# Markov-Embedded Affinity Learning with Connectivity Constraints for Subspace Clustering
## 6 Experiments
### Experimental Setup  
In this subsection, we introduce the details of the experimental setup. Comparison experiments are conducted in Matlab 2018a on a machine with an Intel (R) Core (TM) i7-8700 CPU @ 3.20 GHz and 32.0 G memory. The time cost study is executed in Matlab 2018a on a machine with an 11 th-Gen Intel Core i7-11700T CPU @ 1.40 GHz and 16 G memory. In certain scenarios (e.g., classification), the label information of the data is crucial. However, it is generally expensive to manually label unlabeled data. Clustering can directly and effectively produce fairly accurate labeling results. This can greatly enhance the work efficiency and guarantee the operational performance. To verify the universality of the proposed method's labeling capability, we enumerate three real application scenarios to conduct the experiments, including faces, handwritten digits and letters, and actions. Figure 3 shows some examples of these eight data sets. Firstly, on the face real application data sets, we perform clustering based on the facial features of different individuals, with all images of the same individual grouped into one cluster. The details of these data sets are as follows. The Jaffe data set contains 213 images, collected from 10 Japanese female students making 7 facial expressions, and each image's size is 26 \(\times\) 26 pixels. The PIX data set comprises 100 images of 10 objects, with each image sized at 100 \(\times\) 100 pixels. The YALEB data set contains 165 grayscale face images of 15 individuals; all images are 32 \(\times\) 32 pixels. The ORL data set includes face images of 40 different individuals, with each individual represented by 10 images. Each image measures 32 \(\times\) 32 pixels. Secondly, on the real application datasets of handwritten digits and letters, we obtain the final clusters based on the categories of handwritten digits 0-9 and letters A-Z. This allows all images of the same digit or letter to be grouped into the same cluster. The details of these data sets are as follows. The Binary Alphadigits (Alphadigit)  
Figure 3: Examples of images selected from three different real application data sets. data set contains 36 categories of digits 0-9 and letters A-Z, each category has 39 images, and each image is 20 \(\times\) 16 pixels. The Semeion Handwritten Digit (Semeion) data set contains 1593 handwritten digit images from 80 people, encompassing 10 categories. Each image is 16 \(\times\) 16 pixels and features 256 gray levels. The Modified National Institute of Standards and Technology (MNIST) data set comprises 7000 images of digits 0-9. For this experiment, we randomly select 400 images; each image is 28 \(\times\) 28 pixels. Among these images, 50% are collected from high school students and 50% from the Census Bureau. Finally, on the Still Images (StillDB) action real application data set [28], we group the images into different clusters based on different actions. The StillDB data set comprises 467 images, encompassing six distinct actions: running, walking, catching, throwing, crouching, and kicking. We compare the proposed method with ten baseline methods, namely Non-Negative Sparse Hyper-Laplacian Regularized LRR (NSLLRR) [29], SSC [9], Subspace Clustering Using Log-Determinant Rank Approximation (SCLA) [20], Scaled Simplex Representation for Subspace Clustering (SSRSC) [30], S-TLRR [31], R-TLRR [31], Tensor Low-Rank Sparse Representation for Tensor Subspace Learning (TLRSR) [32], Enhanced Tensor Low-Rank Representation for Clustering and Denoising (ETLRR) [33], Efficient Deep Embedded Subspace Clustering (EDESC) [34], and Pseudo-Supervised Deep Subspace Clustering (PSSC) [35]. Among them, the first four are traditional subspace clustering methods, the last two are deep subspace clustering methods, and the remaining four are tensor-based subspace clustering methods. For all methods, the range of the balance parameter is \(\{0.001,0.01,0.1,10,100,1000\}\), the binary kernel is used in this experiment, and 5 neighbors are retained to construct the similarity matrix.