Project: 057_The_Geometry_of_Categorical_and_Hierarchical_Conce | Function: get_categories (iclr)

system: You are an expert Python programmer implementing algorithms from scientific papers.
Complete the masked function based on the algorithm description.
Follow Python best practices and maintain consistent code style.
Return **only** the complete Python function code.

user: Complete this Python function:

**DESCRIPTION:** Implements the hierarchical concept processing algorithm that constructs a clean taxonomic hierarchy from WordNet data by removing redundant nodes and maintaining semantic relationships. This function implements the core data preprocessing for hierarchical concept analysis.

**KEY TERMS:** {
  "cats": "synset_attributes",
  "G": "hierarchy_graph",
  "reversed_nodes": "topological_ordering",
  "children": "successor_nodes"
}

**CONTEXT CODE:** import json
import networkx as nx

import torch
from sklearn.covariance import ledoit_wolf


def get_categories(noun_or_verb = 'noun', model_name = 'gemma'):

    raise NotImplementedError("Function implementation has been masked for testing")

def category_to_indices(category, vocab_dict):
    return [vocab_dict[w] for w in category]

def get_words_sim_to_vec(query: torch.tensor, unembed, vocab_list, k=300):
    similar_indices = torch.topk(unembed @ query, k, largest=True).indices.cpu().numpy()
    return [vocab_list[idx] for idx in similar_indices]

def estimate_single_dir_from_embeddings(category_embeddings):
    raise NotImplementedError("Function implementation has been masked for testing")

def estimate_cat_dir(category_lemmas, unembed, vocab_dict):
    category_embeddings = unembed[category_to_indices(category_lemmas, vocab_dict)]
    lda_dir, category_mean = estimate_single_dir_from_embeddings(category_embeddings)
    
    return {'lda': lda_dir, 'mean': category_mean}



import inflect
p = inflect.engine()

def noun_to_gemma_vocab_elements(word, vocab_set):
    word = word.lower()
    plural = p.plural(word)
    add_cap_and_plural = [word, word.capitalize(), plural, plural.capitalize()]
    add_space = ["▁" + w for w in add_cap_and_plural]
    return vocab_set.intersection(add_space)


def get_animal_category(data, categories, vocab_dict, g):
    vocab_set = set(vocab_dict.keys())

    animals = {}
    animals_ind = {}
    animals_g = {}
    animals_token = {}

    for category in categories:
        animals[category] = []
        animals_ind[category] = []
        animals_g[category] = []
        animals_token[category] = []

    for category in categories:
        lemmas = data[category]
        for w in lemmas:
            animals[category].extend(noun_to_gemma_vocab_elements(w, vocab_set))
        
        for word in animals[category]:
            animals_ind[category].append(vocab_dict[word])
            animals_token[category].append(word)
            animals_g[category] = g[animals_ind[category]]
    return animals_token, animals_ind, animals_g

Complete the function implementation replacing "raise NotImplementedError".