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<!DOCTYPE html>
<html lang="" xml:lang="">
<head>
<title>Targeted Metabolomics Data Analysis: Unlocking Insights with Machine Learning, AI and Statistics</title>
<meta charset="utf-8" />
<meta name="author" content="June 11-14, 2024" />
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<body>
<textarea id="source">
class: center, middle, inverse, title-slide
.title[
# Targeted Metabolomics Data Analysis: Unlocking Insights with Machine Learning, AI and Statistics
]
.subtitle[
## Day 3 – Lecture 2
]
.author[
### June 11-14, 2024
]
.institute[
### Barcelona, Spain
]
---
<style type="text/css">
.remark-slide-content {
font-size: 22px;
padding: 1em 4em 1em 4em;
}
.left-code {
color: #777;
width: 38%;
height: 92%;
float: left;
}
.right-plot {
width: 60%;
float: right;
padding-left: 1%;
}
</style>
# Outline
.columnwide[
### 1) Introduction
### 2) Class Discovery (clustering)
### 3) Dimension Reduction (PCA)
### 4) Predictive modeling
### 5) Other Approaches
### 6) Performance Assessment
### ) References and Resources
]
---
class: inverse, middle, center
name: Introduction
# Introduction and motivation
---
# Omics data are high dimensional
- So far, our analyses are dealing with a single variable (i.e. univariate analysis)
- T-tests: one variable, two groups
- ANOVA: one variable, > 2 groups
- Even when we analyze many variables, we proceed *one at a time*
- Determine how to analyze one single variable separatedly
- Apply the procedure to all variables,
- Perform multiple test adjustment
- This is not wrong, but, at least it can be criticized because interactions (correlations) are missed.
- Even if we attempt to account for interactions, visualization are limited to three dimensions.
- So the question arises of __*How can we analyze & visualize high-dimensional data in a global ("holistic") way, that is considering all data together?*__
---
# The analysis of high dimensional data
- The classical approach to analyzing high dimensional data is Multivariate Statistics which orginates in the early 20th century.
- Pearson 1901, Hottelling 1933: Principal Components Analysis
- TW Anderson (1958): First Multivariate Statistics (as we know today) book
- Although classical MV Statistics considered Exploratory Analysis it was strongly rooted in Statistical Modelling and Distribution theory.
- By the end of the 20th century, as computing power became available and data did not stop growing many aspects of multivariate statistics were re-casted from the side of computer science
- Their approach was not so much in modelling multivariate distributions but on the algorithms.
- The underlying idea of this *Machine Learning* approach is that instead of focussing on a model, we focus on howw to build an algorithm to solve a certain problem given a set of of examples.
- This lead to the idea of *Learning from Data*
---
# Machine learning and Statistics
<img src="images/2-MultivariateStat-and-ML_insertimage_1.png" width="100%" style="display: block; margin: auto;" />
---
# More actors in the field
<img src="images/2-MultivariateStat-and-ML_insertimage_2.png" width="100%" style="display: block; margin: auto;" />
---
# In any case, what do we need it for?
<img src="images/2-MultivariateStat-and-ML_insertimage_4.png" width="100%" style="display: block; margin: auto;" />
---
# Types of (multivariate) problems
-**Class discovery (Unsupervised learning)**
- Goal: explore the data to find some intrinsic structures in them
- Disregard whether they are related to the class labels or not)
- These patterns can be used to understand the key information within the data itself
- Methods: Clustering / Principal Components
- **Class prediction / Predictive modelling**
- Goal: discover patterns in the data that relate data attributes with related to a target (categorical or numerical) attribute.
- These patterns can be utilized to predict the values of the target attribute in future data instances.
- Methods: Regresion(s), Classification
---
class: inverse, middle, center
name: Unsupervised
# Unsupervised methods (1) : Clustering
---
# Discovering Groups in Data
.pull-left[
- Clustering techniques allow for the identification of patterns and structures in data.
- They work by partition the data space in regions where the data are more similar within each region than among regions.
- Many methods and approaches. Here we only consider:
- Hierarchichal clustering
- K-Means, a partiive algorith
]
.pull-right[
<img src="images/2-MultivariateStat-and-ML_insertimage_6.png" width="100%" style="display: block; margin: auto;" /><img src="images/2-MultivariateStat-and-ML_insertimage_7.png" width="100%" style="display: block; margin: auto;" />
]
---
# The components of clustering
- There are many clustering methods and algorithms but they all have a common goal: *Try to put togeher objects that are logically similar in characteristics*
- Cluster analysis is based on two main ingredients:
- A *Distance measure*: to quantify the (dis)similarity of objects.
- Notice we need to be able to measure the distance between individuals, but also between clusters.
- *Cluster algorithm*: A procedure to group objects. Aim: small within-cluster distances, large between-cluster distances.
---
# What distance to use?
.pull-left[
<img src="images/2-MultivariateStat-and-ML_insertimage_8.png" width="100%" style="display: block; margin: auto;" />
<img src="images/2-MultivariateStat-and-ML_insertimage_9.png" width="60%" style="display: block; margin: auto;" />
]
.pull-right[
- Base the choice of distance in:
- the application area
- your understanding of what sort of similarities you wish to detect?
- Correlation distance dc measures trends or relative differences.
- Euclidean and Manhattan distance both measure absolute differences between vectors.
- Manhattan distance is more robust against outliers.
- After standardization, Euclidean and correlation distance are equivalent
]
---
# Hierarchichal clustering
.pull-left[
- Hierarchical Clustring Analysis (HCA) seeks to build a hierarchy of clusters by iteratively grouping/splitting groups by their similarity.
- The result of HCA is a tree-based representation of the objects, which is also known as *dendrogram.*
- Observations can be subdivided into groups by *cutting the dendrogram at a desired similarity level*.
- HCA avoid specifying the number of clusters by providing a partition for each k obtained from cutting the tree at some level.
]
.pull-right[
]
---
# Strategies for Hierarchical clustering
.pull-left[
They generally fall into two categories:
- *Agglomerative*
- This is a "bottom-up" approach:
- Each observation starts in its own cluster, and
- Pairs of clusters are merged as one moves up the hierarchy.
- *Divisive*:
- This is a "top-down" approach:
- All observations start in one cluster, and
- Splits are performed recursively as one moves down the hierarchy.
]
.pull-right[
<img src="images/2-MultivariateStat-and-ML_insertimage_10.png" width="90%" style="display: block; margin: auto;" />
<img src="images/2-MultivariateStat-and-ML_insertimage_11.png" width="90%" style="display: block; margin: auto;" />
Source: [Hierarchichal clustering in R](https://www.datanovia.com/en/courses/hierarchical-clustering-in-r-the-essentials/)
]
---
# Partitioning Methods
- These algorithms partition the data into a **pre-specified** number, `\(k\)`, of mutually exclusive and exhaustive groups.
- They work by iteratively reallocating the observations to clusters
until some criterion is met,
- For example until "within cluster sums of squares" is minimized.
- Some Partitioning methods are:
- k-means,
- Partitioning Around Medoids, PAM.
- Self-organizing maps (SOM)
- Fuzzy clustering which needs to have un underlying stochastic model, e.g. Gaussian mixtures.
---
# The K-means algorithm
.pull-left[
1. Randomly chooses `\(k\)` observations from the dataset and uses these as the initial means.
2. For the next object calculate the similarity to each existing centroid.
3. If the similarity is greater than a threshold add the object to the existing cluster and re-compute the centroid, else use the object to start new cluster
4. Return to step 2 and repeat until done
]
.pull-right[
<img src="images/kMeansIllustration.png" width="90%" style="display: block; margin: auto;" />
]
---
# Other clustering related issues
- Selecting the number of clusters
- Often an important issue. Needs to devote some time
- There exist criteria such as "maximize average silhouette"
- Determining the validity of clusters
- All cluster algorithms will yield clusters
- Need some way to determine if *they are real*
- Typical approximation: Use resampling to build multiple clusterings and check consistency.
---
class: inverse, middle, center
name: Factorizations
# Dimension Reduction
---
# Motivation for PCA
- High dimensional data consist of dataset with
- many observations (samples, individuals ...)
- many measurements (variables, features) performed on each sample.
- Although a priori it seems they must be informative this is not immediate because
- The data may have structures that we don't see at first sight
- The data may contain noise
- Many variables may be correlated: they do not contribute as much as one might expect.
<!-- - Principal Component Analysis is a technique entitled to reveal hidden (latent) data structures by transforming the data into a new set of features (the "components") which -->
<!-- - Are independent from every each other -->
<!-- - It may suffice to take a few of these to have much information. Thaht's why we talo of dimension reduction. -->
---
# Principal Component Analysis
.pull-left[
- Given a `\(KxN\)` data matrix containing
- `\(K\)` variables (probably correlated measurements) in
- `\(N\)` samples (objects/individuals...)
- Assuming `\(K < N\)`, PCA transforms the variables into `\(K\)` new components that:
- Reflect the different sources of variability in the data, but
- Are not correlated, i.e., *each component represents a different source of variability,*
]
.pull-right[
<img src="images/AMV4Omics-Overview-EN_insertimage_1.png" width="60%" style="display: block; margin: auto;" />
]
<!-- [Source](https://towardsdatascience.com/tidying-up-with-pca-an-introduction-to-principal-components-analysis-f876599af383) -->
<!-- ] -->
---
# Designed to Improve
.pull-left[
- These new components are constructed in such a way that:
- They are orthogonal (perpendicular) to each other
- *They have decreasing explanatory power*: each component explains more (variance) than the next one.
- I most cases, a few components (2 or 3) suffice to summarize most of the information contained in the original variables.
- That is, one can use PCA values to obtain a decent representation in *reduced dimension*.
]
.pull-right[
This picture depicts how, after performing PCA and retining the two first components, almost no information is lost.
]
---
# PCA highlights latent information
.pull-left[
- It is generally assumed that PCA can be the basis to
- Highlight dominant latent structures in the data,
- As well as revealing natural groups, like genotypes or metabotypes,
- And alos non natural unexpected groupings, due to batch effect.
- The image on the right shows the aspect of a PCA plot of a dataset before and after performing a batch adjustment.
]
.pull-right[
<img src="images/AMV4Omics-Xaringan_insertimage_21.png" width="60%" style="display: block; margin: auto;" />
]
---
# How does PCA work?
- Let's assume a KxN data matrix of two correlated variables.
- Because the data is correlated, it is difficult to separate each source of variability
- To obtain a new system of coordinates the following optimization problem is considered:
- Searching, sequentially, for a transformation of the original matrix
- in which the resulting vectors are orthogonal two to two, that is, The new variables (new coordinate axes) are independent of each other.
- Notice that, what we are asking is that our variance-covariance matrix becomes diagonal, since
the covariance of independent variables is zero.
---
# Obtaining the PCs
- Under general conditions, the way to obtain a new coordinate system where the covariance matrix is diagonal can be obtained by *diagonalizing the variance-covariance matrix of the centered data*
- Diagonalization is a calculation performed on a matrix that results in:
- A vector of eigenvalues (VAPs) proportional to the variance of each variable in the new coordinates
- A matrix of eigenvectors (VEPs) that are, precisely, the scores or scores of the observations in these new coordinates.
- This operation yields a new system of coordinates where
- the covariances of the new variables become 0, that is, independent variables are obtained.
- the eigenvalues (the diagonal of the new matrix) are ordered from highest to smallest, which corresponds to the idea that each one has a greater variability than the next ones.
---
# PCA in a nutshell
<img src="images/2-MultivariateStat-and-ML_insertimage_13.png" width="70%" style="display: block; margin: auto;" />
---
# Interpreting Principal Components
- The first main component is
- A linear combination (LC) of the original variables
- That goes in the direction of greater variability in the data
- Explains the *maximum amount of variation* in the data
- The 2nd and successive PCs are also a LC of all the original variables, although with other coefficients calculated in such a way that:
- It aligns with the next direction of greatest variability, orthogonally to the previous PCs.
- Explain the maximum amount of *remaining variation*
- Sometimes interpretation of the new components may be clear, corresponding to real biological dimensions or, sometimes, not at all.
- To facilitate this, the correlation between components and the original variables is computed.
---
# Data visualization in the PCA space
- Scores are the new coordinates in the orthogonal system defined by the PCs
- They have been built so that
- the first PC explains the highest quantity of variability,
- the second PC explains explains the highest quantity of remaining variability, and so on ...
- This means that it is not necessary to use all PCs to visualize the data in this new coordinate system, so a visualization can be made in a lower dimension.]
- Often, takin only the first 2 or 3 first PCs is enough,
- It should always be verified that this is the case
- The "scree plot" graph together with a criterion of "change of slope" or elbow, are usually useful.
---
# Examples
- [PCA example in MetaboAnalystR](https://www.metaboanalyst.ca/resources/vignettes/Statistical_Analysis_Module.html)
- [FactoMineR Decathlon Tutorial](http://factominer.free.fr/factomethods/principal-components-analysis.html)
- [R tutorial: Principal Component Analysis with Metabolomics Data](https://juanpacarreon.com/posts/pca-matabolomics/)
---
class: inverse, middle, center
name: PredictiveModeling
# Predictive Modeling: regression and Relatives
---
# Why predictive modeling
- We are interested in `\(Y\)`, an informative quantity but difficult (or expensive, or slow) to measure,
- If `\(Y\)` is related to others, say `\(X_1, X_2, ...X_n\)` that may be easier (faster, cheaper) to obtain, we may attempt
1. To model the relation
$$
Y= f(X_1, ..., X_n) + \epsilon
$$
2. Fit the model to obtain an approximation, `\(\hat f\)`, to `\(f\)` or its parameters
3. Use that approximation to predict the values of `\(Y\)` for a set given certain values `\(x_1, ..., x_n\)`.
$$
\hat y = \hat f(x_1, ..., x_n)
$$
- The most common approach to model such relations is using *Regression models*
---
# The (multiple) linear regression model
- The relation between the response and the independent variable is assumed to be linear.
- Restrictive and very simple, but powerful when assumptions hold and the model is valid.
---
# Logistic regression
- If the response variable is dichotomous (yes/no) the MLR is not adequate.
- Logistic regression models the probabilities of a sample being a member of either of two groups for a set of predictors.
<img src="images/2-MultivariateStat-and-ML_insertimage_15.png" width="60%" style="display: block; margin: auto;" />
- Notice that it is also a linear regression model where the response variable is the log odds.
---
# High dimensional data issues
Working with high dimensional data requires to account for a series of issues that may not be apparent in lower dimensions
- **Curse of Dimensionality:** High-dimensional spaces can dilute the signal, making it hard to distinguish between true signal and noise.
- **Computational Complexity:** Processing and analyzing high-dimensional data requires substantial computational resources.
- **Scalability:** Classical methods struggle to scale efficiently with increasing dimensionality.
- **Sparse Data:** High-dimensional data can lead to sparsity, making it challenging to detect meaningful patterns.
---
# Limitations of classical linear models
The high dimensionality of omics data usually determines that these models are not adequate due to a variety of reasons
- **Overfitting:** High-dimensional data can lead to overfitting, where the model captures noise instead of the underlying pattern.
- **Multicollinearity:** Metabolomics data often have highly correlated variables, causing instability in coefficient estimates.
- **Feature Selection:** Requires manual or algorithmic feature selection, which can be computationally intensive and prone to bias.
- **Interpretability:** Coefficients become harder to interpret with a large number of features.
- **Class Imbalance:** Performance can be significantly affected if there is an imbalance in the class distribution.
---
# Alternatives for predictive models
- The fields of Statistics and Machine Learning have developed a long collection of alternatives.
- Each type of solution may be appropriate for one or more of the problems highlighted above.
- Regularization Techniques
- Dimension Reduction Techniques
- Non linear methods
- Ensemble methods
- Machine learning methods
- Sparse models
- Neural networks
---
# Regularization Techniques
.pull-left[
- **Lasso Regression (L1):** Adds a penalty for the absolute value of coefficients to induce sparsity.
- **Ridge Regression (L2):** Adds a penalty for the square of coefficients to handle multicollinearity.
- **Elastic Net:** Combines L1 and L2 penalties to balance sparsity and multicollinearity handling.
]
.pull-right[
<img src="images/2-MultivariateStat-and-ML_insertimage_16.png" width="90%" style="display: block; margin: auto;" />
]
---
# Dimension Reduction Techniques
.pull-left[
- **Principal Component Analysis (PCA):** Reduces dimensionality by projecting data onto principal components.
- **Principal Component Regression (PCR):** Reduces dimensionality projecting independent variables (predictors) onto principal components and fits a regression model to PCs.
- **Partial Least Squares (PLS):** Projects predictors and response variables onto a new space to maximize covariance.
]
.pull-right[
<img src="images/2-MultivariateStat-and-ML_insertimage_17.png" width="90%" style="display: block; margin: auto;" />
]
---
# Nonlinear Methods
.pull-left[
- **Kernel Methods:** Extend linear methods to nonlinear relationships using kernel functions.
- **Decision Trees:** Nonlinear models that split data based on feature values, leading to simple and interpretable predictive models.
]
.pull-right[
<img src="images/2-MultivariateStat-and-ML_insertimage_18.png" width="90%" style="display: block; margin: auto;" />
]
---
# Ensemble methods
.pull-left[
- **Bagging:** Ensemble method that handles high-dimensional data by averaging multiple decision trees built on bootstrap resamples of the original sample.
- **Random Forest:** Ensemble method that handles high-dimensional data by averaging multiple decision trees built on resamples, but also using random sets of features at each node.
- **Gradient Boosting Machines (GBM):** Builds an ensemble of weak learners to improve predictive performance.
]
.pull-right[
<img src="images/2-MultivariateStat-and-ML_insertimage_20.png" width="90%" style="display: block; margin: auto;" />
]
---
# Machine Learning Methods (SVMs)
.pull-left[
- **Support Vector Machine (SVM):**
- Find the hyperplane that best separates data points of different classes by maximizing the margin between them.
- They are effective in high-dimensional spaces and can handle nonlinear data using kernel functions. SVMs are robust to overfitting, especially in high-dimensional datasets.
]
.pull-right[
<img src="images/2-MultivariateStat-and-ML_insertimage_19.png" width="90%" style="display: block; margin: auto;" />
]
---
# Neural Networks
.pull-left[
- **Neural Networks** Deals with non-linear realtions in a black-box automatic approach.
- **Deep Learning:** Handles high-dimensional data with multiple layers of abstraction, especially useful with large datasets.
- **Autoencoders:** Unsupervised neural networks that learn efficient codings of input data for dimensionality reduction.
]
.pull-right[
<img src="images/2-MultivariateStat-and-ML_insertimage_21.png" width="60%" style="display: block; margin: auto;" />
]
---
# Other approaches
## Sparse models
- **Sparse Partial Least Squares (sPLS):** Combines PLS with sparsity to handle high-dimensional data.
- **Sparse Logistic Regression:** Applies sparsity constraints to logistic regression for feature selection.
## Bayesian Methods
- **Bayesian Regression:** Incorporates prior information and deals with uncertainty in high-dimensional settings.
- **Bayesian Networks:** Models complex relationships between variables and handles high-dimensional data efficiently.
---
class: inverse, middle, center
name: PLS
# PLS and PLS-LDA
---
# Partial Least Squares
- From all the presented alternatives, probably the best known, most used in chemometrics and metabolomics is PLS and PLS-LDA
- PLS appears as a natural alternative to MLR and PCR
- **Multiple Linear Regression (MLR)**: MLR directly models the relationship between predictors and response variables but can suffer from multicollinearity and overfitting in high-dimensional data.
- **Principal Component Regression (PCR)**: PCR first reduces the dimensionality of predictors using PCA and then applies MLR. However, PCA does not consider the response variable in the dimension reduction step.
- **PLS vs. PCR**: PLS, unlike PCR, takes the response variable into account when determining the components, leading to better predictive performance when predictors are highly correlated.
---
# Interlude: Linear Discriminant Analysis
.pull-left[
- LDA is a classification technique, developed by R.A. Fisher used to find a linear combination of features that best separates two or more classes.
- It works by maximizing the ratio of between-class variance to within-class variance, ensuring that the classes are as distinct as possible.
]
.pull-right[
]
---
# Key Points of LDA
- LDA projects data onto a lower-dimensional space where the classes are well separated.
- It assumes that the features follow a Gaussian distribution and that each class has the same covariance matrix.
- LDA is *particularly usefu*l when the class separability is linear and the dimensionality of the data needs to be reduced for efficient computation and improved classification performance.
---
# Combining PLS and LDA
- PLS-LDA is a classification technique that combines PLS for dimensionality reduction with LDA for classification.
- PLS-LDA uses PLS to reduce the dimensionality of the predictor variables while considering the response variable (class labels).
- After reducing the dimensionality, LDA is applied to classify the samples based on the new PLS components.
- PLS-LDA is effective for high-dimensional classification tasks, leveraging the strengths of both PLS in handling multicollinearity and LDA in classification.
---
class: inverse, middle, center
name: ClassPredictionProcess
# Performance assessment in class prediction
---
# Performance assessment
- The process of building and validating classifiers involves more than simply fitting a predictive model and performing the classification.
- Before using a classifier for prediction or prognostic one needs some performance measures
- For instance the accuracy of a predictor is usually measured by the *missclassification rate*: The % of individuals belonging to a class which are erroneously assigned to another class by the predictor.
- This is however more complicated than simply computing error rates because *we are not interested in the ability of the predictor for classifying current samples*
- One needs to estimate *future performance* based on what is available.
---
# Error rate estimation
- Using the same dataset on which we have built the predictor to estimate the missclassification rate may lead to erroneously low values due to overfitting.
- This erroneous estimator is known as the *resubstitution estimator*.
- Ideally, we should use a *completely independent* dataset to evaluate the classifier, but it is rarely available.
- Usually alternatives approaches such as
- Test set estimators
- Cross-validation estimators
---
# Performance assesment (1)
- **Resubstitution estimator**
- Computes the error rate on the learning set.
- Problem: downward bias
- Should never be used to provide final error estimates!
- **Test set estimation**
- Proceeds in two steps
- Divide learning set into two sub-sets, Test and Train
- Build the classifier on the train set
- Compute error rate on the test set
- This is a better approach, but not free from problems
- Test and Train sets should be independent and i.d.
- This approach reduces effective sample size.
---
# Performance assesment (2)
- If spliting the learning set can yield to too small sets, cross-validation can be an alternative.
- It works by splitting the data into multiple subsets as follows:
- 1. **Data Splitting:** The original dataset is divided into \( k \) subsets, or folds, of approximately equal size.
- 2. **Training and Validation:** The model is trained \( k \) times, each time using \( k-1 \) folds for training and the remaining fold for validation.
- 3. **Performance Evaluation:** Performance metrics such as accuracy, precision, recall, and F1 score are computed for each validation fold.
- 4. **Aggregation:** The performance metrics from all folds are averaged to obtain a final assessment of the classifier's performance.
---
# Key Benefits of CV
- **Reduced Bias:** Cross-validation provides a more robust estimate of model performance compared to a single train-test split, reducing the risk of bias from a particular data split.
- **Maximized Data Utility:** Every data point is used for both training and validation, maximizing the use of available data and ensuring thorough evaluation.
- **Parameter Tuning:** Cross-validation aids in hyperparameter tuning by evaluating multiple parameter configurations across different folds, helping to find optimal model settings.
Cross-validation is essential for accurately assessing a classifier's performance, providing insights into its generalization capabilities across different data subsets and ensuring reliable predictions in real-world applications.
---
# Types of Cross-Validation
- **K-Fold Cross-Validation:** The dataset is divided into \( k \) folds, and each fold is used as the validation set once while the remaining \( k-1 \) folds are used for training.
- **Stratified K-Fold Cross-Validation:** Ensures each fold preserves the proportion of classes, useful for imbalanced datasets.
- **Leave-One-Out Cross-Validation (LOOCV):** Each data point is sequentially used as a single data point validation set while the remaining \( n-1 \) points are used for training, which is computationally expensive but useful for smaller datasets.
---
class: inverse, middle, center
name: Resources
# References and Resources
---
# Resources
- [MetaboAnalystR Statistical Tutorials](https://www.metaboanalyst.ca/resources/vignettes/Statistical_Analysis_Module.html)
- Multivariate Data Analysis Course. Carlos O. Sanchez
[Course Slides](http://i2pc.es/coss/Docencia/ADAM/Notes/MultivariateAnalysisSlides.pdf)
- Principal Component Analysis Overview
[PCA Overview](https://towardsdatascience.com/tidying-up-with-pca-an-introduction-to-principal-components-analysis-f876599af383)
- Hierarchical Clustering
- [Hierarchical Clustering Overview](https://se.mathworks.com/discovery/hierarchical-clustering.html)
- [Hierarchichal clustering in R](https://www.datanovia.com/en/courses/hierarchical-clustering-in-r-the-essentials/)
- Iris Data PCA
[Iris Data PCA Code](https://gist.github.com/chriddyp/7c6c43682a8f57a1f999)
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