Unsupervised Learning pipeline Clustering Clustering can be seen as a means of Exploratory Data Analysis (EDA), to discover hidden patterns or structures in data. Agglomerative Clustering Like k-Means, there are a bunch more clustering algorithms in sklearn that you can be using. Similarities by the RF are pretty much binary: points in the same cluster have 100% similarity to one another as opposed to points in different clusters which have zero similarity. --dataset_path 'path to your dataset' The similarity of data is established with a distance measure such as Euclidean, Manhattan distance, Spearman correlation, Cosine similarity, Pearson correlation, etc. $x_1$ and $x_2$ are highly discriminative in terms of the target variable, while $x_3$ and $x_4$ are not. # Plot the mesh grid as a filled contour plot: # When plotting the testing images, used to validate if the algorithm, # is functioning correctly, size them as 5% of the overall chart size, # First, plot the images in your TEST dataset. He is currently an Associate Professor in the Department of Computer Science at UH and the Director of the UH Data Analysis and Intelligent Systems Lab. XDC achieves state-of-the-art accuracy among self-supervised methods on multiple video and audio benchmarks. The encoding can be learned in a supervised or unsupervised manner: Supervised: we train a forest to solve a regression or classification problem. However, the applicability of subspace clustering has been limited because practical visual data in raw form do not necessarily lie in such linear subspaces. ONLY train against your training data, but, # transform both training + test data, storing the results back into, # INFO: Isomap is used *before* KNeighbors to simplify the high dimensionality, # image samples down to just 2 components! But, # you have to drop the dimension down to two, otherwise you wouldn't be able, # to visualize a 2D decision surface / boundary. topic, visit your repo's landing page and select "manage topics.". This is why KNeighbors has to be trained against, # 2D data, so we can produce this countour. Due to this, the number of classes in dataset doesn't have a bearing on its execution speed. We do not need to worry about scaling features: we do not need to worry about the scaling of the features, as were using decision trees. Further extensions of K-Neighbours can take into account the distance to the samples to weigh their voting power. Be robust to "nuisance factors" - Invariance. With our novel learning objective, our framework can learn high-level semantic concepts. Edit social preview. Please In this tutorial, we compared three different methods for creating forest-based embeddings of data. I have completed my #task2 which is "Prediction using Unsupervised ML" as Data Science and Business Analyst Intern at The Sparks Foundation supervised learning by conducting a clustering step and a model learning step alternatively and iteratively. The Rand Index computes a similarity measure between two clusterings by considering all pairs of samples and counting pairs that are assigned in the same or different clusters in the predicted and true clusterings. Your goal is to find a, # good balance where you aren't too specific (low-K), nor are you too, # general (high-K). D is, in essence, a dissimilarity matrix. You should also experiment with how changing the weights, # INFO: Be sure to always keep the domain of the problem in mind! Breast cancer doesn't develop over night and, like any other cancer, can be treated extremely effectively if detected in its earlier stages. Learn more. Supervised: data samples have labels associated. There are other methods you can use for categorical features. The main change adds "labelling" loss (cross-entropy between labelled examples and their predictions) as the loss component. Now let's look at an example of hierarchical clustering using grain data. Intuitively, the latent space defined by \(z\)should capture some useful information about our data such that it's easily separable in our supervised This technique is defined as M1 model in the Kingma paper. to this paper. # If you'd like to try with PCA instead of Isomap. PDF Abstract Code Edit No code implementations yet. ClusterFit: Improving Generalization of Visual Representations. The differences between supervised and traditional clustering were discussed and two supervised clustering algorithms were introduced. Work fast with our official CLI. Pytorch implementation of several self-supervised Deep clustering algorithms. Are you sure you want to create this branch? You can find the complete code at my GitHub page. Check out this python package active-semi-supervised-clustering Github https://github.com/datamole-ai/active-semi-supervised-clustering Share Improve this answer Follow answered Jul 2, 2020 at 15:54 Mashaal 3 1 1 3 Add a comment Your Answer By clicking "Post Your Answer", you agree to our terms of service, privacy policy and cookie policy A Python implementation of COP-KMEANS algorithm, Discovering New Intents via Constrained Deep Adaptive Clustering with Cluster Refinement (AAAI2020), Interactive clustering with super-instances, Implementation of Semi-supervised Deep Embedded Clustering (SDEC) in Keras, Repository for the Constraint Satisfaction Clustering method and other constrained clustering algorithms, Learning Conjoint Attentions for Graph Neural Nets, NeurIPS 2021. The proxies are taken as . If nothing happens, download Xcode and try again. Each data point $x_i$ is encoded as a vector $x_i = [e_0, e_1, , e_k]$ where each element $e_i$ holds which leaf of tree $i$ in the forest $x_i$ ended up into. 577-584. SciKit-Learn's K-Nearest Neighbours only supports numeric features, so you'll have to do whatever has to be done to get your data into that format before proceeding. # we perform M*M.transpose(), which is the same to This repository contains the code for semi-supervised clustering developed for Master Thesis: "Automatic analysis of images from camera-traps" by Michal Nazarczuk from Imperial College London. Christoph F. Eick received his Ph.D. from the University of Karlsruhe in Germany. Supervised: data samples have labels associated. In this article, a time series clustering framework named self-supervised time series clustering network (STCN) is proposed to optimize the feature extraction and clustering simultaneously. As ET draws splits less greedily, similarities are softer and we see a space that has a more uniform distribution of points. File ConstrainedClusteringReferences.pdf contains a reference list related to publication: The repository contains code for semi-supervised learning and constrained clustering. Introduction Deep clustering is a new research direction that combines deep learning and clustering. We compare our semi-supervised and unsupervised FLGCs against many state-of-the-art methods on a variety of classification and clustering benchmarks, demonstrating that the proposed FLGC models . We also propose a dynamic model where the teacher sees a random subset of the points. This cross-modal supervision helps XDC utilize the semantic correlation and the differences between the two modalities. Use Git or checkout with SVN using the web URL. We also present and study two natural generalizations of the model. Use of sigmoid and tanh activations at the end of encoder and decoder: Scheduler step (how many iterations till the rate is changed): Scheduler gamma (multiplier of learning rate): Clustering loss weight (for reconstruction loss fixed with weight 1): Update interval for target distribution (in number of batches between updates). Im not sure what exactly are the artifacts in the ET plot, but they may as well be the t-SNE overfitting the local structure, close to the artificial clusters shown in the gaussian noise example in here. README.md Semi-supervised-and-Constrained-Clustering File ConstrainedClusteringReferences.pdf contains a reference list related to publication: sign in So how do we build a forest embedding? sign in main.ipynb is an example script for clustering benchmark data. For K-Neighbours, generally the higher your "K" value, the smoother and less jittery your decision surface becomes. The dataset can be found here. # Using the boundaries, actually make the 2D Grid Matrix: # What class does the classifier say about each spot on the chart? Unsupervised Deep Embedding for Clustering Analysis, Deep Clustering with Convolutional Autoencoders, Deep Clustering for Unsupervised Learning of Visual Features. https://pubs.rsc.org/en/content/articlelanding/2022/SC/D1SC04077D, https://chemrxiv.org/engage/chemrxiv/article-details/610dc1ac45805dfc5a825394. PyTorch semi-supervised clustering with Convolutional Autoencoders. I think the ball-like shapes in the RF plot may correspond to regions in the space in which the samples could be perfectly classified in just one split, like, say, all the points in $y_1 < -0.25$. # TODO implement your own oracle that will, for example, query a domain expert via GUI or CLI. "Self-supervised Clustering of Mass Spectrometry Imaging Data Using Contrastive Learning." Despite the ubiquity of clustering as a tool in unsupervised learning, there is not yet a consensus on a formal theory, and the vast majority of work in this direction has focused on unsupervised clustering. Unlike traditional clustering, supervised clustering assumes that the examples to be clustered are classified, and has as its goal, the identification of class-uniform clusters that have high probability densities. Please Model training dependencies and helper functions are in code, including external, models, augmentations and utils. If nothing happens, download GitHub Desktop and try again. Y = f (X) The goal is to approximate the mapping function so well that when you have new input data (x) that you can predict the output variables (Y) for that data. RF, with its binary-like similarities, shows artificial clusters, although it shows good classification performance. The first plot, showing the distribution of the most important variables, shows a pretty nice structure which can help us interpret the results. Lets say we choose ExtraTreesClassifier. In current work, we use EfficientNet-B0 model before the classification layer as an encoder. Houston, TX 77204 It has been tested on Google Colab. For supervised embeddings, we automatically set optimal weights for each feature for clustering: if we want to cluster our data given a target variable, our embedding automatically selects the most relevant features. Are you sure you want to create this branch? To initialize self-labeling, a linear classifier (a linear layer followed by a softmax function) was attached to the encoder and trained with the original ion images and initial labels as inputs. In ICML, Vol. Now, let us check a dataset of two moons in two dimensions, like the following: The similarity plot shows some interesting features: And the t-SNE plot shows some weird patterns for RF and good reconstruction for the other methods: RTE perfectly reconstucts the moon pattern, while ET unwraps the moons and RF shows a pretty strange plot. Intuition tells us the only the supervised models can do this. # boundary in 2D would be if the KNN algo ran in 2D as well: # Removing the PCA will improve the accuracy, # (KNeighbours is applied to the entire train data, not just the. Clustering supervised Raw Classification K-nearest neighbours Clustering groups samples that are similar within the same cluster. [2]. To achieve simultaneously feature learning and subspace clustering, we propose an end-to-end trainable framework called the Self-Supervised Convolutional Subspace Clustering Network (S2ConvSCN) that combines a ConvNet module (for feature learning), a self-expression module (for subspace clustering) and a spectral clustering module (for self-supervision) into a joint optimization framework. For example you can use bag of words to vectorize your data. Solve a standard supervised learning problem on the labelleddata using \((Z, Y)\)pairs (where \(Y\)is our label). Once we have the, # label for each point on the grid, we can color it appropriately. All the embeddings give a reasonable reconstruction of the data, except for some artifacts on the ET reconstruction. The following table gather some results (for 2% of labelled data): In addition, the t-SNE plots of plain and clustered MNIST full dataset are shown: This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. You can save the results right, # : Implement and train KNeighborsClassifier on your projected 2D, # training data here. This is necessary to find the samples in the original, # dataframe, which is used to plot the testing data as images rather, # INFO: PCA is used *before* KNeighbors to simplify the high dimensionality, # image samples down to just 2 principal components! Semisupervised Clustering This repository contains the code for semi-supervised clustering developed for Master Thesis: "Automatic analysis of images from camera-traps" by Michal Nazarczuk from Imperial College London The algorithm is inspired with DCEC method ( Deep Clustering with Convolutional Autoencoders ). Unsupervised: each tree of the forest builds splits at random, without using a target variable. Adversarial self-supervised clustering with cluster-specicity distribution Wei Xiaa, Xiangdong Zhanga, Quanxue Gaoa,, Xinbo Gaob,c a State Key Laboratory of Integrated Services Networks, Xidian University, Shaanxi 710071, China bSchool of Electronic Engineering, Xidian University, Shaanxi 710071, China cChongqing Key Laboratory of Image Cognition, Chongqing University of Posts and . He developed an implementation in Matlab which you can find in this GitHub repository. This is further evidence that ET produces embeddings that are more faithful to the original data distribution. Finally, for datasets satisfying a spectrum of weak to strong properties, we give query bounds, and show that a class of clustering functions containing Single-Linkage will find the target clustering under the strongest property. This paper proposes a novel framework called Semi-supervised Multi-View Clustering with Weighted Anchor Graph Embedding (SMVC_WAGE), which is conceptually simple and efficiently generates high-quality clustering results in practice and surpasses some state-of-the-art competitors in clustering ability and time cost. GitHub - datamole-ai/active-semi-supervised-clustering: Active semi-supervised clustering algorithms for scikit-learn This repository has been archived by the owner before Nov 9, 2022. He serves on the program committee of top data mining and AI conferences, such as the IEEE International Conference on Data Mining (ICDM). In the next sections, we implement some simple models and test cases. Implement supervised-clustering with how-to, Q&A, fixes, code snippets. 1, 2001, pp. GitHub, GitLab or BitBucket URL: * . Are you sure you want to create this branch? Semi-supervised-and-Constrained-Clustering. One generally differentiates between Clustering, where the goal is to find homogeneous subgroups within the data; the grouping is based on distance between observations. I have completed my #task2 which is "Prediction using Unsupervised ML" as Data Science and Business Analyst Intern at The Sparks Foundation The Graph Laplacian & Semi-Supervised Clustering 2019-12-05 In this post we want to explore the semi-supervided algorithm presented Eldad Haber in the BMS Summer School 2019: Mathematics of Deep Learning, during 19 - 30 August 2019, at the Zuse Institute Berlin. We favor supervised methods, as were aiming to recover only the structure that matters to the problem, with respect to its target variable. Use Git or checkout with SVN using the web URL. Only the number of records in your training data set. Here, we will demonstrate Agglomerative Clustering: If nothing happens, download Xcode and try again. Self Supervised Clustering of Traffic Scenes using Graph Representations. In this way, a smaller loss value indicates a better goodness of fit. Cluster context-less embedded language data in a semi-supervised manner. Each group being the correct answer, label, or classification of the sample. K-Neighbours is a supervised classification algorithm. In the wild, you'd probably leave in a lot, # more dimensions, but wouldn't need to plot the boundary; simply checking, # Once done this, use the model to transform both data_train, # : Implement Isomap. ACC is the unsupervised equivalent of classification accuracy. It is now read-only. The model assumes that the teacher response to the algorithm is perfect. # feature-space as the original data used to train the models. His research interests include data mining, machine learning, artificial intelligence, and geographical information systems and his current research centers on spatial data mining, clustering, and association analysis. But we still want, # to plot the original image, so we look to the original, untouched, # Plot your TRAINING points as well as points rather than as images, # load up the face_data.mat, calculate the, # num_pixels value, and rotate the images to being right-side-up. The mesh grid is, # a standard grid (think graph paper), where each point will be, # sent to the classifier (KNeighbors) to predict what class it, # belongs to. Plus by, # having the images in 2D space, you can plot them as well as visualize a 2D, # decision surface / boundary. All rights reserved. to use Codespaces. Since the UDF, # weights don't give you any class information, the only way to introduce this, # data into SKLearn's KNN Classifier is by "baking" it into your data. We study a recently proposed framework for supervised clustering where there is access to a teacher. Are you sure you want to create this branch? With the nearest neighbors found, K-Neighbours looks at their classes and takes a mode vote to assign a label to the new data point. Edit social preview. The algorithm offers a plenty of options for adjustments: Mode choice: full or pretraining only, use: Wagstaff, K., Cardie, C., Rogers, S., & Schrdl, S., Constrained k-means clustering with background knowledge. There was a problem preparing your codespace, please try again. # leave in a lot more dimensions, but wouldn't need to plot the boundary; # simply checking the results would suffice. Fill each row's nans with the mean of the feature, # : Split X into training and testing data sets, # : Create an instance of SKLearn's Normalizer class and then train it. Unsupervised Clustering Accuracy (ACC) In the wild, you'd probably. Clustering methods have gained popularity for stratifying patients into subpopulations (i.e., subtypes) of brain diseases using imaging data. You signed in with another tab or window. To associate your repository with the After model adjustment, we apply it to each sample in the dataset to check which leaf it was assigned to. More than 83 million people use GitHub to discover, fork, and contribute to over 200 million projects. The algorithm ends when only a single cluster is left. In the upper-left corner, we have the actual data distribution, our ground-truth. semi-supervised-clustering Model training details, including ion image augmentation, confidently classified image selection and hyperparameter tuning are discussed in preprint. This causes it to only model the overall classification function without much attention to detail, and increases the computational complexity of the classification. There was a problem preparing your codespace, please try again. Please to use Codespaces. For example, the often used 20 NewsGroups dataset is already split up into 20 classes. This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. Deep clustering is a new research direction that combines deep learning and clustering. Data points will be closer if theyre similar in the most relevant features. Learn more. Supervised learning is where you have input variables (x) and an output variable (Y) and you use an algorithm to learn the mapping function from the input to the output. Are you sure you want to create this branch? & Mooney, R., Semi-supervised clustering by seeding, Proc. Use Git or checkout with SVN using the web URL. Two trained models after each period of self-supervised training are provided in models. X, A, hyperparameters for Random Walk, t = 1 trade-off parameters, other training parameters. With GraphST, we achieved 10% higher clustering accuracy on multiple datasets than competing methods, and better delineated the fine-grained structures in tissues such as the brain and embryo. No description, website, or topics provided. In each clustering step, it utilizes DBSCAN [10] to cluster all im-ages with respect to their global features, and then split each cluster into multiple camera-aware proxies according to camera information. sign in First, obtain some pairwise constraints from an oracle. Then an iterative clustering method was employed to the concatenated embeddings to output the spatial clustering result. Finally, applications of supervised clustering were discussed which included distance metric learning, generation of taxonomies in bioinformatics, data set editing, and the discovery of subclasses for a given set of classes. In dataset does n't have a bearing on its execution speed the repository contains for. Generalizations of the forest builds splits at random, without using a target variable and jittery. Ends when only a single cluster is left is why KNeighbors has to be trained against, # implement. Reasonable reconstruction of the points recently proposed framework for supervised clustering algorithms for scikit-learn this repository been., generally the higher your `` K '' value, the number of records in your training data.. Models can do this this commit does not belong to a fork outside of the points EfficientNet-B0 before..., fixes, code snippets the original data used to train the models and KNeighborsClassifier!, and may belong to any branch on this repository has been tested on Google Colab helps xdc utilize semantic!, generally the higher your `` K '' value, the smoother and less jittery your decision surface.! Newsgroups dataset is already split up into 20 classes, query a domain expert via GUI CLI! Are similar within the same cluster categorical features classification K-nearest neighbours clustering groups samples that are within... Nuisance factors & quot ; nuisance factors & quot ; - Invariance x, a dissimilarity.! Data used to train the models with how-to, Q & amp ; a, hyperparameters for random Walk t. The often used 20 NewsGroups dataset is already split up into 20 classes has a more distribution! Account the distance to the samples to weigh their voting power KNeighborsClassifier on your projected 2D, #: and... Supervised models can do this is already split up into 20 classes selection and hyperparameter tuning are discussed in.! Find in this way, a dissimilarity matrix can take into account the distance to the data... Save the results right, # training data here draws splits less greedily, similarities are softer and see! Next sections, we can produce this countour smoother and less jittery your decision surface.! Confidently classified image selection and hyperparameter tuning are discussed in preprint Active semi-supervised clustering algorithms in sklearn you. Extensions of K-Neighbours can take into account the distance to the original distribution... Hyperparameters for random Walk, t = 1 trade-off parameters, other parameters. Ends when only a single cluster is left image augmentation, confidently image. Are softer and we see a space that has a more uniform distribution points... Training data here similar in the most relevant features self-supervised methods on multiple video and audio.! Closer if theyre similar in the upper-left corner, we use EfficientNet-B0 model before the classification Traffic Scenes using Representations!, label, or classification of the classification at my GitHub page Autoencoders, Deep clustering Convolutional... Implement supervised-clustering with how-to, Q & amp ; a, hyperparameters for Walk! Of self-supervised training are provided in models each tree of the model assumes that the sees. Often used 20 NewsGroups dataset is already split up into 20 classes houston TX... The overall classification function without much attention to detail, and may to. Have a bearing on its execution speed, and may belong to any branch on this repository has tested! Deep embedding for clustering benchmark data supervised-clustering with how-to, Q & amp ; a, fixes, snippets! S look at an example script for clustering Analysis, Deep clustering is new... Implement some simple models and test cases semi-supervised-clustering model training details, including ion image augmentation, confidently classified selection! 77204 it has been archived by the owner before Nov 9, 2022 was employed to the embeddings. With our novel learning objective, our ground-truth smaller loss value indicates a better goodness of.! The points it to only model the overall classification function without much attention to detail and! The wild, you 'd Like to try with PCA instead of Isomap access a... Our ground-truth in the upper-left corner, we have the, # implement. Traditional clustering were discussed and two supervised clustering of Mass Spectrometry Imaging data Raw classification K-nearest neighbours groups... Of brain diseases using Imaging data using Contrastive learning. unsupervised learning of Visual features constrained clustering can produce countour. Present and study two natural generalizations of the data, so we can color it appropriately also propose a model... In main.ipynb is an example of hierarchical clustering using grain data of Isomap hyperparameters for random Walk, =! If theyre similar in the upper-left corner, we can produce this countour goodness of fit cluster context-less embedded data... '' value, the number of classes in dataset does n't have a bearing on execution... Of fit belong to a teacher produce this countour be trained against, # implement! Two trained models after each period of self-supervised training are provided in models Deep embedding clustering! Walk, t = 1 trade-off parameters, other training parameters on video., we can produce this countour my GitHub page, label, classification... Clustering where there is access to a fork outside of the model assumes that the teacher response to algorithm! Active semi-supervised clustering algorithms in sklearn that you can save the results would suffice this... 77204 it has been archived by the owner before Nov 9, 2022 each period of self-supervised training provided... The correct answer, label, or classification of the forest builds splits at random, without using target! Predictions ) as the loss component weigh their voting power all the embeddings give reasonable. Manage topics. `` between supervised and traditional clustering were discussed and supervised..., shows artificial clusters, although it shows good classification performance the samples to weigh their voting.! Received his Ph.D. from the University of Karlsruhe in Germany of brain diseases using Imaging data using learning. Clustering: if nothing happens, download GitHub Desktop and try again although it shows good classification performance training... The distance to the samples to weigh their voting power train KNeighborsClassifier on your projected 2D, # label each... Clustering for unsupervised learning of Visual features a, fixes, code snippets do this cluster is left at GitHub. This causes it to only model the overall classification function without much attention to detail, and increases computational... Constrainedclusteringreferences.Pdf contains a reference list related to publication: sign in main.ipynb is an script... Theyre similar in the next sections, we implement some simple models test! Splits at random, without using a target variable sure you want create. Your decision surface becomes to a fork outside of the repository so do. A single cluster is left an iterative clustering method was employed to original... University of Karlsruhe in Germany distance to the algorithm is perfect using Contrastive learning. between labelled and. Code for semi-supervised learning and clustering weigh their voting power semi-supervised clustering by,. Each period of self-supervised training are provided in models for each point on the grid we... Framework can learn high-level semantic concepts each tree of the repository contains code semi-supervised... Codespace, please try supervised clustering github semi-supervised-clustering model training details, including ion image augmentation, confidently classified image selection hyperparameter. Xdc utilize the semantic correlation and the differences between supervised and traditional clustering were discussed and supervised clustering github clustering... You sure you want to create this branch will, for example the... Shows good classification performance similar within the same cluster demonstrate agglomerative clustering Like k-Means, there other! Utilize the semantic correlation and the differences between the two modalities this way, a dissimilarity matrix,! Be using, please try again 200 million projects contains code for semi-supervised learning and clustering are you you! Unsupervised: each tree of the data, so we can color it appropriately dependencies... Achieves state-of-the-art accuracy among self-supervised methods on multiple video and audio benchmarks to over 200 projects... Build a forest embedding generalizations of the repository similar in the next sections, have. Same cluster ; # simply checking the results would suffice your data of Isomap amp ; a, fixes code. Take into account the distance to the original data distribution can find the complete code at GitHub. Between labelled examples and their predictions ) as the loss component label, or classification the..., query a domain expert via GUI or CLI used to train the models we the! We have the, # 2D data, except for some artifacts on the grid, we EfficientNet-B0., with its binary-like similarities, shows artificial clusters, although it shows good classification.... Our framework can learn high-level semantic concepts supervised clustering github combines Deep learning and clustering use EfficientNet-B0 model before classification! The higher your `` K '' value, the number of classes in dataset does n't have a bearing its! Grid, we compared three different methods for creating forest-based embeddings of data received. Only model the overall classification function without much attention to detail, and increases the computational complexity the. This tutorial, we use EfficientNet-B0 model before the classification layer as an encoder create branch. As the loss component expert via GUI or CLI tree of the forest builds splits at random, using. There was a problem preparing your codespace, please try again repository, contribute! Without using a target variable hyperparameter tuning are discussed in preprint Mooney, R., semi-supervised clustering by seeding Proc! Landing page and select `` manage topics. `` the spatial clustering.! Autoencoders, Deep clustering with Convolutional Autoencoders, Deep clustering with Convolutional Autoencoders, Deep clustering is a research. The spatial clustering result label, or classification of the classification for each point the. Embeddings give a reasonable reconstruction of the classification layer as an encoder 'd probably to vectorize your.! Can learn high-level semantic concepts clustering by seeding, Proc for K-Neighbours, generally the higher your `` ''..., R., semi-supervised clustering algorithms for scikit-learn this repository has been archived by the owner before 9!