diff --git a/source/index.rst b/source/index.rst index 0cc6924..9c1f413 100644 --- a/source/index.rst +++ b/source/index.rst @@ -57,11 +57,9 @@ Data widgets/data/applydomain widgets/data/purgedomain widgets/data/rank - widgets/data/correlations widgets/data/color widgets/data/featurestatistics widgets/data/melt - widgets/data/neighbors widgets/data/unique widgets/data/groupby @@ -150,6 +148,8 @@ Unsupervised :maxdepth: 1 widgets/unsupervised/PCA + widgets/unsupervised/neighbors + widgets/unsupervised/correlations widgets/unsupervised/correspondenceanalysis widgets/unsupervised/distancemap widgets/unsupervised/distances diff --git a/source/widgets/data/images/Correlations-Example.png b/source/widgets/data/images/Correlations-Example.png deleted file mode 100644 index 7babef0..0000000 Binary files a/source/widgets/data/images/Correlations-Example.png and /dev/null differ diff --git a/source/widgets/data/images/Correlations-links.png b/source/widgets/data/images/Correlations-links.png deleted file mode 100644 index cce0c9f..0000000 Binary files a/source/widgets/data/images/Correlations-links.png and /dev/null differ diff --git a/source/widgets/data/images/Correlations-stamped.png b/source/widgets/data/images/Correlations-stamped.png deleted file mode 100644 index 30cc12b..0000000 Binary files a/source/widgets/data/images/Correlations-stamped.png and /dev/null differ diff --git a/source/widgets/data/images/neighbours-example-multiple.png b/source/widgets/data/images/neighbours-example-multiple.png deleted file mode 100644 index 09e6a8b..0000000 Binary files a/source/widgets/data/images/neighbours-example-multiple.png and /dev/null differ diff --git a/source/widgets/data/images/neighbours-example1.png b/source/widgets/data/images/neighbours-example1.png deleted file mode 100644 index 3a0465d..0000000 Binary files a/source/widgets/data/images/neighbours-example1.png and /dev/null differ diff --git a/source/widgets/data/images/neighbours-example2.png b/source/widgets/data/images/neighbours-example2.png deleted file mode 100644 index 0a654d2..0000000 Binary files a/source/widgets/data/images/neighbours-example2.png and /dev/null differ diff --git a/source/widgets/data/images/neighbours-stamped.png b/source/widgets/data/images/neighbours-stamped.png deleted file mode 100644 index a8ec4f1..0000000 Binary files a/source/widgets/data/images/neighbours-stamped.png and /dev/null differ diff --git a/source/widgets/data/neighbors.md b/source/widgets/data/neighbors.md deleted file mode 100644 index 423c64e..0000000 --- a/source/widgets/data/neighbors.md +++ /dev/null @@ -1,42 +0,0 @@ -Neighbors -========= - -Compute nearest neighbors in data according to reference. - -**Inputs** - -- Data: An input data set. -- Reference: A reference data for neighbor computation. - -**Outputs** - -- Neighbors: A data table of nearest neighbors according to reference. - -The **Neighbors** widget computes nearest neighbors for a given reference and for a given distance measure. The reference can be either one instance or more instances. In the case with one reference widget outputs closest `n` instances from data where `n` is set by the **Number of neighbors** option in the widget. When reference contains more instances widget computes the combined distance for each data instance as a minimum of distances to each reference. Widget outputs `n` data instances with lowest combined distance. - -![](images/neighbours-stamped.png) - -1. Distance measure for computing neighbors. Supported measures are: Euclidean, Manhattan, Mahalanobis, Cosine, Jaccard, Spearman, absolute Spearman, Pearson, absolute Pearson. -2. Number of neighbors on the output. -3. If *Exclude rows (equal to) references* is ticked, data instances that are highly similar to the reference (distance < 1e-5), will be excluded. -4. Click *Apply* to commit the changes. To communicate changes automatically tick *Apply Automatically*. -5. Status bar with access to widget help and information on the input and output data. - -Examples --------- - -In the first example, we used *iris* data and passed it to **Neighbors** and to [Data Table](../data/datatable.md). In **Data Table**, we selected an instance of iris, that will serve as our reference, meaning we wish to retrieve 10 closest examples to the select data instance. We connect **Data Table** to **Neighbors** as well. - -We can observe the results of neighbor computation in **Data Table (1)**, where we can see 10 closest images to our selected iris flower. - -![](images/neighbours-example1.png) - -Now change the selection **Data Table** to multiple examples. As a result, we get instances with closest combined distances to the references. The method computes the combined distance as a minimum of distances to each reference. - -![](images/neighbours-example-multiple.png) - -Another example requires the installation of Image Analytics add-on. We loaded 15 paintings from famous painters with **Import Images** widget and passed them to **Image Embedding**, where we selected *Painters* embedder. - -Then the procedure is the same as above. We passed embedded images to **Image Viewer** and selected a painting from Monet to serve as our reference image. We passed the image to **Neighbors**, where we set the distance measure to *cosine*, ticked off *Exclude reference* and set the neighbors to 2. This allows us to find the actual closest neighbor to a reference painting and observe them side by side in **Image Viewer (1)**. - -![](images/neighbours-example2.png) diff --git a/source/widgets/unsupervised/PCA.md b/source/widgets/unsupervised/PCA.md index f4b3fdd..d9a8dcb 100644 --- a/source/widgets/unsupervised/PCA.md +++ b/source/widgets/unsupervised/PCA.md @@ -10,20 +10,19 @@ PCA linear transformation of input data. **Outputs** - Transformed Data: PCA transformed data -- Components: [Eigenvectors](https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors). +- Data: original data with PCA components as meta variables +- Components: [Eigenvectors](https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors) +- PCA: PCA to use as Scorer in [Rank](../data/rank.md) [Principal Component Analysis](https://en.wikipedia.org/wiki/Principal_component_analysis) (PCA) computes the PCA linear transformation of the input data. It outputs either a transformed dataset with weights of individual instances or weights of principal components. -![](images/PCA-stamped.png) +![](images/PCA-stamped.png){width=500px} -1. Select how many principal components you wish in your output. It is best to choose as few as possible with variance covered as high as possible. You can also set how much variance you wish to cover with your principal components. -2. You can normalize data to adjust the values to common scale. If checked, columns are divided by their standard deviations. +1. Select how many principal components you wish in your output. It is best to choose as few as possible with variance (parameter *Explained variance*) covered as high as possible. You can also set how much variance you wish to cover with your principal components. +2. You can normalize data to adjust the values to common scale. If checked, columns are divided by their standard deviations. One can also set how many components to display in the graph. 3. When *Apply Automatically* is ticked, the widget will automatically communicate all changes. Alternatively, click *Apply*. -4. Press *Save Image* if you want to save the created image to your computer. -5. Produce a report. -6. Principal components graph, where the red (lower) line is the variance covered per component and the green (upper) line is cumulative variance covered by components. -The number of components of the transformation can be selected either in the *Components Selection* input box or by dragging the vertical cutoff line in the graph. +The principal components graph, called a scree plot, show the red (lower) line, representing the variance covered per component, and the green (upper) line, representing the cumulative variance covered by components. The number of components of the transformation can be selected either in the *Components* input box or by dragging the vertical cutoff line in the graph. Preprocessing ------------- @@ -39,8 +38,8 @@ Examples **PCA** can be used to simplify visualizations of large datasets. Below, we used the *Iris* dataset to show how we can improve the visualization of the dataset with PCA. The transformed data in the [Scatter Plot](../visualize/scatterplot.md) show a much clearer distinction between classes than the default settings. -![](images/PCAExample.png) +![](images/PCA-Example1.png) -The widget provides two outputs: transformed data and principal components. Transformed data are weights for individual instances in the new coordinate system, while components are the system descriptors (weights for principal components). When fed into the [Data Table](../data/datatable.md), we can see both outputs in numerical form. We used two data tables in order to provide a more clean visualization of the workflow, but you can also choose to edit the links in such a way that you display the data in just one data table. You only need to create two links and connect the *Transformed data* and *Components* inputs to the *Data* output. +PCA can also be used as a scorer for the [Rank](../data/rank.md) widget. We used the *iris* data for this example. The data is passed both to Rank and to PCA. PCA passes the Scorer output to the Rank widget. Rank now shows feature scores for the first two principal components. -![](images/PCAExample2.png) +![](images/PCA-Example2.png) diff --git a/source/widgets/data/correlations.md b/source/widgets/unsupervised/correlations.md similarity index 52% rename from source/widgets/data/correlations.md rename to source/widgets/unsupervised/correlations.md index 18263b7..db0e99f 100644 --- a/source/widgets/data/correlations.md +++ b/source/widgets/unsupervised/correlations.md @@ -15,22 +15,23 @@ Compute all pairwise attribute correlations. **Correlations** computes Pearson or Spearman correlation scores for all pairs of features in a dataset. These methods can only detect monotonic relationship. -![](images/Correlations-stamped.png) +![](images/Correlations-stamped.png){width=400px} 1. Correlation measure: - Pairwise [Pearson](https://en.wikipedia.org/wiki/Pearson_correlation_coefficient) correlation. - Pairwise [Spearman](https://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient) correlation. +2. Select the attribute for computing correlations. Useful for large datasets. 2. Filter for finding attribute pairs. -3. A list of attribute pairs with correlation coefficient. Press *Finished* to stop computation for large datasets. -4. Access widget help and produce report. + +Press *Finished* to stop computation for large datasets. Example ------- -Correlations can be computed only for numeric (continuous) features, so we will use *housing* as an example data set. Load it in the [File](file.md) widget and connect it to **Correlations**. Positively correlated feature pairs will be at the top of the list and negatively correlated will be at the bottom. +Correlations can be computed only for numeric (continuous) features, so we will use *brown-selected* as an example data set. Load it in the [File](file.md) widget and connect it to **Correlations**. Positively correlated feature pairs will be at the top of the list and negatively correlated will be at the bottom. ![](images/Correlations-links.png) -Go to the most negatively correlated pair, DIS-NOX. Now connect [Scatter Plot](../visualize/scatterplot.md) to **Correlations** and set two outputs, Data to Data and Features to Features. Observe how the feature pair is immediately set in the scatter plot. Looks like the two features are indeed negatively correlated. +Select the most correlated feature pair. Now connect [Scatter Plot](../visualize/scatterplot.md) to **Correlations** and set two outputs, Data to Data and Features to Features. Observe how the feature pair is immediately set in the scatter plot. Looks like the two features are indeed positively correlated. ![](images/Correlations-Example.png) diff --git a/source/widgets/unsupervised/distancefile.md b/source/widgets/unsupervised/distancefile.md index bbb6989..42f683c 100644 --- a/source/widgets/unsupervised/distancefile.md +++ b/source/widgets/unsupervised/distancefile.md @@ -7,21 +7,23 @@ Loads an existing distance file. - Distance File: distance matrix -![](images/DistanceFile-stamped.png) +![](images/DistanceFile-stamped.png){width=400px} 1. Choose from a list of previously saved distance files. -2. Browse for saved distance files. -3. Reload the selected distance file. -4. Information about the distance file (number of points, - labelled/unlabelled). -5. Browse documentation datasets. -6. Produce a report. + Browse for saved distance files. + Reload the selected distance file. +2. If *Treat triangular matrices as symmetric* is checked, triangular matrices will be mirrored over diagonal. +3. Browse documentation datasets. The simplest way to prepare a distance file is to use Excel. The widget currently processes only single-sheet workbooks. The matrix can be either rectangular, or upper- or lower-triangular, with labels given for columns (immediately above) or rows (immediately to the left) or both. Empty cells are treated as zeros. If the matrix is triangular and only one set of labels is given or both sets are equal, the other half can be filled automatically, making the matrix symmetric. +![](images/DistanceFile-Excel.png){width=400px} + +Above is an example of am upper-triangular matrix. + Example ------- -When you want to use a custom-set distance file that you've saved before, open the **Distance File** widget and select the desired file with the *Browse* icon. This widget loads the existing distance file. In the snapshot below, we loaded the transformed *Iris* distance matrix from the [Save Distance Matrix](../unsupervised/savedistancematrix.md) example. We displayed the transformed data matrix in the [Distance Map](../unsupervised/distancemap.md) widget. We also decided to display a distance map of the original *Iris* dataset for comparison. +When you want to use a custom-set distance file that you've saved before, open the **Distance File** widget and select the desired file with the *Browse* icon. This widget loads the existing distance file. In the snapshot below, we loaded the test square matrix. We displayed the matrix in the [Distance Matrix](../unsupervised/distancematrix.md) widget. ![](images/DistanceFile-Example.png) diff --git a/source/widgets/unsupervised/distancemap.md b/source/widgets/unsupervised/distancemap.md index 61a3766..21dd6e2 100644 --- a/source/widgets/unsupervised/distancemap.md +++ b/source/widgets/unsupervised/distancemap.md @@ -12,13 +12,13 @@ Visualizes distances between items. - Data: instances selected from the matrix - Features: attributes selected from the matrix -The **Distance Map** visualizes distances between objects. The visualization is the same as if we printed out a table of numbers, except that the numbers are replaced by colored spots. +The **Distance Map** visualizes distances between objects. The visualization is the same as if we printed out a table of numbers, except that the numbers are replaced by colored spots. Conceptually, it is similar to the [Heat Map](../visualize/heatmap.md) widget. -Distances are most often those between instances ("*rows*" in the [Distances](../unsupervised/distances.md) widget) or attributes ("*columns*" in Distances widget). The only suitable input for **Distance Map** is the [Distances](../unsupervised/distances.md) widget. For the output, the user can select a region of the map and the widget will output the corresponding instances or attributes. Also note that the **Distances** widget ignores discrete values and calculates distances only for continuous data, thus it can only display distance map for discrete data if you [Continuize](../data/continuize.md) them first. +Distances are most often those between instances ("*rows*" in the [Distances](distances.md) widget) or attributes ("*columns*" in Distances widget). The two suitable inputs for **Distance Map** are the [Distances](distances.md) and the [Distance File](distancefile.md) widget. For the output, the user can select a region of the map and the widget will output the corresponding instances or attributes. Also note that the **Distances** widget ignores discrete values and calculates distances only for continuous data, thus it can only display distance map for discrete data if you [Continuize](../data/continuize.md) them first. -The snapshot shows distances between columns in the *heart disease* data, where smaller distances are represented with light and larger with dark orange. The matrix is symmetric and the diagonal is a light shade of orange - no attribute is different from itself. Symmetricity is always assumed, while the diagonal may also be non-zero. +The snapshot shows distances between columns in the *heart_disease* data, where smaller distances are represented with blue and larger with yellow/white. The matrix is symmetric and the diagonal is blue - no attribute is different from itself. Symmetricity is always assumed, while the diagonal may also be non-zero. -![](images/DistanceMap-stamped.png) +![](images/DistanceMap-stamped.png){width=500px} 1. *Element sorting* arranges elements in the map by - None (lists instances as found in the dataset) @@ -26,27 +26,21 @@ The snapshot shows distances between columns in the *heart disease* data, where - **Clustering with ordered leaves** (maximizes the sum of similarities of adjacent elements) 2. *Colors* - **Colors** (select the color palette for your distance map) - - **Low** and **High** are thresholds for the color palette (low for instances or attributes with low distances and high for instances or attributes with high distances). + - **Range**: Define the low and high thresholds for the color palette (low for instances or attributes with low distances and high for instances or attributes with high distances). 3. Select *Annotations*. 4. If *Send Selected Automatically* is on, the data subset is communicated automatically, otherwise you need to press *Send Selected*. -5. Press *Save Image* if you want to save the created image to your computer. -6. Produce a report. -Normally, a color palette is used to visualize the entire range of distances appearing in the matrix. This can be changed by setting the low and high threshold. In this way we ignore the differences in distances outside this interval and visualize the interesting part of the distribution. +Normally, a color palette is used to visualize the entire range of distances appearing in the matrix. This can be changed by setting the low and high threshold. In this way, we ignore the differences in distances outside this interval and visualize the interesting part of the distribution. -Below, we visualized the most correlated attributes (distances by columns) in the *heart disease* dataset by setting the color threshold for high distances to the minimum. We get a predominantly black square, where attributes with the lowest distance scores are represented by a lighter shade of the selected color schema (in our case: orange). Beside the diagonal line, we see that in our example *ST by exercise* and *major vessels colored* are the two attributes closest together. +Below, we visualized the most correlated attributes (distances by columns) in the *heart_disease* dataset by lowering the color threshold for high distances. We get a predominantly white square, where attributes with the lowest distance scores are represented by blue. We see that, beside the diagonal line, *age* and *major vessels colored* are the two attributes closest together. -![](images/DistanceMap-Highlighted.png) +![](images/DistanceMap-Threshold.png){width=400px} The user can select a region in the map with the usual click-and-drag of the cursor. When a part of the map is selected, the widget outputs all items from the selected cells. -Examples --------- +Example +------- -The first workflow shows a very standard use of the **Distance Map** widget. We select 70% of the original *Iris* data as our sample and view the distances between rows in **Distance Map**. - -![](images/DistanceMap-Example1.png) - -In the second example, we use the *heart disease* data again and select a subset of women only from the [Scatter Plot](../visualize/scatterplot.md). Then, we visualize distances between columns in the **Distance Map**. Since the subset also contains some discrete data, the [Distances](../unsupervised/distances.md) widget warns us it will ignore the discrete features, thus we will see only continuous instances/attributes in the map. +The workflow shows a very standard use of the **Distance Map** widget. We select the *Iris* data and view the distances between rows in **Distance Map**. ![](images/DistanceMap-Example.png) diff --git a/source/widgets/unsupervised/distances.md b/source/widgets/unsupervised/distances.md index 613e082..ff44950 100644 --- a/source/widgets/unsupervised/distances.md +++ b/source/widgets/unsupervised/distances.md @@ -11,45 +11,43 @@ Computes distances between rows/columns in a dataset. - Distances: distance matrix -The **Distances** widget computes distances between rows or columns in a dataset. By default, the data will be normalized to ensure equal treatment of individual features. Normalization is always done column-wise. +The **Distances** widget computes distances between rows or columns in a dataset. By default, *Euclidean (normalized)* distance metric is used, to ensure equal treatment of individual features. Normalization is always done column-wise. In case of missing values, the widget automatically imputes the average value of the row or the column. The widget works for both numeric and categorical data. In case of categorical data, the distance is 0 if the two values are the same ('green' and 'green') and 1 if they are not ('green' and 'blue'). Sparse data can only be used with Euclidean, Manhattan and Cosine metric. The resulting distance matrix can be fed further to [Hierarchical Clustering](hierarchicalclustering.md) for uncovering groups in the data, to [Distance Map](distancemap.md) or [Distance Matrix](distancematrix.md) for visualizing the distances (Distance Matrix can be quite slow for larger data sets), to [MDS](mds.md) for mapping the data instances using the distance matrix and finally, saved with [Save Distance Matrix](savedistancematrix.md). Distance file can be loaded with [Distance File](distancefile.md). -Distances work well with Orange add-ons, too. The distance matrix can be fed to Network from Distances (Network add-on) to convert the matrix into a graph and to Duplicate Detection (Text add-on) to find duplicate documents in the corpus. +Distances work well with Orange add-ons, too. The distance matrix can be fed to [Network from Distances](https://orangedatamining.com/widget-catalog/networks/networkfromdistances/) (Network add-on) to convert the matrix into a graph and to [Duplicate Detection](https://orangedatamining.com/widget-catalog/text-mining/duplicatedetection/) (Text add-on) to find duplicate documents in the corpus. -![](images/Distances-stamped.png) +![](images/Distances-stamped.png){width=70%} 1. Choose whether to measure distances between rows or columns. 2. Choose the *Distance Metric*: + - [Euclidean (normalized)](https://en.wikipedia.org/wiki/Euclidean_distance) ("straight line", distance between two points). Normalization is always done column-wise. Values are zero centered and scaled. - [Euclidean](https://en.wikipedia.org/wiki/Euclidean_distance) ("straight line", distance between two points) - - [Manhattan](https://en.wiktionary.org/wiki/Manhattan_distance) (the sum of absolute differences for all attributes) + - [Manhattan (normalized)](https://en.wiktionary.org/wiki/Manhattan_distance) (the sum of absolute differences for all attributes) + - [Manhattan](https://en.wiktionary.org/wiki/Manhattan_distance) (the sum of absolute differences for all attributes). Normalization is always done column-wise. Values are zero centered and scaled. + - [Mahalanobis](https://en.wikipedia.org/wiki/Mahalanobis_distance) (distance between a point and a probability distribution) + - [Hamming](https://en.wikipedia.org/wiki/Hamming_distance) (the number of features at which the corresponding values are different) - [Cosine](https://en.wikipedia.org/wiki/Cosine_similarity) (the cosine of the angle between two vectors of an inner product space). Orange computes the cosine distance, which is 1-similarity. - - [Jaccard](https://en.wikipedia.org/wiki/Jaccard_index) (the size of the intersection divided by the size of the union of the sample sets) - - [Spearman](https://en.wikipedia.org/wiki/Spearman's_rank_correlation_coefficient)(linear correlation between the rank of the values, remapped as a distance in a [0, 1] interval) - - [Spearman absolute](https://en.wikipedia.org/wiki/Spearman's_rank_correlation_coefficient)(linear correlation between the rank of the absolute values, remapped as a distance in a [0, 1] interval) - [Pearson](https://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient) (linear correlation between the values, remapped as a distance in a [0, 1] interval) - [Pearson absolute](https://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient) (linear correlation between the absolute values, remapped as a distance in a [0, 1] interval) - - [Hamming](https://en.wikipedia.org/wiki/Hamming_distance) (the number of features at which the corresponding values are different) - - [Bhattacharyya distance](https://en.wikipedia.org/wiki/Bhattacharyya_distance) (Similarity between two probability distributions, not a real distance as it doesn't obey triangle inequality.) - - Normalize the features. Normalization is always done column-wise. Values are zero centered and scaled. - In case of missing values, the widget automatically imputes the average value of the row or the column. - The widget works for both numeric and categorical data. In case of categorical data, the distance is 0 if the two values are the same ('green' and 'green') and 1 if they are not ('green' and 'blue'). + - [Spearman](https://en.wikipedia.org/wiki/Spearman's_rank_correlation_coefficient)(linear correlation between the rank of the values, remapped as a distance in a [0, 1] interval) + - [Spearman absolute](https://en.wikipedia.org/wiki/Spearman's_rank_correlation_coefficient)(linear correlation between the rank of the absolute values, remapped as a distance in a [0, 1] interval) + - [Jaccard](https://en.wikipedia.org/wiki/Jaccard_index) (the size of the intersection divided by the size of the union of the sample sets) 3. Tick *Apply Automatically* to automatically commit changes to other widgets. Alternatively, press '*Apply*'. Examples -------- -The first example shows a typical use of the **Distances** widget. We are using the *iris.tab* data from the [File](../data/file.md) widget. We compute distances between data instances (rows) and pass the result to the [Hierarchical Clustering](hierarchicalclustering.md). This is a simple workflow to find groups of data instances. +The first example shows a typical use of the **Distances** widget. We are using the *zoo.tab* data from the [File](../data/file.md) widget. We compute distances between data instances (rows) and pass the result to the [Hierarchical Clustering](hierarchicalclustering.md). This is a simple workflow to find groups of data instances. -![](images/Distances-Example1-rows.png) +![](images/Distances-Example1.1.png) -Alternatively, we can compute distance between columns and find how similar our features are. +Alternatively, we can compute distance between columns and find how similar our features are. Here, we are using *housing* dataset for demonstration (as *zoo* does not contain numeric features for computing distances between columns). -![](images/Distances-Example1-columns.png) +![](images/Distances-Example1.2.png) -The second example shows how to visualize the resulting distance matrix. A nice way to observe data similarity is in a [Distance Map](distancemap.md) or in [MDS](mds.md). +The second example shows how to visualize the resulting distance matrix on the *zoo* dataset. A nice way to observe data similarity is in a [Distance Map](distancemap.md) or in [MDS](mds.md). ![](images/Distances-Example2.png) diff --git a/source/widgets/unsupervised/hierarchicalclustering.md b/source/widgets/unsupervised/hierarchicalclustering.md index 0689d35..5b13376 100644 --- a/source/widgets/unsupervised/hierarchicalclustering.md +++ b/source/widgets/unsupervised/hierarchicalclustering.md @@ -6,15 +6,16 @@ Groups items using a hierarchical clustering algorithm. **Inputs** - Distances: distance matrix +- Data Subset: **Outputs** - Selected Data: instances selected from the plot - Data: data with an additional column showing whether an instance is selected -The widget computes [hierarchical clustering](https://en.wikipedia.org/wiki/Hierarchical_clustering) of arbitrary types of objects from a matrix of distances and shows a corresponding [dendrogram](https://en.wikipedia.org/wiki/Dendrogram). Distances can be computed with the [Distances](../unsupervised/distances.md) widget +The widget computes [hierarchical clustering](https://en.wikipedia.org/wiki/Hierarchical_clustering) of arbitrary types of objects from a matrix of distances and shows a corresponding [dendrogram](https://en.wikipedia.org/wiki/Dendrogram). Distances can be computed with the [Distances](distances.md) widget. -![](images/Hierarchical-Clustering.png) +![](images/HierarchicalClustering-stamped.png){width=600px} 1. The widget supports the following ways of measuring distances between clusters: - **Single linkage** computes the distance between the closest elements of the two clusters @@ -23,15 +24,16 @@ The widget computes [hierarchical clustering](https://en.wikipedia.org/wiki/Hier - **Complete linkage** computes the distance between the clusters' most distant elements - **Ward linkage** computes the increase of the error sum of squares. In other words, the [Ward's minimum variance criterion](https://en.wikipedia.org/wiki/Ward%27s_method) minimizes the total within-cluster variance. 2. Labels of nodes in the dendrogram can be chosen in the **Annotation** box. -3. Huge dendrograms can be pruned in the *Pruning* box by selecting the maximum depth of the dendrogram. This only affects the display, not the actual clustering. + *Show labels only for subset* exposes only labels passed as instances in the **Data Subset** input. +3. Large dendrograms can be pruned in the *Pruning* box by selecting the maximum depth of the dendrogram. This only affects the display, not the actual clustering. 4. The widget offers three different selection methods: - **Manual** (Clicking inside the dendrogram will select a cluster. Multiple clusters can be selected by holding Ctrl/Cmd. Each selected cluster is shown in a different color and is treated as a separate cluster in the output.) - **Height ratio** (Clicking on the bottom or top ruler of the dendrogram places a cutoff line in the graph. Items to the right of the line are selected.) - - **Top N** (Selects the number of top nodes.) -5. Use *Zoom* and scroll to zoom in or out. -6. The data can be automatically output on any change (*Send Automatically*) or, if the box isn't ticked, by pushing *Send Selection*. + - **Top N** (Selects the number of top nodes creating N clusters.) +5. Use *Zoom* to zoom in or out. +6. If *Send Selected Automatically* is on, the data subset is communicated automatically, otherwise you need to press *Send Selected*. -To output the cluster, click on the ruler at the top or the bottom of the visualization. This will create a cut-off for the clusters. +To output clusters, click on the ruler at the top or the bottom of the visualization. This will create a cut-off for the clusters. Examples -------- @@ -40,20 +42,20 @@ Examples We start with the *Grades for English and Math* data set from the [Datasets](../data/datasets.md) widget. The data contains two numeric variables, grades for English and for Algebra. -**Hierarchical Clustering** requires distance matrix on the input. We compute it with [Distances](../unsupervised/distances.md), where we use the *Euclidean* distance metric. +**Hierarchical Clustering** requires distance matrix on the input. We compute it with [Distances](../unsupervised/distances.md), where we use the *Euclidean (normalized)* distance metric. Once the data is passed to the hierarchical clustering, the widget displays a dendrogram, a tree-like clustering structure. Each node represents an instance in the data set, in our case a student. Tree nodes are labelled with student names. -To create the clusters, we click on the ruler at the desired threshold. In this case, we chose three clusters. We pass those clusters to [MDS](../unsupervised/mds.md), which shows a 2D projection of data instances, colored by cluster label. +To create the clusters, we click on the ruler at the desired threshold. In this case, we chose three clusters. Since our dataset comes in 2D, we pass those clusters to [Scatter Plot](../visualize/scatterplot.md), which shows a plot of data instances, colored by cluster label. -![](images/Hierarchical-Example1.png) +![](images/HierarchicalClustering-Example1.png) #### Cluster explanation -In the second example, we continue the *Grades for English and Math* data. Say we wish to explain what characterizes the cluster with Maya, George, Lea, and Phill. +In the second example, we continue with the *Grades for English and Math* data. Say we wish to explain what characterizes the cluster with Maya, George, Lea, and Phill. We select the cluster in the dendrogram and pass the entire data set to [Box Plot](../visualize/boxplot.md). Note that the connection here is *Data*, not *Selected Data*. To rewire the connection, double-click on it. -In **Box Plot**, we set *Selected* variable as the Subgroup. This will split the plot into selected data instances (our cluster) and the remaining data. Next, we use *Order by relevance to subgroup* option, which sorts the variables according to how well they distinguish between subgroups. It turns out, that our cluster contains students who are bad at math (they have low values of the Algebra variable). +In **Box Plot**, we set *Selected* variable as the Subgroup. This will split the plot into selected data instances (our cluster, labeled as *Yes*) and the remaining data (labeled as *No*). Next, we use *Order by relevance to subgroups* option, which sorts the variables according to how well they distinguish between subgroups. 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[Manifold Learning](https://en.wikipedia.org/wiki/Nonlinear_dimensionality_reduction) is a technique which finds a non-linear manifold within the higher-dimensional space. The widget then outputs new coordinates which correspond to a two-dimensional space. Such data can be later visualized with [Scatter Plot](../visualize/scatterplot.md) or other visualization widgets. -![](images/manifold-learning-stamped.png) +![](images/ManifoldLearning-stamped.png){width=50%} 1. Method for manifold learning: - - [t-SNE](http://scikit-learn.org/stable/modules/manifold.html#t-distributed-stochastic-neighbor-embedding-t-sne) + - [t-SNE](http://scikit-learn.org/stable/modules/manifold.html#t-distributed-stochastic-neighbor-embedding-t-sne), see also [t-SNE](../unsupervised/tsne.md) widget + - Metric: set a distance measure (Euclidean, Manhattan, Chebyshev, Jaccard) + - Perplexity: roughly the number of nearest neighbors to which distances will be preserved + - Early exaggeration: increase the attractive forces between points + - Learning rate: how much parameters are adjusted during each optimization step + - Max iterations: maximum number of times optimization is run + - Initialization: method for initialization of the algorithm (PCA or random) - [MDS](http://scikit-learn.org/stable/modules/manifold.html#multi-dimensional-scaling-mds), see also [MDS widget](../unsupervised/mds.md) + - *max iterations*: maximum number of times optimization is run + - *initialization*: method for initialization of the algorithm (PCA or random) - [Isomap](http://scikit-learn.org/stable/modules/manifold.html#isomap) + - number of *neighbors*: local geometry to consider in dimensionality reduction - [Locally Linear Embedding](http://scikit-learn.org/stable/modules/manifold.html#locally-linear-embedding) + - *method*: standard, modified, [hessian eigenmap](http://scikit-learn.org/stable/modules/manifold.html#hessian-eigenmapping), or local + - number of *neighbors*: local geometry to consider in dimensionality reduction + - *max iterations*: maximum number of times optimization is run - [Spectral Embedding](http://scikit-learn.org/stable/modules/manifold.html#spectral-embedding) -2. Set parameters for the method: - - t-SNE (distance measures): - - *Euclidean* distance - - *Manhattan* - - *Chebyshev* - - *Jaccard* - - *Mahalanobis* - - *Cosine* - - MDS (iterations and initialization): - - *max iterations*: maximum number of optimization interactions - - *initialization*: method for initialization of the algorithm (PCA or random) - - Isomap: - - number of *neighbors* - - Locally Linear Embedding: - - *method*: - - standard - - modified - - [hessian eigenmap](http://scikit-learn.org/stable/modules/manifold.html#hessian-eigenmapping) - - local - - number of *neighbors* - - *max iterations* - - Spectral Embedding: - - *affinity*: - - nearest neighbors - - RFB kernel -3. Output: the number of reduced features (components). -4. If *Apply automatically* is ticked, changes will be propagated automatically. Alternatively, click *Apply*. -5. Produce a report. + - *affinity*: method for constructing affinity matrix (nearest neighbors or RFB kernel) +2. Output: the number of reduced features (components). +3. If *Apply automatically* is ticked, changes will be propagated automatically. Alternatively, click *Apply*. **Manifold Learning** widget produces different embeddings for high-dimensional data. @@ -71,4 +58,4 @@ Example *Manifold Learning* widget transforms high-dimensional data into a lower dimensional approximation. This makes it great for visualizing datasets with many features. We used *voting.tab* to map 16-dimensional data onto a 2D graph. Then we used [Scatter Plot](../visualize/scatterplot.md) to plot the embeddings. -![](images/manifold-learning-example.png) +![](images/ManifoldLearning-Example.png) diff --git a/source/widgets/unsupervised/mds.md b/source/widgets/unsupervised/mds.md index 238a724..5ea36e1 100644 --- a/source/widgets/unsupervised/mds.md +++ b/source/widgets/unsupervised/mds.md @@ -6,65 +6,66 @@ Multidimensional scaling (MDS) projects items onto a plane fitted to given dista **Inputs** - Data: input dataset -- Distances: distance matrix - Data Subset: subset of instances +- Distances: distance matrix **Outputs** - Selected Data: instances selected from the plot -- Data: dataset with MDS coordinates +- Data: dataset with MDS coordinates and an additional column showing whether a point is selected [Multidimensional scaling](https://en.wikipedia.org/wiki/Multidimensional_scaling) is a technique which finds a low-dimensional (in our case a two-dimensional) projection of points, where it tries to fit distances between points as well as possible. The perfect fit is typically impossible to obtain since the data is high-dimensional or the distances are not [Euclidean](https://en.wikipedia.org/wiki/Euclidean_distance). In the input, the widget needs either a dataset or a matrix of distances. When visualizing distances between rows, you can also adjust the color of the points, change their shape, mark them, and output them upon selection. -The algorithm iteratively moves the points around in a kind of a simulation of a physical model: if two points are too close to each other (or too far away), there is a force pushing them apart (or together). The change of the point’s position at each time interval corresponds to the sum of forces acting on it. +The algorithm iteratively moves the points around in a kind of a simulation of a physical model: if two points are too close to each other (or too far away), there is a force pushing them apart (or together). The change of the point's position at each time interval corresponds to the sum of forces acting on it. -![](images/MDS-zoo-stamped.png) +![](images/MDS-stamped.png) -1. The widget redraws the projection during optimization. Optimization is run automatically in the beginning and later by pushing *Start*. - - **Max iterations**: The optimization stops either when the projection changes only minimally at the last iteration or when a maximum number of iterations has been reached. - - **Initialization**: PCA (Torgerson) positions the initial points along principal coordinate axes. *Random* sets the initial points to a random position and then readjusts them. - - **Refresh**: Set how often you want to refresh the visualization. It can be at *Every iteration*, *Every 5/10/25/50 steps* or never (*None*). Setting a lower refresh interval makes the animation more visually appealing, but can be slow if the number of points is high. +1. The widget redraws the projection during optimization. Optimization is run automatically in the beginning and later by pushing *Start*. Pushing the *forward* button runs the optimisation to the next step, defined in the *Referesh* rate. + Optimize the projection using PCA (Torgerson) or random initialization. **PCA** positions the initial points along principal coordinate axes. **Random** sets the initial points to a random position and then readjusts them. **Jitter** randomly scatters data points within a small neighborhood (jitters them from their positions). + **Refresh**: Set how often you want to refresh the visualization. It can be at *Every iteration*, *Every 5/10/25/50 steps* or never (*None*). Setting a lower refresh interval makes the animation more visually appealing, but can be slow if the number of points is high. + Kruskal's stress measures the goodness of fit of the projection to the original data. Lower value indicates better fit. 2. Defines how the points are visualized. These options are available only when visualizing distances between rows (selected in the [Distances](../unsupervised/distances.md) widget). - **Color**: Color of points by attribute (gray for continuous, colored for discrete). - **Shape**: Shape of points by attribute (only for discrete). - **Size**: Set the size of points (*Same size* or select an attribute) or let the size depend on the value of the continuous attribute the point represents (Stress). - **Label**: Discrete attributes can serve as a label. + *Label only selected points* allows you to select individual data instances and label only those. +3. Adjust graph attributes: - **Symbol size**: Adjust the size of the dots. - - **Symbol opacity**: Adjust the transparency level of the dots. + - **Opacity**: Adjust the transparency level of the dots. + - **Jittering**: Set [jittering](https://en.wikipedia.org/wiki/Jitter) to prevent the dots from overlapping. - **Show similar pairs**: Adjust the strength of network lines. - - **Jitter**: Set [jittering](https://en.wikipedia.org/wiki/Jitter) to prevent the dots from overlapping. -3. Adjust the graph with *Zoom/Select*. The arrow enables you to select data instances. The magnifying glass enables zooming, which can be also done by scrolling in and out. The hand allows you to move the graph around. The rectangle readjusts the graph proportionally. -4. Select the desired output: - - **Original features only** (input dataset) - - **Coordinates only** (MDS coordinates) - - **Coordinates as features** (input dataset + MDS coordinates as regular attributes) - - **Coordinates as meta attributes** (input dataset + MDS coordinates as meta attributes) + + *Show color regions*: colors the graph by class. + *Show legend*: displays a legend on the right. Click and drag the legend to move it. +4. Adjust the graph with *Zoom/Select*. The arrow enables you to select data instances. The magnifying glass enables zooming, which can be also done by scrolling in and out. The hand allows you to move the graph around. The rectangle readjusts the graph proportionally. 5. Sending the instances can be automatic if *Send selected automatically* is ticked. Alternatively, click *Send selected*. -6. **Save Image** allows you to save the created image either as .svg or .png file to your device. -7. Produce a report. -The MDS graph performs many of the functions of the Visualizations widget. It is in many respects similar to the [Scatter Plot](../visualize/scatterplot.md) widget, so we recommend reading that widget's description as well. +The MDS graph is in many respects similar to the [Scatter Plot](../visualize/scatterplot.md) widget, so we recommend reading that widget's description as well. Preprocessing ------------- When given *Distances* on the input, preprocessing is not applied. When given *Data*, MDS uses default preprocessing if necessary. Preprocessing is executed in the following order: -- continuizes categorical variables (with one feature per value) -- imputes missing values with mean values +- continuizing categorical variables (with one feature per value) +- imputing missing values with mean values To override default preprocessing, preprocess the data beforehand with [Preprocess](../data/preprocess.md) widget. -# Example +Examples +-------- + +In the first example, we used the *zoo.tab* dataset. We pass the data to MDS and to [Data Table](../data/datatable.md). In the data table, we selected four mammals, namely bear, boar, buffalo, and calf. We wish to observe them in a visualization, so we pass them to MDS, which exposes their position in the graph. + +![](images/MDS-Example1.png) -The above graphs were drawn using the following simple schema. We used the *iris.tab* dataset. Using the [Distances](../unsupervised/distances.md) widget we input the distance matrix into the **MDS** widget, where we see the *Iris* data displayed in a 2-dimensional plane. We can see the appended coordinates in the [Data Table](../data/datatable.md) widget. +In the second example, we used the *brown-selected* data set and passed it to the [Distances](../unsupervised/distances.md) widget to compute the distance matrix based on *cosine* distances. We observe the 2D embedding in the MDS widget. -![](images/MDS-Example.png) +![](images/MDS-Example2.png) -# References +### References -Wickelmaier, F. (2003). An Introduction to MDS. Sound Quality Research -Unit, Aalborg University. Available -[here](https://homepages.uni-tuebingen.de/florian.wickelmaier/pubs/Wickelmaier2003SQRU.pdf). +Wickelmaier, F. (2003). An Introduction to MDS. Sound Quality Research Unit, Aalborg University. Available [here](https://homepages.uni-tuebingen.de/florian.wickelmaier/pubs/Wickelmaier2003SQRU.pdf). diff --git a/source/widgets/unsupervised/neighbors.md b/source/widgets/unsupervised/neighbors.md new file mode 100644 index 0000000..93c2740 --- /dev/null +++ b/source/widgets/unsupervised/neighbors.md @@ -0,0 +1,36 @@ +Neighbors +========= + +Compute nearest neighbors in data according to reference. + +**Inputs** + +- Data: An input data set. +- Reference: A reference data for neighbor computation. + +**Outputs** + +- Neighbors: A data table of nearest neighbors according to reference. + +The **Neighbors** widget computes nearest neighbors for a given reference and for a given distance measure. The reference can be either one instance or more instances. In the case with one reference widget outputs closest `n` instances from data where `n` is set by the *Limit number of neighbors to* option in the widget. When reference contains more instances, widget computes the combined distance for each data instance as a minimum of distances to each reference. Widget outputs `n` data instances with lowest combined distance. + +![](images/Neighbors-stamped.png){width=50%} + +1. *Distance metric* for computing neighbors. Supported measures are: Euclidean, Manhattan, Mahalanobis, Cosine, Jaccard, Spearman, absolute Spearman, Pearson, absolute Pearson. + *Limit number of neighbors to*: Number of neighbors on the output. +2. Click *Apply* to commit the changes. To communicate changes automatically tick *Apply Automatically*. + +Examples +-------- + +In the first example, we used *iris* data and passed it to **Neighbors** and to [Scatter Plot](../visualize/scatterplot.md). In Scatter Plot, we selected an instance of iris, that will serve as our reference, meaning we wish to retrieve 10 closest examples to the selected data instance. We connect Data Table to Neighbors as well. + +We can observe the results of neighbor computation in Data Table, where we can see 10 closest images to our selected iris flower. We see that, expectedly, some are iris virginicas and some are versicolors. + +![](images/Neighbors-Example1.png) + +Another example requires the installation of Image Analytics add-on. We loaded traffic signs dataset from the [Datasets](../data/datasets.md) widget and passed them to [Image Embedding](https://orangedatamining.com/widget-catalog/image-analytics/imageembedding/), with which we embedded the images. Remember, Neighbors widget (and any kind of downstream processing of images), requires numerically described instances. + +Then the procedure is the same as above. We passed embedded images to [Image Viewer](https://orangedatamining.com/widget-catalog/image-analytics/imageviewer/) and selected an interesting traffic sign as our reference image. We passed the image to Neighbors, where we set the distance measure to *cosine*. We can observe the results in another Image Viewer. + +![](images/Neighbors-Example2.png) diff --git a/source/widgets/unsupervised/savedistancematrix.md b/source/widgets/unsupervised/savedistancematrix.md index 7e735f0..2c87080 100644 --- a/source/widgets/unsupervised/savedistancematrix.md +++ b/source/widgets/unsupervised/savedistancematrix.md @@ -3,20 +3,20 @@ Save Distance Matrix Saves a distance matrix. -If the file is saved to the same directory as the workflow or in the subtree of that directory, the widget remembers the relative path. Otherwise it will store an absolute path, but disable auto save for security reasons. - **Inputs** - Distances: distance matrix -![](images/SaveDistanceMatrix-stamped.png) +![](images/SaveDistanceMatrix-stamped.png){width=200px} + +1. By selecting *Autosave when receiving new data*, all incoming changes will be saved automatically, thus overwriting the selected file. +2. By clicking *Save*, the input distance matrix will be saved as an .xlsx or .dst file. The standard save dialogue will open the first time you click the button. By clicking *Save as*, the save dialogue will re-open, enabling you to save the file under a new name. -1. By clicking *Save*, you choose from previously saved distance matrices. Alternatively, tick the box on the left side of the *Save* button and changes will be communicated automatically. -2. By clicking *Save as*, you save the distance matrix to your computer, you only need to enter the name of the file and click *Save*. +Load the saved matrix with the [Distance File](../unsupervised/distancefile.md) widget. Example ------- -In the snapshot below, we used the [Distance Transformation](../unsupervised/distancetransformation.md) widget to transform the distances in the *Iris* dataset. We then chose to save the transformed version to our computer, so we could use it later on. We decided to output all data instances. You can choose to output just a minor subset of the data matrix. Pairs are marked automatically. If you wish to know what happened to our changed file, see [Distance File](../unsupervised/distancefile.md). +In the snapshot below, we used computed distance matrix on the *iris* data using the [Distances](../unsupervised/distances.md) widget. Then, we used the [Distance Transformation](../unsupervised/distancetransformation.md) widget to transform the distances to the [0, 1] interval. We then chose to save the transformed version to our computer, so we could use it later on. We can observe the transformed matrix in a [Distance Matrix](../unsupervised/distancematrix.md). ![](images/SaveDistanceMatrix-Example.png) diff --git a/source/widgets/unsupervised/workflows/correlations.ows b/source/widgets/unsupervised/workflows/correlations.ows new file mode 100644 index 0000000..d30ac15 --- /dev/null +++ b/source/widgets/unsupervised/workflows/correlations.ows @@ -0,0 +1,148 @@ + + + + + + + + + + + + + + + + gASVvQ4AAAAAAAB9lCiMEmNvbnRyb2xBcmVhVmlzaWJsZZSIjAxyZWNlbnRfcGF0aHOUXZQojB5v +cmFuZ2V3aWRnZXQudXRpbHMuZmlsZWRpYWxvZ3OUjApSZWNlbnRQYXRolJOUKYGUfZQojAdhYnNw +YXRolIw9L1VzZXJzL2FqZGEvb3JhbmdlL29yYW5nZTMvT3JhbmdlL2RhdGFzZXRzL2Jyb3duLXNl +bGVjdGVkLnRhYpSMBnByZWZpeJSMD3NhbXBsZS1kYXRhc2V0c5SMB3JlbHBhdGiUjBJicm93bi1z +ZWxlY3RlZC50YWKUjAV0aXRsZZSMAJSMBXNoZWV0lGgQjAtmaWxlX2Zvcm1hdJROdWJoBimBlH2U +KGgJjDMvVXNlcnMvYWpkYS9vcmFuZ2Uvb3JhbmdlMy9PcmFuZ2UvZGF0YXNldHMvaXJpcy50YWKU +aAtoDGgNjAhpcmlzLnRhYpRoD2gQaBFoEGgSTnViaAYpgZR9lChoCYw2L1VzZXJzL2FqZGEvb3Jh 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