Han’s MetaCell Model

Han Wang at 2024/6/11.

Step 1: Data Preparation and Preprocessing

1. Filtering Low-Quality Cells:

Remove cells with low total expression, few detected genes, or high mitochondrial gene expression percentage.

2. Filtering Low-Expression Genes:

Remove genes with low or no expression in most cells.

3. Data Normalization:

Normalize expression levels for comparability.

4. Data Transformation:

Log-transform the normalized expression data.

Step 2: NMF Decomposition

1. NMF Decomposition:

Decompose the preprocessed expression matrix $X$ into two non-negative matrices $W$ and $H$.

Where $W \in \mathbb{R}^{n \times k}$, $H \in \mathbb{R}^{k \times m}$.

2. Objective to Minimize Reconstruction Error:

3. Optimization Algorithms:

Use Alternating Least Squares (ALS) or Multiplicative Update Rules (MUR):

Step 3: Constructing the Cell Similarity Graph

1. Construct Cell Similarity Graph:

Use the weight matrix $H$ from NMF.

2. Calculate Similarity Measures:

Calculate pairwise cell similarities using cosine similarity or Pearson correlation.

3. Construct Cell Similarity Graph $G$:

Edges in $G$ represent similarities above a threshold.

Step 4: Graph-Based Clustering (Leiden Algorithm)

1. Local Moving:

Initialization:

Each node starts as an independent community.

Local Optimization:

For each node $i$ , calculate the modularity gain $\Delta Q$ when moved to a neighboring community $C_j$:

Where $w_{uv}$ is the edge weight between $u$ and $v$, $k_i^{\text{in}}$ is the internal edge weight of node $i$, $k_i$ is the degree of node $i$, and $m$ is the total edge weight of the graph.

Move Nodes:

Move the node to the community that maximizes $\Delta Q$ and repeat until no further improvement.

2. Refinement Phase:

Community Merging:

Treat communities as supernodes and construct a new graph where supernodes are connected by aggregated edge weights.

3. Fine-Tuning Phase:

Apply Local Optimization Again:

Optimize modularity in the new graph of supernodes.

Modularity Definition:

Modularity $Q$:

Where $w_{ij}$ is the edge weight between nodes $i$ and $j$, $k_i$ and $k_j$ are the degrees of nodes $i$ and $j$, and $\delta(C_i, C_j)$ is the Kronecker delta function indicating whether nodes $i$ and $j$ are in the same community.

Step 5: Evaluation and Annotation of Metacells

1. Statistical Metrics Calculation:

Calculate various metrics for each metacell.

2. Differential Expression Analysis:

Identify genes that are differentially expressed in each metacell.

3. Functional Enrichment Analysis:

Perform functional enrichment analysis on marker genes.

4. Cell Type Comparison:

Compare metacells with known cell types or states.

5. Visualization:

Visualize metacells using dimensionality reduction techniques such as t-SNE or UMAP.