R语言TDAmapper包高维数据适配的替代滤波函数咨询

Great question—high-dimensional data (like your 76x316 dataset) can make standard kernel density estimation (KDE) unreliable or computationally expensive, especially beyond 6 dimensions. Below are practical, effective filtering functions tailored for high-dimensional use with the TDAmapper package in R:

1. Principal Component (PC) Scores #

PCA is a go-to linear dimensionality reduction method that retains the maximum variance in your data. Using PC scores as filter functions works well for high-dimensional data with linear structure, and it’s computationally fast even for large feature sets.

Example Code: #

library(TDAmapper)
library(stats)

# Load your dataset (replace with your actual data object)
data <- your_data_matrix

# Perform PCA (scaling is recommended for high-dimensional data)
pca_result <- prcomp(data, scale. = TRUE)
# Use the first 2-3 principal components as filters (adjust based on variance explained)
filters <- pca_result$x[, 1:2]

# Run TDAmapper
mapper_obj <- mapper(
  data = data,
  filter = filters,
  num_intervals = 10,
  percent_overlap = 30,
  num_bins_when_clustering = 10
)

2. UMAP or t-SNE Embeddings #

For non-linear high-dimensional structures, nonlinear dimensionality reduction methods like UMAP or t-SNE create low-dimensional embeddings that preserve local and global data structure. These work better than PCA if your data has complex, non-linear relationships.

UMAP Example Code: #

library(umap)
library(TDAmapper)

# Generate UMAP embedding (tweak n_neighbors and min_dist for your data)
umap_result <- umap(data, n_neighbors = 15, min_dist = 0.1)
filters <- umap_result$layout

# Run mapper
mapper_obj <- mapper(
  data = data,
  filter = filters,
  num_intervals = 8,
  percent_overlap = 35,
  num_bins_when_clustering = 8
)

3. Distance-Based Filters #

Simple distance metrics are computationally efficient and work well for any dimensionality. You can use:

• Distance to the data centroid (mean vector)
• Distance to a specific cluster center (from k-means, for example)
• Pairwise distance sums (sum of distances to all other samples)

Centroid Distance Example: #

library(TDAmapper)

# Calculate centroid of your data
centroid <- colMeans(data)
# Compute Euclidean distance from each sample to centroid
distance_filter <- sqrt(rowSums((data - centroid)^2))

# Run mapper with a single filter (you can combine with another filter for richer structure)
mapper_obj <- mapper(
  data = data,
  filter = distance_filter,
  num_intervals = 12,
  percent_overlap = 25,
  num_bins_when_clustering = 10
)

4. Autoencoder Latent Variables #

If you want to capture complex, hierarchical patterns in your high-dimensional data, an autoencoder (a type of neural network) learns a compressed low-dimensional representation (latent space) of your data. This is great for unsupervised learning in high dimensions.

Example (using Keras): #

library(keras)
library(TDAmapper)

# Define a simple autoencoder
input_layer <- layer_input(shape = ncol(data))
encoder <- input_layer %>%
  layer_dense(units = 64, activation = "relu") %>%
  layer_dense(units = 2, activation = "linear") # 2-dimensional latent space
decoder <- encoder %>%
  layer_dense(units = 64, activation = "relu") %>%
  layer_dense(units = ncol(data), activation = "linear")

autoencoder <- keras_model(inputs = input_layer, outputs = decoder)
autoencoder %>% compile(optimizer = "adam", loss = "mse")

# Train the autoencoder (adjust epochs/batch size based on your data)
autoencoder %>% fit(
  x = data, y = data,
  epochs = 50, batch_size = 8, validation_split = 0.1
)

# Extract latent variables as filters
encoder_model <- keras_model(inputs = input_layer, outputs = encoder)
latent_filters <- predict(encoder_model, data)

# Run mapper
mapper_obj <- mapper(
  data = data,
  filter = latent_filters,
  num_intervals = 9,
  percent_overlap = 30,
  num_bins_when_clustering = 9
)

Key Notes for Your 76-Sample Dataset #

• Since you have a small sample size, avoid overly complex methods that risk overfitting (e.g., t-SNE with very high perplexity). Stick to values like perplexity = 10-15 for t-SNE.
• Combine multiple filters (e.g., PCA + distance) to capture more aspects of your data structure.
• Adjust num_intervals and percent_overlap in mapper() based on how granular you want the resulting graph to be.

内容的提问来源于stack exchange，提问作者Katherina