检查 Wine 化学测量的聚类

from pathlib import Path
import base64, gzip, hashlib, json, platform
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from IPython.display import display, HTML
from IPython.display import display as _display
def display(value):
    if isinstance(value,pd.DataFrame):
        table=value.to_html(max_rows=12,escape=True)
        style="<style>.vibeit-readable-table{max-width:100%;overflow-x:auto}.vibeit-readable-table table{width:max-content;max-width:none;border-collapse:collapse}.vibeit-readable-table td,.vibeit-readable-table th{white-space:nowrap!important;word-break:normal!important;overflow-wrap:normal!important}</style>"
        return _display(HTML(style+'<div class="vibeit-readable-table">'+table+'</div>'))
    return _display(value)
RECIPE_ID='ds04-wine-clusters'
OUTPUT_DIR=Path.cwd()/"results"/RECIPE_ID
plt.rcParams.update({"figure.dpi":120,"font.size":10,"axes.spines.top":False,"axes.spines.right":False,
                      "axes.prop_cycle":plt.cycler(color=["#18785f","#416aa6","#bc6541","#9974a5"])})
print("Python:",platform.python_version(),"; NumPy:",np.__version__,"; Pandas:",pd.__version__)
print("Working folder:",Path.cwd())
print("Core data mode: embedded snapshot; no network requests")

Python: 3.13.13 ; NumPy: 2.5.3 ; Pandas: 3.0.6
Working folder: /Users/zhiluo/Developer/vibeit-cookbook/cookbook/downloads
Core data mode: embedded snapshot; no network requests

def load_snapshot(recipe_id, expected_sha256, snapshot_key):
    """Read embedded data from this notebook, including a renamed copy."""
    for path in sorted(Path.cwd().glob("*.ipynb")):
        try:
            notebook = json.loads(path.read_text(encoding="utf-8"))
            metadata = notebook.get("metadata", {}).get("vibeit_cookbook", {})
            blob = metadata.get("snapshots", {}).get(snapshot_key)
            if metadata.get("recipe_id") != recipe_id or not blob:
                continue
            if blob.get("sha256") != expected_sha256:
                continue
            raw = gzip.decompress(base64.b64decode(blob["gzip_base64"], validate=True))
            if hashlib.sha256(raw).hexdigest() != expected_sha256:
                raise ValueError("Embedded snapshot checksum mismatch: " + snapshot_key)
            return json.loads(raw)
        except (OSError, json.JSONDecodeError):
            continue
    raise FileNotFoundError(
        "Save/open the complete .ipynb in the active working folder. "
        "The embedded snapshot could not be located for " + recipe_id)

SNAPSHOT_HASHES={'wine': '9ee00bf430da1fd1a13b7ee8a1efc74427730e4bd5fb22c6543673b57e37da6b'}
def snapshot(key):
    return load_snapshot(RECIPE_ID,SNAPSHOT_HASHES[key],key)
print("Embedded snapshots:",list(SNAPSHOT_HASHES))

Embedded snapshots: ['wine']

def audit_numeric_table(frame,columns):
    """Audit observed rows; never silently impute or remove them."""
    if frame.empty or frame.index.has_duplicates:
        raise ValueError('Expected a nonempty table with unique row IDs')
    missing=[name for name in columns if name not in frame.columns]
    if missing:raise ValueError('Missing required columns: '+str(missing))
    values=frame[columns].to_numpy(dtype=float)
    if not np.isfinite(values).all():raise ValueError('Non-finite measurements; inspect missing values explicitly')
    return {'rows':len(frame),'features':len(columns),'finite':True,'duplicate_measurement_rows':int(frame[columns].duplicated().sum())}

print("Method ready: audit_numeric_table")

Method ready: audit_numeric_table

def standardized_pca(values,components=2):
    """Population-SD standardization followed by an SVD of centered observations."""
    values=np.asarray(values,dtype=float)
    if values.ndim!=2 or min(values.shape)<2 or not np.isfinite(values).all():
        raise ValueError('PCA requires a finite observations × features matrix')
    if not 1<=components<=min(values.shape):raise ValueError('Invalid number of components')
    mean=values.mean(axis=0);scale=values.std(axis=0,ddof=0)
    if np.any(scale==0):raise ValueError('Constant features must be removed or handled explicitly')
    standardized=(values-mean)/scale
    left,singular,loadings=np.linalg.svd(standardized,full_matrices=False)
    # Fix signs for reproducible plots, without changing distances or explained variance.
    for j in range(len(singular)):
        pivot=np.argmax(np.abs(loadings[j]))
        if loadings[j,pivot]<0:loadings[j]*=-1;left[:,j]*=-1
    variance=singular**2/(len(values)-1)
    return dict(mean=mean,scale=scale,scores=left[:,:components]*singular[:components],
                loadings=loadings[:components],explained_ratio=variance/variance.sum(),standardized=standardized)

print("Method ready: standardized_pca")

Method ready: standardized_pca

def kmeans(values,k=3,seed=42,restarts=10,max_iterations=100):
    """Lloyd's algorithm with k-means++ seeds; labels are excluded from fitting."""
    values=np.asarray(values,dtype=float)
    if values.ndim!=2 or not isinstance(k,(int,np.integer)) or not np.isfinite(values).all() or not 1<=k<=len(np.unique(values,axis=0)):
        raise ValueError('Invalid observations or number of distinct clusters')
    if not isinstance(restarts,(int,np.integer)) or not isinstance(max_iterations,(int,np.integer)) or min(restarts,max_iterations)<1:
        raise ValueError('Restarts and maximum iterations must be positive integers')
    rng=np.random.default_rng(seed);best=None
    for restart in range(restarts):
        centers=[values[rng.integers(len(values))]]
        for _ in range(1,k):
            distance=np.min(np.sum((values[:,None,:]-np.asarray(centers)[None,:,:])**2,axis=2),axis=1)
            centers.append(values[rng.choice(len(values),p=distance/distance.sum())])
        centers=np.asarray(centers);history=[]
        for _ in range(max_iterations):
            distance=np.sum((values[:,None,:]-centers[None,:,:])**2,axis=2)
            assigned=np.argmin(distance,axis=1)
            updated=np.array([values[assigned==j].mean(axis=0) if np.any(assigned==j) else centers[j] for j in range(k)])
            objective=float(np.sum((values-updated[assigned])**2));history.append(objective)
            if np.allclose(updated,centers,atol=1e-10,rtol=0):centers=updated;break
            centers=updated
        assigned=np.argmin(np.sum((values[:,None,:]-centers[None,:,:])**2,axis=2),axis=1)
        objective=float(np.sum((values-centers[assigned])**2))
        if best is None or objective<best['inertia']:
            best=dict(centers=centers,labels=assigned,inertia=objective,history=np.asarray(history))
    return best

print("Method ready: kmeans")

Method ready: kmeans

wine=snapshot("wine");frame=pd.DataFrame(wine["rows"],columns=wine["columns"])
features=list(frame.columns[1:]);audit=audit_numeric_table(frame,features)
assert len(frame)==178 and len(features)==13
values=frame[features].to_numpy(float);standardized=(values-values.mean(axis=0))/values.std(axis=0)
print("Audit:",audit,"; standardized features are dimensionless")
display(frame.head(6))

Audit: {'rows': 178, 'features': 13, 'finite': True, 'duplicate_measurement_rows': 0} ; standardized features are dimensionless

solutions={k:kmeans(standardized,k,seed=42,restarts=10) for k in range(1,7)}
solution=solutions[3]
fig,ax=plt.subplots(figsize=(7,4));ax.plot(list(solutions),[solutions[k]["inertia"] for k in solutions],"o-")
ax.axvline(3,color="gray",linestyle="--");ax.set(xlabel="k",ylabel="Standardized squared-distance sum",title="Inertia is an objective, not classification accuracy");plt.tight_layout();plt.show()

pca=standardized_pca(values,2)
fig,ax=plt.subplots(figsize=(7,5))
for cluster in range(3):
 mask=solution["labels"]==cluster;ax.scatter(*pca["scores"][mask].T,label=f"Cluster {cluster}",s=25)
ax.set(xlabel="PC1 score",ylabel="PC2 score",title="Wine clusters; fitted in 13 dimensions");ax.legend();plt.tight_layout();plt.show()

table=pd.crosstab(frame.cultivar,pd.Series(solution["labels"],name="cluster"))
display(table)
fig,ax=plt.subplots(figsize=(6,4));im=ax.imshow(table,cmap="Blues")
ax.set_xticks(range(3),table.columns);ax.set_yticks(range(3),table.index)
for i in range(3):
 for j in range(3):ax.text(j,i,str(table.iloc[i,j]),ha="center",va="center")
ax.set(xlabel="Anonymous cluster",ylabel="Source cultivar code",title="Post-fit contingency counts");fig.colorbar(im,ax=ax,label="Observations");plt.tight_layout();plt.show()

cluster	0	1	2
cultivar
1	59	0	0
2	3	65	3
3	0	0	48

assert table.to_numpy().sum()==178
assert np.isclose(solution["inertia"],np.sum((standardized-solution["centers"][solution["labels"]])**2))
assert np.all(np.diff(solution["history"])<=1e-8)
OUTPUT_DIR.mkdir(parents=True,exist_ok=True)
frame.assign(cluster=solution["labels"]).to_csv(OUTPUT_DIR/"wine-clusters.csv",index=False)
pd.DataFrame(solution["centers"],columns=features).to_csv(OUTPUT_DIR/"standardized-centres.csv",index=False)
pd.DataFrame({"k":list(solutions),"inertia":[solutions[k]["inertia"] for k in solutions]}).to_csv(OUTPUT_DIR/"inertia.csv",index=False)
print("Objective and count checks passed; exports:",OUTPUT_DIR)

Objective and count checks passed; exports: /Users/zhiluo/Developer/vibeit-cookbook/cookbook/downloads/results/ds04-wine-clusters

RUN_ONLINE_UPDATE=False
if RUN_ONLINE_UPDATE:
    import requests
    try:
        response=requests.get('https://archive.ics.uci.edu/dataset/109',timeout=20)
        response.raise_for_status()
        print("Source:",response.url)
        print(response.text[:700])
    except requests.RequestException as error:
        print("Online extension unavailable:",type(error).__name__,str(error)[:160])
else:
    print("Online extension skipped; embedded core data unchanged")

Online extension skipped; embedded core data unchanged