在R中，我们可以比较按列划分的行以返回相似性分数吗？

# 示例数据
data <- matrix(runif(30), nrow = 6, ncol = 5)
rownames(data) <- paste("Row", 1:nrow(data))
colnames(data) <- paste("Col", 1:ncol(data))

# 计算余弦相似度
cosine_similarity <- function(x, y) {
  dot_product <- sum(x * y)
  norm_x <- sqrt(sum(x^2))
  norm_y <- sqrt(sum(y^2))
  return(dot_product / (norm_x * norm_y))
}

similarity_matrix <- matrix(NA, nrow = nrow(data), ncol = nrow(data))
for (i in 1:nrow(data)) {
  for (j in 1:nrow(data)) {
    similarity_matrix[i, j] <- cosine_similarity(data[i, ], data[j, ])
  }
}

print(similarity_matrix)

# 计算欧几里得距离
euclidean_distance <- function(x, y) {
  return(sqrt(sum((x - y)^2)))
}

distance_matrix <- matrix(NA, nrow = nrow(data), ncol = nrow(data))
for (i in 1:nrow(data)) {
  for (j in 1:nrow(data)) {
    distance_matrix[i, j] <- euclidean_distance(data[i, ], data[j, ])
  }
}

# 转换为相似度分数（1 / (1 + 距离)）
similarity_matrix <- 1 / (1 + distance_matrix)
print(similarity_matrix)

# 计算Jaccard相似度
jaccard_similarity <- function(x, y) {
  intersection <- sum(x * y)
  union <- sum(x) + sum(y) - intersection
  return(intersection / union)
}

similarity_matrix <- matrix(NA, nrow = nrow(data), ncol = nrow(data))
for (i in 1:nrow(data)) {
  for (j in 1:nrow(data)) {
    similarity_matrix[i, j] <- jaccard_similarity(data[i, ], data[j, ])
  }
}

print(similarity_matrix)