg
percent variance	0.0059043	624	pca_XZ5Kg
percent variance	0.0058706	625	pca_XZ5Kg
percent variance	0.0058577	626	pca_XZ5Kg
percent variance	0.0058015	627	pca_XZ5Kg
percent variance	0.0057955	628	pca_XZ5Kg
percent variance	0.0057276	629	pca_XZ5Kg
percent variance	0.0057034	630	pca_XZ5Kg
percent variance	0.0056647	631	pca_XZ5Kg
percent variance	0.0056402	632	pca_XZ5Kg
percent variance	0.0056266	633	pca_XZ5Kg
percent variance	0.0055989	634	pca_XZ5Kg
percent variance	0.0055727	635	pca_XZ5Kg
percent variance	0.0055582	636	pca_XZ5Kg
percent variance	0.0055052	637	pca_XZ5Kg
percent variance	0.0054918	638	pca_XZ5Kg
percent variance	0.0054350	639	pca_XZ5Kg
percent variance	0.0053897	640	pca_XZ5Kg
percent variance	0.0053489	641	pca_XZ5Kg
percent variance	0.0053390	642	pca_XZ5Kg
percent variance	0.0052816	643	pca_XZ5Kg
percent variance	0.0052300	644	pca_XZ5Kg
percent variance	0.0052000	645	pca_XZ5Kg
percent variance	0.0051760	646	pca_XZ5Kg
percent variance	0.0051233	647	pca_XZ5Kg
percent variance	0.0050992	648	pca_XZ5Kg
percent variance	0.0050471	649	pca_XZ5Kg
percent variance	0.0050200	650	pca_XZ5Kg
percent variance	0.0050092	651	pca_XZ5Kg
percent variance	0.0049460	652	pca_XZ5Kg
percent variance	0.0049375	653	pca_XZ5Kg
percent variance	0.0048864	654	pca_XZ5Kg
percent variance	0.0048604	655	pca_XZ5Kg
percent variance	0.0048271	656	pca_XZ5Kg
percent variance	0.0048150	657	pca_XZ5Kg
percent variance	0.0047856	658	pca_XZ5Kg
percent variance	0.0047627	659	pca_XZ5Kg
percent variance	0.0047355	660	pca_XZ5Kg
percent variance	0.0046490	661	pca_XZ5Kg
percent variance	0.0046084	662	pca_XZ5Kg
percent variance	0.0046069	663	pca_XZ5Kg
percent variance	0.0045827	664	pca_XZ5Kg
percent variance	0.0045280	665	pca_XZ5Kg
percent variance	0.0045063	666	pca_XZ5Kg
percent variance	0.0044774	667	pca_XZ5Kg
percent variance	0.0044341	668	pca_XZ5Kg
percent variance	0.0044011	669	pca_XZ5Kg
percent variance	0.0043658	670	pca_XZ5Kg
percent variance	0.0043430	671	pca_XZ5Kg
percent variance	0.0043052	672	pca_XZ5Kg
percent variance	0.0042687	673	pca_XZ5Kg
percent variance	0.0041937	674	pca_XZ5Kg
percent variance	0.0041791	675	pca_XZ5Kg
percent variance	0.0041554	676	pca_XZ5Kg
percent variance	0.0041048	677	pca_XZ5Kg
percent variance	0.0040813	678	pca_XZ5Kg
percent variance	0.0040283	679	pca_XZ5Kg
percent variance	0.0039956	680	pca_XZ5Kg
percent variance	0.0039847	681	pca_XZ5Kg
percent variance	0.0039483	682	pca_XZ5Kg
percent variance	0.0038798	683	pca_XZ5Kg
percent variance	0.0038714	684	pca_XZ5Kg
percent variance	0.0038274	685	pca_XZ5Kg
percent variance	0.0038196	686	pca_XZ5Kg
percent variance	0.0037671	687	pca_XZ5Kg
percent variance	0.0037438	688	pca_XZ5Kg
percent variance	0.0037044	689	pca_XZ5Kg
percent variance	0.0036434	690	pca_XZ5Kg
percent variance	0.0036372	691	pca_XZ5Kg
percent variance	0.0035713	692	pca_XZ5Kg
percent variance	0.0035447	693	pca_XZ5Kg
percent variance	0.0035013	694	pca_XZ5Kg
percent variance	0.0034676	695	pca_XZ5Kg
percent variance	0.0034124	696	pca_XZ5Kg
percent variance	0.0033782	697	pca_XZ5Kg
percent variance	0.0033406	698	pca_XZ5Kg
percent variance	0.0033188	699	pca_XZ5Kg
percent variance	0.0032897	700	pca_XZ5Kg
percent variance	0.0032546	701	pca_XZ5Kg
percent variance	0.0032076	702	pca_XZ5Kg
percent variance	0.0031052	703	pca_XZ5Kg
percent variance	0.0030217	704	pca_XZ5Kg
percent variance	0.0029985	705	pca_XZ5Kg
percent variance	0.0029388	706	pca_XZ5Kg
percent variance	0.0028301	707	pca_XZ5Kg
percent variance	0.0026421	708	pca_XZ5Kg
percent variance	0.0025553	709	pca_XZ5Kg
percent variance	0.0019366	710	pca_XZ5Kg
percent variance	0.0010003	711	pca_XZ5Kg
percent variance	0.0009157	712	pca_XZ5Kg
percent variance	0.0000000	713	pca_XZ5Kg
percent variance	0.0000000	714	pca_XZ5Kg
percent variance	0.0000000	715	pca_XZ5Kg
percent variance	0.0000000	716	pca_XZ5Kg
percent variance	0.0000000	717	pca_XZ5Kg
percent variance	0.0000000	718	pca_XZ5Kg
percent variance	0.0000000	719	pca_XZ5Kg
percent variance	0.0000000	720	pca_XZ5Kg
percent variance	0.0000000	721	pca_XZ5Kg
percent variance	0.0000000	722	pca_XZ5Kg
percent variance	0.0000000	723	pca_XZ5Kg
percent variance	0.0000000	724	pca_XZ5Kg
percent variance	0.0000000	725	pca_XZ5Kg
percent variance	0.0000000	726	pca_XZ5Kg
percent variance	0.0000000	727	pca_XZ5Kg
percent variance	0.0000000	728	pca_XZ5Kg
percent variance	0.0000000	729	pca_XZ5Kg
percent variance	0.0000000	730	pca_XZ5Kg
percent variance	0.0000000	731	pca_XZ5Kg
percent variance	0.0000000	732	pca_XZ5Kg
percent variance	0.0000000	733	pca_XZ5Kg
percent variance	0.0000000	734	pca_XZ5Kg
percent variance	0.0000000	735	pca_XZ5Kg
percent variance	0.0000000	736	pca_XZ5Kg
percent variance	0.0000000	737	pca_XZ5Kg
percent variance	0.0000000	738	pca_XZ5Kg
percent variance	0.0000000	739	pca_XZ5Kg
percent variance	0.0000000	740	pca_XZ5Kg
percent variance	0.0000000	741	pca_XZ5Kg
percent variance	0.0000000	742	pca_XZ5Kg
percent variance	0.0000000	743	pca_XZ5Kg
percent variance	0.0000000	744	pca_XZ5Kg
percent variance	0.0000000	745	pca_XZ5Kg
percent variance	0.0000000	746	pca_XZ5Kg
percent variance	0.0000000	747	pca_XZ5Kg
percent variance	0.0000000	748	pca_XZ5Kg
percent variance	0.0000000	749	pca_XZ5Kg
percent variance	0.0000000	750	pca_XZ5Kg
percent variance	0.0000000	751	pca_XZ5Kg
percent variance	0.0000000	752	pca_XZ5Kg
percent variance	0.0000000	753	pca_XZ5Kg
percent variance	0.0000000	754	pca_XZ5Kg
percent variance	0.0000000	755	pca_XZ5Kg
percent variance	0.0000000	756	pca_XZ5Kg
percent variance	0.0000000	757	pca_XZ5Kg
percent variance	0.0000000	758	pca_XZ5Kg
percent variance	0.0000000	759	pca_XZ5Kg
percent variance	0.0000000	760	pca_XZ5Kg
percent variance	0.0000000	761	pca_XZ5Kg
percent variance	0.0000000	762	pca_XZ5Kg
percent variance	0.0000000	763	pca_XZ5Kg
percent variance	0.0000000	764	pca_XZ5Kg
percent variance	0.0000000	765	pca_XZ5Kg
percent variance	0.0000000	766	pca_XZ5Kg
percent variance	0.0000000	767	pca_XZ5Kg
percent variance	0.0000000	768	pca_XZ5Kg
percent variance	0.0000000	769	pca_XZ5Kg
percent variance	0.0000000	770	pca_XZ5Kg
percent variance	0.0000000	771	pca_XZ5Kg
percent variance	0.0000000	772	pca_XZ5Kg
percent variance	0.0000000	773	pca_XZ5Kg
percent variance	0.0000000	774	pca_XZ5Kg
percent variance	0.0000000	775	pca_XZ5Kg
percent variance	0.0000000	776	pca_XZ5Kg
percent variance	0.0000000	777	pca_XZ5Kg
percent variance	0.0000000	778	pca_XZ5Kg
percent variance	0.0000000	779	pca_XZ5Kg
percent variance	0.0000000	780	pca_XZ5Kg
percent variance	0.0000000	781	pca_XZ5Kg
percent variance	0.0000000	782	pca_XZ5Kg
percent variance	0.0000000	783	pca_XZ5Kg
percent variance	0.0000000	784	pca_XZ5Kg

Scree Plot

• Percent variance against number of components

prepped_pca |> 
  tidy(2, type = "variance") |> 
  filter(terms == "percent variance") |> 
  ggplot(aes(x = component, y = value)) +
  geom_line() +
  labs(
    x = "PCAs",
    y = "% of variance",
    title = "Scree plot"
  )

Scree Plot

• Percent variance against number of components

prepped_pca |> 
  tidy(2, type = "variance") |> 
  filter(terms == "percent variance", component < 40) |>
  ggplot(aes(x = component, y = value)) +
  geom_line() +
  labs(
    x = "PCAs",
    y = "% of variance",
    title = "Scree plot"
  )

Heuristic

• Set number of components to be where you see a “big drop”
• Choose number of components where plot starts to level off

New Scores

mnist_pca |> head() |> kable()

PC01	PC02	PC03	PC04	PC05	PC06	PC07	PC08	PC09	PC10	PC11	PC12	PC13	PC14	PC15	PC16	PC17	PC18	PC19	PC20
0.9221511	-4.814750	0.0675593	-8.0512622	0.9853391	-0.9516077	0.3361365	-1.3934615	-1.0523056	2.3241877	-1.520368	3.1626599	-1.1837683	9.2008053	-4.4196858	1.6432947	-7.5116268	5.212185	-4.1801314	3.8211714
-8.7089044	-7.754338	-3.4478817	-1.6683075	-0.8347884	5.1446213	-0.2722768	-3.1354301	-0.1983909	-1.1961859	-3.251257	-1.1838362	1.6347196	-4.4051467	-2.9243789	-1.3810971	-0.3620996	-1.307530	-3.4556711	0.3211000
-2.3283699	9.431260	-6.1840625	1.7250517	-4.0924219	-2.2913712	18.6913830	-3.9924399	2.1701000	-0.1511394	-7.383439	2.0300298	-0.5865363	0.1094830	11.3288811	10.3145412	4.6287307	-3.465988	-5.3164712	3.5571589
6.5821185	-3.746287	3.6908205	-0.4610368	-5.6272777	-3.4615154	1.5614022	4.6004233	-0.6248143	-2.6171627	-2.046650	3.9413188	-0.7617708	-3.7772303	-0.9635426	2.2071743	0.6448561	-1.710684	-0.0514925	-0.3227111
5.1832080	3.133271	-6.2778951	1.4596418	1.6088289	0.6125598	-0.5800603	3.2059835	0.0129479	-0.6990456	4.812231	0.1232363	-0.7611926	-1.9712651	-1.4728054	-0.8389647	0.9075877	-5.817357	-0.9964415	1.8889851
-2.1983838	-3.068341	-0.2312553	2.7525776	1.2168772	-5.7912779	-0.6937827	-0.3355727	-0.7865303	-1.9459007	2.753515	-1.6144086	1.2155606	0.2366206	-4.4797497	-0.4558847	-2.7655543	-2.910686	-1.2932355	0.7981577

Visualizing Scores

library(GGally)

mnist_pca |> ggpairs(columns = 1: 5, aes(color = as_factor(mnist$train$labels)),
                     lower = list(continuous = wrap("points", alpha = 0.1,    size=0.1)))

Visualizing PCs

prepped_pca |> tidy(2) |> 
  filter(component == "PC1") |> 
  ggplot(aes(x = terms, y = value)) +
  geom_col() +
  theme(axis.text.x=element_blank(),
        axis.ticks.x=element_blank())

Visualizing PC1

pc_matrix <- prepped_pca |> tidy(2) |> 
  filter(component == "PC1") |> 
  pull(value) |> 
  matrix(nrow = 28, byrow=FALSE)

image(x = 1:28, y = 1:28,
      z = pc_matrix[,28:1],
      col=gray((0:255)/255))

Visualizing PC2

pc_matrix <- prepped_pca |> tidy(2) |> 
  filter(component == "PC2") |> 
  pull(value) |> 
  matrix(nrow = 28, byrow=FALSE)

image(x = 1:28, y = 1:28,
      z = pc_matrix[,28:1],
      col=gray((0:255)/255))

Visualizing PCs

pc_matrix <- prepped_pca |> tidy(2) |> 
  filter(component == "PC3") |> 
  pull(value) |> 
  matrix(nrow = 28, byrow=FALSE)

image(x = 1:28, y = 1:28,
      z = pc_matrix[,28:1],
      col=gray((0:255)/255))

Twos and Sevens

mnist_train_27 <- mnist_train[mnist$train$labels %in% c(2, 7),]
prepped_pca27 <- pca_recipe |> prep(mnist_train_27)
mnist27_pca <- prepped_pca27 |> bake(new_data = mnist_train_27)

Visualizing PCs

pc_matrix <- prepped_pca27 |> tidy(2) |> 
  filter(component == "PC1") |> 
  pull(value) |> 
  matrix(nrow = 28, byrow=FALSE)

image(x = 1:28, y = 1:28,
      z = pc_matrix[,28:1],
      col=gray((0:255)/255))

Visualizing PCs

pc_matrix <- prepped_pca27 |> tidy(2) |> 
  filter(component == "PC2") |> 
  pull(value) |> 
  matrix(nrow = 28, byrow=FALSE)

image(x = 1:28, y = 1:28,
      z = pc_matrix[,28:1],
      col=gray((0:255)/255))

Visualizing PCs

pc_matrix <- prepped_pca27 |> tidy(2) |> 
  filter(component == "PC3") |> 
  pull(value) |> 
  matrix(nrow = 28, byrow=FALSE)

image(x = 1:28, y = 1:28,
      z = pc_matrix[,28:1],
      col=gray((0:255)/255))